Green Supplier Evaluation and Selection: Models, Methods and Applications 9811603812, 9789811603815

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Hu-Chen Liu Xiao-Yue You

Green Supplier Evaluation and Selection: Models, Methods and Applications

Green Supplier Evaluation and Selection: Models, Methods and Applications

Hu-Chen Liu · Xiao-Yue You

Green Supplier Evaluation and Selection: Models, Methods and Applications

Hu-Chen Liu School of Economics and Management Tongji University Shanghai, China

Xiao-Yue You Sino-German College of Applied Sciences Tongji University Shanghai, China

ISBN 978-981-16-0381-5 ISBN 978-981-16-0382-2 (eBook) https://doi.org/10.1007/978-981-16-0382-2 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Foreword

Over the recent decade, sustainable development has become more significant due to public awareness, environmental policies and societal issues. As the second-largest economy in the world, China has proposed an ecological civilization framework to rigorously promote sustainable development. Guided by the conviction that “lucid waters and lush mountains are invaluable assets”, the framework advocates harmonious coexistence between humans and nature, and a path towards eco-friendly, green and sustainable development. In this regard, manufacturing firms are facing a lot of pressure on incorporating environmental concerns in their supply chains, and Green Supply Chain Management (GSCM) has received growing attention from both managers and academicians. The GSCM practices can help to foster environmental capability of a supply chain, achieve operational performance and improve ecological efficiency of a firm. It includes a wide of range of activities beginning from green purchasing, to product life cycle management, and finally closing of loop. Green Supplier Evaluation and Selection (GSES) is a critical part of GSCM, which is a main element of the decisionmaking procedure in production operation management. Through GSES, organizations can effectively improve their environmental performance and customer satisfaction, and finally improve the overall benefits. But it is a challenging work that needs to take multiple and conflict criteria into the supplier selection. This is exactly where the book has its focus and why it is that important. In this book, the authors developed a variety of models and methods for evaluating and selecting green suppliers in different real-world applications. They also consider very critically the touchiest points in solving real GSES problems, namely, quantification of qualitative data and determination of the ranking of candidate green suppliers. What makes this book so valuable and different from other GSCM books is that even though the analyses are very rigorous, the results are described very clearly and are understandable even to the non-specialist. I congratulate the authors on this work and believe that the book is highly appropriate for use by practitioners and

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researchers working in the fields of supply chain management, operation management and industrial engineering, and by all decision-makers in the manufacturing environment.

February 2021 Academician of Chinese Academy of Engineering Central South University Hunan, China

Preface

With the increasing awareness on environmental issues and stricter governmental regulations, manufacturing organizations are adopting Green Supply Chain Management (GSCM) in their production operation practices nowadays to achieve positive outcomes on environmental, social and economic aspects. GSCM is important in reducing the total negative environmental impact of a manufacturing plant involved in supply chain operations which can contribute to sustainable development and ensure performance enhancement. Selecting the best green supplier is a critical part of GSCM and is also essential for companies to promote GSCM. The performance of suppliers not only affects the producers’ performance, but also affects the performance of downstream enterprises. An appropriate green supplier makes a great difference in enhancing the quality of end products and the satisfaction degree of customers. Through Green Supplier Evaluation and Selection (GSES), companies can save costs, enhance their sustainability performance, improve customer satisfaction, and thus build competitive advantage. Moreover, an accurate supplier selection is useful for organizations to integrate supply chain and maximize the overall benefits. Therefore, the GSES has received considerable attention from both academicians and practitioners in recent years. Green supplier selection is a challenging work because of the diversity of factors affecting supplier selection, the uncertainty of quantitative and qualitative evaluation criteria, and the quantity and variety of alternative suppliers. Compared with the traditional supplier selection, GSES not only considers a supplier’s economic performance, such as product quality, price, transportation, after-sales service and production management, but also considers their environmental protection, energy-saving performance and social responsibility. It is very difficult for decision-makers to select the most appropriate supplier that meets all the evaluation criteria. Thus, selecting the optimal green supplier can be viewed as a complex Multi-criteria Decision-Making (MCDM) problem. In this book, we provide an in-depth and systematic introduction to different types of models based on uncertainty theories and MCDM methods for evaluating and selecting green suppliers. In addition, many empirical examples in different industries are given to demonstrate the applicability and effectiveness of our developed GSES models. The strengths and weaknesses of the proposed methods vii

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are further discussed by using comparative analysis with other methods. The book is structured in 13 chapters as follows. Chapter 1 offers a broad perspective on the fundamentals of this book, including supply chain, supply chain management and GSCM. Chapter 2 presents a comprehensive review of the studies which aim to develop GSES models and methods to assess and select the best green supplier(s), based on which the current research trends and future research directions in the research area are identified. Chapter 3 provides an extended intuitionistic fuzzy VIKOR (VIsekriterijumska optimizacija I KOmpromisno Resenje) method for GSES and illustrates it by two application examples for a general hospital and a car manufacturer, respectively. Chapter 4 proposes an extended picture fuzzy VIKOR approach for GSES and verifies its feasibility and superiority using a case study in the beef supply chain. Chapter 5 reports a GSES model based on some interval 2-tuple linguistic distance operators and demonstrate its efficiency with a supplier selection example from the healthcare industry. Chapter 6 introduces a GSES model based on interval 2-tuple linguistic variables and VIKOR method, and gives its illustration with healthcare and international supplier selection cases. Chapter 7 is concerned with an interval-valued intuitionistic uncertain linguistic GSES approach using Best-Worst Method (BWM) and Alternative Queuing Method (AQM), and uses a real example of a watch manufacturer to demonstrate the proposed approach. Chapter 8 is dedicated to an interval-valued intuitionistic uncertain linguistic GSES approach, which adopts Grey Relation Analysis-Technique for Order Preference by Similarity to Ideal Solution (GRA-TOPSIS) method for the evaluation and selection of green suppliers, and applies it to green supplier selection in the agri-food industry. In Chap. 9, we describe a large group GSES method integrating interval-valued intuitionistic uncertain linguistic sets and multi-objective optimization by a ratio analysis plus full multiplicative form (MULTIMOORA), and show its application by an empirical example of a real estate company. In Chap. 10, we develop a GSES model combining cloud model and QUALIFLEX (qualitative flexible multiple criteria method). Furthermore, this GSES model is applied to select the optimum green supplier for an automobile manufacturer to confirm its rationality and effectiveness. In Chap. 11, we construct a GSES model that utilizes heterogeneous information to evaluate alternative suppliers against each criterion, and a modified Multi-attributive Border Approximation Area Comparison (MABAC) method to derive the ranking of green suppliers. A case study from the automobile industry is given to demonstrate the developed GSES model. Chapter 12 puts forward a Green Supplier Selection and Order Allocation (GSSOA) method, which combines double hierarchy hesitant linguistic term sets, an extended decision field theory and Multi-objective Linear Programming (MOLP) model, and verifies its practicability and efficiency via a case study in the electronic industry. Chapter 13 proposes a GSSOA method through the combination of linguistic Z-numbers, AQM and MOLP model, and illustrates it by a practical case in the pulp and paper industry.

Preface

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This book is very interesting for practitioners and academics working in the fields of green supply chain management, production operation management, uncertain decision-making, management science and engineering, etc. It can be considered as the guiding document for a manufacturer to select a environmentally, socially and economically powerful supplier and maintain its competitive advantages in the highly competitive local and global business environment. This book can also serve as a useful reference source for postgraduate and senior undergraduate students in courses related to the areas indicated above. The book contains a large number of illustrations. These will help the reader to understand otherwise difficult concepts, models and methods. We would like to acknowledge support from the National Natural Science Foundation of China (No. 61773250), the Fundamental Research Funds for the Central Universities and the Program for Shanghai Youth Top-Notch Talent. Shanghai, China December 2020

Hu-Chen Liu Xiao-Yue You

Contents

1

Green Supply Chain Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Supply Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Supply Chain Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Green Supply Chain Management . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 4 7 10 10

2

Green Supplier Evaluation and Selection: A Literature Review . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 GSES Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Distance-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Compromise Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Outranking Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Pairwise Comparison Methods . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Mathematical Programming Methods . . . . . . . . . . . . . . . . 2.3.6 Value and Utility Methods . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Aggregation Operator-Based Methods . . . . . . . . . . . . . . . 2.3.8 Combined Supplier Selection Methods . . . . . . . . . . . . . . . 2.3.9 Other Supplier Selection Methods . . . . . . . . . . . . . . . . . . . 2.3.10 Supplier Selection and Order Allocation Methods . . . . . 2.4 Findings and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Green Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Criteria Weighting Methods . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Green Supplier Evaluation Methods . . . . . . . . . . . . . . . . . 2.4.4 Bibliometric Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Future Research Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 15 16 21 22 23 24 25 26 27 28 29 29 31 31 42 46 49 53 55 55

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3

GSES Based on Intuitionistic Fuzzy VIKOR Method . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Intuitionistic Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Objective Weighting Method . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Proposed GSES Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Supplier Selection for a General Hospital . . . . . . . . . . . . . 3.4.2 Supplier Selection for a Car Manufacturer . . . . . . . . . . . . 3.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 67 69 69 72 73 76 76 79 82 83

4

GSES Based on Picture Fuzzy VIKOR Method . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Picture Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 The OWAD Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Picture Fuzzy Distance Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The PFOWSD Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 The PFEOWSD Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 The HPFOWSD Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 The HPFEOWSD Operator . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 The Proposed GSES Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Background Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Implementation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Comparative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87 87 89 89 91 91 91 93 94 95 96 98 98 99 105 106 107 107

5

GSES Using Interval 2-Tuple Linguistic Distance Operators . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 2-Tuple Linguistic Variables . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Interval 2-Tuple Linguistic Variables . . . . . . . . . . . . . . . . 5.3 Interval 2-Tuple Linguistic Distance Operators . . . . . . . . . . . . . . . 5.3.1 Interval 2-Tuple Linguistic Distance Operators . . . . . . . . 5.3.2 Generalizations of the ITOWD Operator . . . . . . . . . . . . . 5.4 The Proposed GSES Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 An Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Example Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Comparative Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

111 111 113 113 114 116 117 121 123 125 125 129 130 130

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6

GSES Using Interval 2-Tuple Linguistic VIKOR Method . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The Proposed GSES Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Interval-Valued Intuitionistic Uncertain Linguistic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Precedence Relationship Between Alternatives . . . . . . . . 7.3 The Proposed GSES Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 The IVIUL-BWM for Computing Criteria Weights . . . . 7.3.2 The IVIUL-AQM for Ranking Alternative Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Calculating the Criteria Weights . . . . . . . . . . . . . . . . . . . . 7.4.2 Determining the Ranking of Green Suppliers . . . . . . . . . 7.4.3 Comparisons Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

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GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 The Proposed GSES Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Case Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.2 Comparison and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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133 133 135 136 139 139 145 148 149 153 153 155 155 158 159 159 162 164 165 169 174 177 177 181 181 183 184 185 190 190 196 197 198

GSES with Large Group Uncertain Linguistic MULTIMOORA Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

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9.3

The Proposed GSES Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Cluster Decision Makers . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Aggregate Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Calculate the Weights of Criteria . . . . . . . . . . . . . . . . . . . . 9.3.4 Rank the Alternative Suppliers . . . . . . . . . . . . . . . . . . . . . . 9.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Comparison and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205 207 207 209 210 211 211 225 226 226

10 GSES with Cloud Model Theory and QUALIFLEX Method . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Cloud Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Laplace Distribution-Based Method . . . . . . . . . . . . . . . . . 10.3 The Proposed GSES Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Assess the Performance of Green Suppliers . . . . . . . . . . . 10.3.2 Compute the Weights of Evaluation Criteria . . . . . . . . . . 10.3.3 Determine the Ranking of Alternatives . . . . . . . . . . . . . . . 10.4 Illustrative Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Background Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Application and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 Discussion Under Incomplete Weight Information . . . . . 10.4.4 Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

229 229 231 231 233 234 234 236 238 239 239 240 244 245 246 246

11 GSES with Heterogeneous Information and MABAC Method . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 The Proposed GSES Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.2 Comparisons and Discussion . . . . . . . . . . . . . . . . . . . . . . . 11.5 Managerial Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

249 249 251 254 259 259 268 269 270 270

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets and Decision Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 The Developed GSSOA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

273 273 275 277

Contents

xv

12.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4.1 Illustration of the Proposed Model . . . . . . . . . . . . . . . . . . 12.4.2 Comparison and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

283 284 291 292 293

13 GSSOA Using Linguistic Z-Numbers and AQM . . . . . . . . . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 The Proposed GSSOA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.1 Suppliers Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3.2 Order Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.2 Model Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.3 Comparisons and Discussions . . . . . . . . . . . . . . . . . . . . . . 13.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

297 297 299 301 302 305 307 307 309 316 318 318

Appendix A: Data Extracted from the Reviewed Studies . . . . . . . . . . . . . . 321 Appendix B: Green Evaluation Criteria Used in the Reviewed Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Abbreviations

AHP ANFIS ANP AQM ARAS BWM COPRAS COWA CWA DEA DEMATEL DFT DHHL DHHLE DHHLTS DHHWG DHLT DHLTS EDAS ELECTRE EOWAD FIS FLIEOWAD FMEA FMLMCDM GDEA GITND GITOWD GITWD GRA GSCM

Analytic hierarchy process Adaptive neuro-fuzzy inference system Analytical network process Alternative queuing method Additive ratio assessment Best-worst method Complex proportional assessment Cloud-ordered weighted averaging Cloud weighted averaging Data envelopment analysis Decision-making trial and evaluation laboratory model Decision field theory Double hierarchy hesitant linguistic Double hierarchy hesitant linguistic element Double hierarchy hesitant linguistic term set Double hierarchy hesitant weighted geometric Double hierarchy linguistic term Double hierarchy linguistic term set Evaluation based on distance from average solution Elimination and choice translating reality Euclidean-ordered weighted averaging distance Fuzzy inference system Fuzzy linguistic-induced Euclidean-ordered weighted averaging distance Failure mode and effect analysis Fuzzy multi-level multi-criteria decision-making Green data envelopment analysis Generalized interval 2-tuple normalized distance Generalized interval 2-tuple-ordered weighted distance Generalized interval 2-tuple weighted distance Grey relational analysis Green supply chain management xvii

xviii

GSES GSSOA GTOWD HA HFHPWA HOWAD HPFEOWSD HPFOWSD IFE IF-GRA IFH IFH-VIKOR IFN IFS IF-TOPSIS IF-VIKOR IOS IRP ISM ITHA ITHWD ITL-VIKOR ITND ITOWAWA ITOWCD ITOWD ITOWED ITOWGD ITOWHD ITWA ITWD IVIFGWHM IVIFS IVIUL IVIULCA IVIULCGM IVIULN IVIULS IVIULWA IVIULWGA

Abbreviations

Green supplier evaluation and selection Green supplier selection and order allocation Generalized 2-tuple-ordered weighted distance Hybrid average Hesitant fuzzy Hamacher power weighted average Heavy-ordered weighted averaging distance Hybrid PFEOWSD Hybrid PFOWSD Intuitionistic fuzzy entropy Intuitionistic fuzzy GRA Intuitionistic fuzzy hybrid Intuitionistic fuzzy hybrid VIKOR Intuitionistic fuzzy number Intuitionistic fuzzy set Intuitionistic fuzzy TOPSIS Intuitionistic fuzzy VIKOR International Organization for Standardization Interpretive ranking process Interpretive structural modelling Interval 2-tuple hybrid averaging Interval 2-tuple hybrid weighted distance Interval 2-tuple linguistic VIKOR Interval 2-tuple normalized distance Interval 2-tuple-ordered weighted averaging weighted averaging Interval 2-tuple-ordered weighted cubic distance Interval 2-tuple-ordered weighted distance Interval 2-tuple-ordered weighted Euclidean distance Interval 2-tuple-ordered weighted geometric distance Interval 2-tuple-ordered weighted harmonic distance Interval 2-tuple weighted average Interval 2-tuple weighted distance Interval-valued intuitionistic fuzzy geometric weighted Heronian means Interval-valued intuitionistic fuzzy set Interval-valued intuitionistic uncertain linguistic Interval-valued intuitionistic uncertain linguistic Choquet averaging Interval-valued intuitionistic uncertain linguistic Choquet geometric mean Interval-valued intuitionistic uncertain linguistic number Interval-valued intuitionistic uncertain linguistic sets Interval-valued intuitionistic uncertain linguistic weighted average Interval-valued intuitionistic uncertain linguistic weighted geometric average

Abbreviations

LHFS LHFWA LHGA LINMAP LOWAD LZWA LZWGA MABAC MACBETH MARCOS MCDM MOLP MOORA MOORA-AS MSGP MULTIMOORA NIS OEM OWA OWAD OWD PFEOWSD PFHOWSD PFN PFNHSD PFOWASD PFOWD PFOWSD PFS PFWA PFWESD PFWHSD PIPRCIA PIS POWAD PRISMA PROMETHEE QFD

xix

Linguistic hesitant fuzzy set Linguistic hesitant fuzzy-weighted averaging Linguistic hybrid geometric averaging Linear programming technique for multidimensional analysis of preference Linguistic-ordered weighted averaging distance Linguistic Z-numbers weighted average Linguistic Z-numbers weighted geometric average Multi-attributive border approximation area comparison Measuring attractiveness by a categorical-based evaluation technique Measurement of alternatives and ranking according to compromise solution Multi-criteria decision-making Multi-objective line programming Multi-objective optimization based on ratio analysis Multi-objective optimization based on ratio analysis with the aspiration level Multi-segment goal programming Multi-objective optimization by ratio analysis plus the full multiplicative form Negative ideal solution Original equipment manufacturer Ordered weighted average Ordered weighted averaging distance Ordered weighted distance Picture fuzzy Euclidean-ordered weighted standardized distance Picture fuzzy Hamming-ordered weighted standardized distance Picture fuzzy number Picture fuzzy normalized Hamming standardized distance Picture fuzzy-ordered weighted average standardized distance Picture fuzzy-ordered weighted distance Picture fuzzy-ordered weighted standardized distance Picture fuzzy set Picture fuzzy-weighted averaging Picture fuzzy-weighted Euclidean standardized distance Picture fuzzy-weighted Hamming standardized distance Pivot pairwise relative criteria importance assessment Positive ideal solution Probabilistic-ordered weighted averaging distance Preferred reporting items for systematic reviews and meta-analyses Preference ranking organization method for enrichment evaluation Quality function deployment

xx

QUALIFLEX Quasi-ITOWD Quasi-TOWD SIFWA SSOA SVTNDPNBM SWARA TFN THWD TODIM TOPSIS TOWA TOWD TWA TWD ULHA ULHGM ULHHM ULWA ULWGM ULWHM UPOWAS VIKOR WASPAS

Abbreviations

Qualitative flexible multiple criteria method Quasi-arithmetic interval 2-tuple-ordered weighted distance Quasi-arithmetic 2-tuple-ordered weighted distance Symmetric intuitionistic fuzzy-weighted averaging Supplier selection and order allocation Single-valued triangular Neutrosophic Dombi prioritized normalized Bonferroni mean Stepwise weight assessment ratio analysis Trapezoidal fuzzy number 2-tuple hybrid weighted distance An acronym in Portuguese of interactive and multi-criteria decision-making Technique for order of preference by similarity to ideal solution 2-tuple-ordered weighted averaging 2-tuple-ordered weighted distance 2-tuple weighted average 2-tuple weighted distance Uncertain linguistic hybrid aggregation Uncertain linguistic hybrid geometric mean Uncertain linguistic hybrid harmonic mean Uncertain linguistic weighted averaging Uncertain linguistic weighted geometric mean Uncertain linguistic weighted harmonic mean Uncertain probabilistic-ordered weighted averaging distance VlseKriterijumska optimizacija i kompromisno resenje Weighted aggregated sum-product assessment

List of Figures

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig. 1.5 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5 Fig. 2.6 Fig. 2.7 Fig. 3.1 Fig. 4.1 Fig. 7.1 Fig. 7.2 Fig. 7.3 Fig. 7.4 Fig. 8.1 Fig. 9.1 Fig. 10.1 Fig. 10.2 Fig. 11.1 Fig. 11.2 Fig. 11.3 Fig. 12.1 Fig. 12.2 Fig. 13.1 Fig. 13.2 Fig. 13.3

Activities in a supply chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supply chain network structure . . . . . . . . . . . . . . . . . . . . . . . . . . . Using intermediaries to simplify a supply chain . . . . . . . . . . . . . . Major drivers of a supply chain . . . . . . . . . . . . . . . . . . . . . . . . . . . Green supply chain framework . . . . . . . . . . . . . . . . . . . . . . . . . . . Article review process based on the PRISMA method . . . . . . . . . Co-occurrence analysis of green evaluation criteria . . . . . . . . . . . Green supplier selection methods in the reviewed literature . . . . Distribution of articles by publication year . . . . . . . . . . . . . . . . . . Distribution of articles by publication journal . . . . . . . . . . . . . . . . Distribution of articles with respect to country . . . . . . . . . . . . . . . Distribution of articles by application area . . . . . . . . . . . . . . . . . . Comparative ranking of the candidate suppliers . . . . . . . . . . . . . . Rankings of suppliers by the compared methods . . . . . . . . . . . . . A directed graph of alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the proposed GSES model . . . . . . . . . . . . . . . . . . . . The final directed graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flowchart of the proposed green supplier selection approach . . . Schematic diagram of the proposed GSES model . . . . . . . . . . . . Flowchart of the proposed GSES approach . . . . . . . . . . . . . . . . . . Dimensions and criteria for green supplier selection . . . . . . . . . . Flowchart of the proposed GSES model . . . . . . . . . . . . . . . . . . . . Upper (G+ ), lower (G− ) and border (G) approximation areas . . . Ranking results of green suppliers by different methods . . . . . . . Flowchart of the developed SSS&OA model . . . . . . . . . . . . . . . . Ranking results via different methods . . . . . . . . . . . . . . . . . . . . . . Flowchart of the proposed GSSOA model . . . . . . . . . . . . . . . . . . Directed graph for the five alternative suppliers . . . . . . . . . . . . . . Ranking results of different methods . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 6 8 16 42 50 51 52 52 53 82 105 158 160 176 176 186 206 235 240 255 258 268 278 291 302 314 317

xxi

List of Tables

Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 3.7 Table 3.8 Table 3.9 Table 3.10 Table 3.11 Table 3.12 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Table 4.7 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5

GSES methods used in the reviewed literature . . . . . . . . . . . . . . Green evaluation criteria frequently used in the literature . . . . . Criteria weighting methods used in the literature . . . . . . . . . . . . Green supplier evaluation methods used in the literature . . . . . Top 10 influential papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linguistic terms for rating alternatives . . . . . . . . . . . . . . . . . . . . Linguistic terms for rating the importance of criteria . . . . . . . . Assessed information on the four alternatives . . . . . . . . . . . . . . Importance weights of criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . Collective intuitionistic fuzzy decision matrix and the subjective weights of criteria . . . . . . . . . . . . . . . . . . . . . Normalized intuitionistic fuzzy differences and normalized subjective weights of criteria . . . . . . . . . . . . . . . Calculated intuitionistic fuzzy entropy (IFE) values and objective weights of criteria . . . . . . . . . . . . . . . . . . . . . . . . . Values of S, R, and Q for the four alternatives . . . . . . . . . . . . . . Ranking of the four alternatives by S, R, and Q . . . . . . . . . . . . . Assessed information of alternatives for Example 2 . . . . . . . . . Importance weights of criteria for Example 2 . . . . . . . . . . . . . . Values of S, R, and Q for Example 2 . . . . . . . . . . . . . . . . . . . . . . Linguistic terms for assessing the alternatives . . . . . . . . . . . . . . Linguistic evaluation matrixes of the decision makers . . . . . . . . Picture fuzzy evaluation matrix of DM1 . . . . . . . . . . . . . . . . . . . Collective picture fuzzy evaluation matrix  R ............... Results with picture fuzzy Hamming operators . . . . . . . . . . . . . Results with picture fuzzy Euclidean operators . . . . . . . . . . . . . Ranking results with the PFOWD-VIKOR model . . . . . . . . . . . Linguistic assessments of the suppliers . . . . . . . . . . . . . . . . . . . . Interval 2-tuple linguistic decision matrix . . . . . . . . . . . . . . . . . Collective interval 2-tuple linguistic decision matrix . . . . . . . . . Collective ideal supplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aggregated results 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 32 43 47 50 71 71 77 77 78 78 78 79 79 80 81 81 96 99 100 101 102 103 104 126 127 128 128 128 xxiii

xxiv

Table 5.6 Table 5.7 Table 5.8 Table 6.1 Table 6.2 Table 6.3 Table 6.4 Table 6.5 Table 6.6 Table 6.7 Table 6.8 Table 6.9 Table 6.10 Table 6.11 Table 6.12 Table 6.13 Table 6.14 Table 6.15 Table 7.1 Table 7.2 Table 7.3 Table 7.4 Table 7.5 Table 7.6 Table 7.7 Table 7.8 Table 8.1 Table 8.2 Table 8.3 Table 8.4 Table 9.1 Table 9.2 Table 9.3 Table 9.4

List of Tables

Aggregated results 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rankings of the alternative suppliers . . . . . . . . . . . . . . . . . . . . . . Ranking comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linguistic assessments of alternatives provided by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linguistic assessments of criteria weights . . . . . . . . . . . . . . . . . Interval 2-tuple linguistic decision matrix of DM1 . . . . . . . . . . . 2-Tuple linguistic criteria weights . . . . . . . . . . . . . . . . . . . . . . . . Aggregated interval 2-tuple linguistic decision matrix . . . . . . . Normalized 2-tuple linguistic distances . . . . . . . . . . . . . . . . . . . The 2-tuples (S p , α p ), (Rp , α p ) and (Op , α p ) of the five alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking of the alternative suppliers . . . . . . . . . . . . . . . . . . . . . . Ranking comparisons for example 1 . . . . . . . . . . . . . . . . . . . . . . Alternative suppliers for example 2 (Wu 2009) . . . . . . . . . . . . . 2-Tuple linguistic decision matrix of DM1 for example 2 . . . . . Aggregated 2-tuple linguistic decision matrix for example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized 2-tuple linguistic distances for example 2 . . . . . . . The (S p , α p ), (Rp , α p ) and (Op , α p ) of alternatives for example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking comparisons for example 2 . . . . . . . . . . . . . . . . . . . . . . Fuzzy measures of decision maker sets . . . . . . . . . . . . . . . . . . . . The best and the worst criteria identified . . . . . . . . . . . . . . . . . . Preference of the best criterion over other criteria . . . . . . . . . . . Preference of the other criteria over the worst criterion . . . . . . . Performance assessments of green suppliers by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collective evaluation matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall weights of each supplier pair . . . . . . . . . . . . . . . . . . . . . Comprehensive pros and cons indicated value of each supplier pair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance assessments of alternatives by the first decision maker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Criteria weight ratings by the five decision makers . . . . . . . . . . The collective evaluation matrix . . . . . . . . . . . . . . . . . . . . . . . . . Ranking comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance values of the first supplier A1 by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance values of the second supplier A2 by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance values of the third supplier A3 by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance values of the fourth supplier A4 by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128 129 129 141 141 142 142 142 143 143 143 144 145 146 146 147 147 148 164 165 166 167 170 172 173 175 192 193 194 196 213 214 215 216

List of Tables

Table 9.5 Table 9.6 Table 9.7 Table 9.8 Table 9.9 Table 10.1 Table 10.2 Table 10.3 Table 10.4 Table 10.5 Table 10.6 Table 11.1 Table 11.2 Table 11.3 Table 11.4 Table 11.5 Table 12.1 Table 12.2 Table 12.3 Table 12.4 Table 12.5 Table 12.6 Table 12.7 Table 13.1 Table 13.2 Table 13.3 Table 13.4 Table 13.5 Table 13.6 Table 13.7 Table 13.8 Table 13.9

xxv

Clustering results of the four suppliers . . . . . . . . . . . . . . . . . . . . Evaluation values by the five clusters . . . . . . . . . . . . . . . . . . . . . Normalized evaluation values by the five clusters . . . . . . . . . . . The normalized collective evaluation matrix . . . . . . . . . . . . . . . Ranking results of different methods . . . . . . . . . . . . . . . . . . . . . Linguistic ratings for alternative suppliers . . . . . . . . . . . . . . . . . Linguistic assessments of alternatives provided by the expert group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The group cloud decision matrix X˜ . . . . . . . . . . . . . . . . . . . . . . . The results of the concordance/discordance index for P1 . . . . . The results of the weighted concordance/discordance indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking results of different methods . . . . . . . . . . . . . . . . . . . . . Heterogeneous evaluation of green suppliers given by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized heterogeneous evaluation of green suppliers . . . . . Collective heterogeneous evaluation matrix . . . . . . . . . . . . . . . . Weighted collective evaluation matrix . . . . . . . . . . . . . . . . . . . . Distance matrix D and the ranking of green suppliers . . . . . . . . Green supplier selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . Comparative importance evaluation of criteria given by decision makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The DHHL evaluation matrix H 1 . . . . . . . . . . . . . . . . . . . . . . . . Computation result of the PIPRCIA method . . . . . . . . . . . . . . . The collective DHHL evaluation matrix H . . . . . . . . . . . . . . . . . Supplier quantitative data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Order allocation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluation criteria for green supplier selection . . . . . . . . . . . . . Performance evaluation matrix of the first decision maker . . . . Comparative importance evaluation information of criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Computation results of the SWARA method . . . . . . . . . . . . . . . The collective performance evaluation matrix . . . . . . . . . . . . . . Overall weights for each pair of suppliers . . . . . . . . . . . . . . . . . Overall pros and cons indicated values among suppliers . . . . . . Supplier quantitative data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results of order allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

217 218 221 224 225 235 241 242 243 244 245 260 262 265 266 267 285 286 287 288 289 290 290 308 310 311 311 312 313 313 315 316

Chapter 1

Green Supply Chain Management

Nowadays, sustainable development through green initiatives has received considerable attention in view of global pressure, legislature, consumers’ awareness, environmental policies and societal issues. So, green initiatives have been given much importance by international organizations, national policies, and industries to reduce energy waste, conserve biodiversity and eco-system, and protect the environment. In response, manufacturing organizations are adopting green supply chain management (GSCM) in their supply chain practices to achieve positive outcomes on environmental, social and economic aspects. The GSCM is able to reduce the total negative environmental impact of a manufacturing plant involved in supply chain operations which can contribute to sustainable development and ensure performance enhancement. In this chapter, the background knowledge related to supply chain, supply chain management, and GSCM are introduced.

1.1 Supply Chain In the reality, an organization does not work in isolation. It acts as a customer when it buys materials from its own suppliers and then act as a supplier when it delivers materials to its own customers. Most products move through a series of organizations as they travel between original suppliers and final customers. These chains of activities and organizations are called different names in different areas (Waters 2019). They are named as a logistics channel when marketing is emphasized; they are called as a value chain when the value added are focused; they are called as a demand chain when people emphasize how customer demands are satisfied. Here we are emphasizing the movement of materials and will use the most general term of supply chain. A supply chain consists of the series of activities and organizations that materials move through on their journey from initial suppliers to final customers (Waters 2019). Along this journey, materials may move through raw materials suppliers, manufacturers, finishing operations, logistics centers, warehouses, third party operators, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_1

1

2

1 Green Supply Chain Management

transport companies, wholesalers, retailers, and a whole range of other operations. Sometimes, the supply chain goes beyond the final customer to add recycling and re-use of materials. Different definitions of supply chain have been given in the literature. Christopher (2016) indicated that supply chain is a network of connected and interdependent organizations mutually and co-operatively working together to control, manage and improve the flow of materials and information from suppliers to end users. In (Lu 2011), supply chain is defined as a group of inter-connected participating companies that add value to a stream of transformed inputs from their source of origin to the end products or services that are demanded by the designated end-consumers. According to (Chopra et al. 2013), a supply chain consists of all parties involved, directly or indirectly, in fulfilling a customer request. It includes not only the manufacturer and suppliers, but also transporters, warehouses, retailers, and even customers themselves. Within each organization, a supply chain includes all functions involved in receiving and filling a customer request. These functions include new product development, marketing, operations, distribution, finance, and customer service. A supply chain is dynamic and involves the constant flow of information, product, and funds between different stages (e.g., customers, retailers, wholesalers/distributors, manufacturers, and component/raw material suppliers). The customer is an integral part of supply chain. So, the primary purpose of any supply chain is to satisfy customer needs and, in the process, generate profit for itself. The term supply chain conjures up images of product or supply moving from suppliers to manufacturers to distributors to retailers to customers along a chain. This is certainly part of the supply chain, but it is also important to visualize information, funds, and product flows along both directions of this chain. The simplest view of a supply chain has a single product moving through a series of organizations, each of which somehow adds value to the product. Taking one organization’s point of view, activities in front of it—moving materials inwards— are called upstream; those after the organization—moving materials outwards—are called downstream. The upstream activities are divided into tiers of suppliers. A supplier that sends materials directly to the operations is a first tier supplier; one that send materials to a first tier supplier is a second tier supplier; one that sends materials to a second tier supplier is a third tier supplier, and so on back to the original sources. Customers are also divided into tiers. One that gets a product directly from the operations is a first tier customer; one that gets a product from a first tier customer is a second tier customer; one that get a product from a second tier customer is a third tier customer, and so on to final customers (see Fig. 1.1). In the real world, most organizations get materials from many different suppliers, and sell products to many different customers. Then the supply chain converges as raw materials move in through the tiers of suppliers, and diverges as products move out through tiers of customers. A manufacturer might see sub-assembly providers as first tier suppliers, component makers as second tier suppliers, materials suppliers as third tier suppliers, and so on. It might see wholesalers as first tier customers, retailers as second tier customers, and end users as third tier customers (see Fig. 1.2).

1.1 Supply Chain

3

Fig. 1.1 Activities in a supply chain

Fig. 1.2 Supply chain network structure

Supply chains exist to overcome the gaps created when suppliers are some distance away from customers. They allow for operations that are best done—or can only be done—at locations that are distant from customers or sources of materials. Also, supply chains allow for mismatches between supply and demand and can make movements a lot simpler. For example, logistics has to organize 32 different delivery routes if four factories directly supplying products to eight customers (see Fig. 1.3). But the number of routes is cut to 12 if the factories use a central wholesaler. Some other benefits of well-designed supply chains are listed as follows (Waters 2019):

4

1 Green Supply Chain Management

Fig. 1.3 Using intermediaries to simplify a supply chain

• Producers locate operations in the best locations, regardless of the locations of their customers; • By concentrating operations in large facilities, producers can get economies of scale; • Producers do not keep large stocks of finished goods, as these are held further down the supply chain nearer to customers; • Wholesalers place large orders, and producers pass on lower unit costs in price discounts; • Wholesalers keep stocks from many suppliers, giving retailers a choice of goods; • Wholesalers are near to retailers and have short lead times; • Retailers carry less stock as wholesalers provide reliable deliveries; • Retailers can have small operations, giving a responsive service near to customers; • Transport is simpler, with fewer, larger deliveries reducing costs; • Organizations can develop expertise in specific types of operation.

1.2 Supply Chain Management In today’s business environment, no enterprise can expect to build competitive advantage without integrating their strategies with those of the supply chain systems in which they are entwined. Logistics is essentially a planning orientation and framework that seeks to create a single plan for the flow of products and information through a business. Supply chain management builds upon this framework and seeks to achieve linkage and co-ordination between the processes of other entities in the pipeline, i.e., suppliers and customers, and the organization itself. Thus, one goal of supply chain management is to reduce or eliminate the buffers of inventory that exist between organizations in a chain through the sharing of information on demand and current stock levels. The focus of supply chain management is on co-operation and trust and the recognition that, properly managed, a more profitable outcome for all parties in the chain can be achieved (Christopher 2016). Effective supply chain

1.2 Supply Chain Management

5

management can provide a major source of competitive advantage. That is, a position of enduring superiority over competitors in terms of customer preference may be achieved through better management of the supply chain. Supply chain management is a fast-growing business. Over the past decades, it has driven companies around the world to change structure and the way they think about operating in a global environment. The definition of supply chain management given in (Christopher 2016) is: The management of upstream and downstream relationships with suppliers and customers in order to deliver superior customer value at less cost to the supply chain as a whole. Lu (2011) stated that supply chain management is simply and ultimately the business management, whatever it may be in its specific context, which is perceived and enacted from the relevant supply chain perspective. Ross et al. (2010) defined supply chain management as a strategic channel management philosophy composed of the continuous regeneration of networks of businesses integrated together through information technologies and empowered to execute superlative, customer-winning value at the lowest cost through the digital, real-time synchronization of products and services, vital marketplace information, and logistics delivery capabilities with demand priorities. Successful supply chain management requires many decisions relating to the flow of information, product, and funds. Each decision should be made to raise the supply chain surplus. According to the frequency and the time frame, these decisions fall into three categories (Chopra et al. 2013): Supply chain strategy or design, supply chain planning, and supply chain operation. Design decisions constrain or enable good planning, which in turn constrains or enables effective operation. The design, planning, and operation of a supply chain have a strong impact on overall profitability and success. It can be said that a large part of the success of firms can be attributed to their effective supply chain design, planning, and operation. Each supply chain has its own unique set of market demands and operating challenges and yet the issues remain essentially the same in every case. Companies in any supply chain must make decisions individually and collectively regarding their actions in five areas (Hugos 2018): (1)

(2)

(3)

Production: What products does the market want? How much of which products should be produced and by when? This activity includes the creation of master production schedules that take into account plant capacities, workload balancing, quality control, and equipment maintenance. Inventory: What inventory should be stocked at each stage in a supply chain? How much inventory should be held as raw materials, semifinished, or finished goods? The primary purpose of inventory is to act as a buffer against uncertainty in the supply chain. However, holding inventory can be expensive, so what are the optimal inventory levels and reorder points? Location: Where should facilities for production and inventory storage be located? Where are the most cost-efficient locations for production and for storage of inventory? Should existing facilities be used or new ones built? Once these decisions are made, they determine the possible paths available for product to flow through for delivery to the final consumer.

6

(4)

(5)

1 Green Supply Chain Management

Transportation: How should inventory be moved from one supply chain location to another? Air-freight and truck delivery are generally fast and reliable but they are expensive. Shipping by sea or rail is much less expensive but usually involves longer transit times and more uncertainty. This uncertainty must be compensated for by stocking higher levels of inventory. When is it better to use which mode of transportation? Information: How much data should be collected and how much information should be shared? Timely and accurate information holds the promise of better coordination and better decision making. With good information, people can make effective decisions about what to produce and how much, about where to locate inventory, and how best to transport it.

The sum of the above decisions will define the capabilities and effectiveness of a company’s supply chain. Figure 1.4 shows the major drivers of a supply chain. Normally, supply chain management practice and activities are captured by three conceptual components (Lu 2011), i.e., supply chain configuration, supply chain relationship, and supply chain coordination. • Supply chain configuration is about how a supply chain is constructed from all its participating firms. This includes how big is the supply base for original equipment manufacturer (OEM); how wide or narrow is the extent of vertical integration; how much of the OEM’s operations are outsourced; how the downstream distribution

Fig. 1.4 Major drivers of a supply chain

1.2 Supply Chain Management

7

channel is designed; and so on. The decision on supply chain configuration is strategic and at a higher level. • Supply chain relationship is about inter firm relationships across the supply chain albeit the key focus of relationship is often around the OEM and its first tier suppliers and first tier customers and the relationship in between. The type and level of the relationship is determined by the contents of inter-organizational exchanges. The relationship is likely to be “arm’s length” if only the volume and price of the transaction are exchanged. The relationship would be regarded as close partnership if the parties exchanged their vision, investment planning, and detailed financial information. The decision on supply chain relationship is both strategic and operational. • Supply chain coordination refers to the inter-firm operational coordination within a supply chain. It involves the coordination of continuous material flows from the suppliers to the buyers and through to the end-consumer. Inventory management throughout the supply chain could be a key focal point for the coordination. Production capacity, forecasting, manufacturing scheduling, even customer services will all constitute the main contents of the coordination activities in the supply chain. The decision on the supply chain coordination tends to be operational.

1.3 Green Supply Chain Management The increasing global demand to meet sustainable development goals is leading to the adoption of processes, production of goods and provision of services that create less waste, reduce energy consumption, conserves resources, and presents less harm to the environment and human lives. Restricted by environmental protection policies and motivated by high consumer demand for green products, enterprise supply chains suffer more pressure on natural resources and a resulting demand to utilize more green energy (Carvalho et al. 2020). Thus, more and more companies are adopting green practices to meet the requirements of government laws, investors, employees, media, trade unions, and non-governmental organizations (Agyabeng-Mensah et al. 2020). Also, companies recognize green practices as a means of penetrating new markets and gaining competitive advantage through enhanced firm reputation. As a result, industries have started to integrate environmental factors throughout their organizations. Furthermore, industries have been gradually shifting towards environmentally friendly supply chains by integrating green technologies into their product designs, production, and distribution processes. In this process of engagement and minimization of environmental impact, designing and producing ecologically correct products, green supply chain management (GSCM) has become a strategic and operational concern for various companies (Sarkis and Dou 2017). Sustainability can be visualized as a development strategy or an operating practice that meets the needs of the present without compromising the ability of future generations to meet their own needs. It is an idea which guides our paths in a direction of how we might live in

8

1 Green Supply Chain Management harmony with the natural world around us, protecting it from damage and destruction. It is tricky though as we strive to find balance between two competing needs; one favoring economic and technological advancements and the other prioritizing the environment. (Ali et al. 2019).

As a focal part of sustainability initiatives, GSCM has emerged as a key strategy that can provide competitive advantage with significant gains for the company’s bottom line. GSCM integrates environmental thinking into supply chain management, ranging from product design, material sourcing and selection, manufacturing processes, delivery of the final product as well as end-of-life management of the product after its useful life (Micheli et al. 2020). The GSCM practices are management actions implemented by a company across a supply chain to reduce pollution and energy consumption and enhance sustainability in the long term (Zhu et al. 2008). The most prevalent components of GSCM are technical and tangible aspects, such as green design, green manufacturing, and reverse logistics. According to (Carvalho et al. 2020), GSCM is an evolution of supply chain management with the aim of minimizing environmental impacts and increasing resource efficiency through all phases of the supply chain, starting with product acquisition until its final disposal after use. The GSCM practices help to build a win–win situation, considering both economic and environmental positive impacts. Green supply chains are defined as the management of material, information and capital flows as well as cooperation among companies along the supply chain while taking goals from all three dimensions of sustainable development, i.e., economic, environmental and social, into account which are derived from customer and stakeholder requirements (Ali et al. 2019). It includes policies, practices and tools that an organization can apply in the context of the sustainable environment. The integrated planning of the green supply chain requires the management of a business or organization to initially determine the inputs, drivers and enablers that must be processed for the production, transportation and distribution, packaging and recycling of green products (Fig. 1.5) (Achillas et al. 2018).

Fig. 1.5 Green supply chain framework

1.3 Green Supply Chain Management

9

The management of green supply includes the planning, execution, monitoring and control of practices, approaches and tools that assists organizations of their “greening” process to become socially responsible and sustainable through environmental protection. Another critical issue is the identification of the key stakeholders within green supply chain initiatives. GSCM expands the concept of sustainability from a company to the supply chain level by providing companies with tools for improving their own and the sector’s competitiveness, sustainability and responsibility towards meeting stakeholder expectations. Principles of accountability, transparency and stakeholder engagement are highly relevant to GSCM. During recent decades, a number of innovative practices and technologies have emerged to achieve the automation, simplification, optimization and redesign of GSCM processes. Specifically, the following initiatives have been promoted: (a) procurement-sourcing, manufacturing, re-manufacturing, warehousing, supply chain network design and waste management; (b) improving the communication and achieving the coordination, cooperation and integration of the supply chain partners of the supply chain; and (c) supporting the decision-making process in the three business levels (operational, tactical and strategic). Moreover, there is a need to identify the outputs and/or services, but also the social, financial and environmental benefits. Selecting the best green supplier is a critical part of GSCM. Through green supplier selection, companies can save costs, improve their green performance, and thus enhance the overall sustainability performance of a company. Green supplier selection determines the best supplier which is capable of providing the buyer with high quality, low cost, quick return, and good environmental performance simultaneously (Quan et al. 2018; Xu et al. 2019). It plays a vital role in maintaining the competitive advantages of a company (Banaeian et al. 2018). An appropriate green supplier makes a great difference in enhancing quality of end products and satisfaction degree of customers. The application of green supplier selection can be presented in the situation of multiple suppliers throughout a product’s life-cycle (Bai and Sarkis 2010; Bai et al. 2019). Consequently, it is significant for organizations to choose the environmentally, socially and economically powerful suppliers and establish a long-term relationship with it for maintaining competitive advantages. Green supplier selection is a challenging work that needs to take green criteria incorporated into the conventional supplier selection (Govindan et al. 2017; Liu et al. 2019; You et al. 2020). According to (Qin et al. 2017), selecting a green supplier is a main element of the decision-making procedure in production operation management. Through green supplier selection, manufactures can effectively improve their environmental performance and customer satisfaction. Moreover, an accurate supplier selection is useful for organizations to integrate supply chain and improve the overall benefits (Ecer 2020; Krishankumar et al. 2020; Stevi´c et al. 2020). Therefore, a large number of green supplier evaluation and selection (GSES) approaches have been proposed in the past decades for helping enterprises to promote GSCM (Zhang et al. 2020). In this book, we mainly aim to develop new GSES models through the combination of uncertainty theories and multi-criteria decision making (MCDM) methods. Moreover, the proposed green supplier selection methods

10

1 Green Supply Chain Management

are applied to real cases from different industries to illustrate their effectiveness, practicability and advantages.

1.4 Chapter Summary With great public awareness of global warming, reduction of non-renewable resources and pollution, manufacturing organizations are incorporating green activities into their supply chains in the last decade. Expanding sustainability understanding across the supply chain has been viewed not only as promising but also as an effective approach bringing innovation and practice into industrial operations. Regrading the very crucial issue of the intersection between environmental and economic pillars for production and supply chains, GSCM has become an important business strategy to improve eco-sustainability, to respond to firm stakeholders’ driver, and to achieve corporate profit and market share objectives by reducing environmental risks and impacts. Selecting an optimal green supplier is a critical part of GSCM, which is essential for companies to reduce the total negative environmental impact of its supply chain operations. This chapter sets the view point for the book by providing relevant research backgrounds. The main theme of this book is proposing and applying GSES models to address the sustainability issues in supply chain management, given the higher complexity involved. This chapter identified existing trends and problems and formulated the objectives of this book.

References Achillas C, Bochtis DD, Aidonis D, Folinas D (2018) Green supply chain management. Routledge, New York Agyabeng-Mensah Y, Ahenkorah E, Afum E, Nana Agyemang A, Agnikpe C, Rogers F (2020) Examining the influence of internal green supply chain practices, green human resource management and supply chain environmental cooperation on firm performance. Supply Chain Manage 25(5):585–599 Ali SS, Kaur R, Saucedo JAM (2019) Best practices in green supply chain management: a developing country perspective. Emerald Publishing, Bingley Bai C, Sarkis J (2010) Integrating sustainability into supplier selection with grey system and rough set methodologies. Int J Prod Econ 124(1):252–264 Bai CG, Kusi-Sarpong S, Ahmadi HB, Sarkis J (2019) Social sustainable supplier evaluation and selection: a group decision-support approach. Int J Prod Res 57(22):7046–7067 Banaeian N, Mobli H, Fahimnia B, Nielsen IE, Omid M (2018) Green supplier selection using fuzzy group decision making methods: a case study from the agri-food industry. Comput Oper Res 89:337–347 Carvalho LS, Stefanelli NO, Viana LC, Vasconcelos DSC, Oliveira BG (2020) Green supply chain management and innovation: a modern review. Manage Environ Qual: Int J 31(2):470–482 Chopra S, Meindl P, Kalra DV (2013) Supply chain management: strategy, planning, and operation, 5th edn. Pearson Education, Boston

References

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Christopher M (2016) Logistics & supply chain management, 5th edn. Financial Times Press, New Jersey Ecer F (2020) Multi-criteria decision making for green supplier selection using interval type-2 fuzzy AHP: a case study of a home appliance manufacturer. Oper Res Int J. https://doi.org/10.1007/s12 351-020-00552-y Govindan K, Kadzi´nski M, Sivakumar R (2017) Application of a novel PROMETHEE-based method for construction of a group compromise ranking to prioritization of green suppliers in food supply chain. Omega 71:129–145 Hugos MH (2018) Essentials of supply chain management, 4th edn. Wiley, New Jersey Krishankumar R, Gowtham Y, Ahmed I, Ravichandran KS, Kar S (2020) Solving green supplier selection problem using q-rung orthopair fuzzy-based decision framework with unknown weight information. Appl Soft Comput 94:106431 Liu HC, Quan MY, Li Z, Wang ZL (2019) A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment. Inf Sci 486:254– 270 Lu D (2011) Fundamentals of supply chain management. Ventus Publishing, Frederiksberg Micheli GJL, Cagno E, Mustillo G, Trianni A (2020) Green supply chain management drivers, practices and performance: a comprehensive study on the moderators. J Clean Prod 259:121024 Qin J, Liu X, Pedrycz W (2017) An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res 258(2):626–638 Quan MY, Wang ZL, Liu HC, Shi H (2018) A hybrid MCDM approach for large group green supplier selection with uncertain linguistic information. IEEE Access 6:50372–50383 Ross DF, Weston FS, Stephen W (2010) Introduction to supply chain management technologies. CRC Press, Boca Raton Sarkis J, Dou Y (2017) Green supply chain management: a concise introduction. Routledge, Oxon Stevi´c Ž, Pamuˇcar D, Puška A, Chatterjee P (2020) Sustainable supplier selection in healthcare industries using a new MCDM method: measurement of alternatives and ranking according to compromise solution (MARCOS). Comput Ind Eng 140:106231 Waters CDJ (2019) Logistics: an introduction to supply chain management. Palgrave Macmillan, New York Xu XG, Shi H, Zhang LJ, Liu HC (2019) Green supplier evaluation and selection with an extended MABAC method under the heterogeneous information environment. Sustainability 11(23):6616 You SY, Zhang LJ, Xu XG, Liu HC (2020) A new integrated multi-criteria decision making and multi-objective programming model for sustainable supplier selection and order allocation. Symmetry 12(2):302 Zhang LJ, Liu R, Liu HC, Shi H (2020) Green supplier evaluation and selections: a state-of-the-art literature review of models, methods, and applications. Math Prob Eng 2020:1783421 Zhu Q, Sarkis J, Lai KH (2008) Confirmation of a measurement model for green supply chain management practices implementation. Int J Prod Econ 111(2):261–273

Chapter 2

Green Supplier Evaluation and Selection: A Literature Review

To improve GSES, a large number of approaches have been proposed in the past decades. This chapter systematically reviews the literature which aim to develop models and methods in helping enterprises to assess and select the right green suppliers. A total of 193 journal article extracted from the Scopus database over the period of 2009 to 2020 were chosen and reviewed. These publications were classified into ten categories based on the adopted GSES models, and analyzed concerning the evaluation criteria, criteria weighting methods, and performance evaluation methods. Moreover, a bibliometric analysis was conducted according to the frequency of supplier selection methods, citation number, publication year, journal, country and application area. The literature review results support practitioners, managers, and researchers in effectively recognizing and applying the GSES methods to enhance organizational competitiveness and provide an insight into its state-of-the-art.

2.1 Introduction Nowadays, the intensification of competition, stringent government laws, increasing environmental issues have forced enterprises to improve sustainable outcomes in their operation and supply chain practices. Achieving sustainability needs the integration of environmental, social and economic attributes into their manufacturing processes and supply chains (Bastas and Liyanage 2018). Supply chains are sophisticated, composed of different organizations dispersed across multiple tiers and different geographies (Koberg and Longoni 2019). Green supply chain management (GSCM) is an enterprise strategy which integrate environmental thinking into the supply chain management (Fahimnia et al. 2015; Maditati et al. 2018). In GSCM, complicated mechanisms were employed to the integration and factory level to appraise or enhance environmental outcomes (Jain and Singh 2020). Via the association among suppliers and consumers, manufacturers could build and practice a compelling arrangement programme while confronting environmental challenges. The implementation of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_2

13

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2 Green Supplier Evaluation and Selection …

green supply chain can reduce the generation of pollutants from the source, and the greening degree of suppliers will directly affect the environmental performance of firms (Malviya and Kant 2015; Zimmer et al. 2016). In addition, implementing green supply chain can bring economic benefits and competitive advantages to a firm, which is paramount important to the development of the firm (Wetzstein et al. 2016). Since GSCM includes different phases from raw material purchase to the final product delivery, a focal company should not only green the intra-organizational supply chain operations but also focus on the inter-organizational aspects. Suppliers, as upstream supply chain partners, play a significant role in the achievement of sustainability objectives of a firm. Thus, selecting the most qualified green supplier in a supply chain is a vital strategic decision to maintain the competitive position of an organization internationally (Malviya and Kant 2015; Jain and Singh 2020). For the purpose of high quality and environmental standards, various aspects and criteria are needed to be considered in the green supplier selection. So, green supplier selection can be seen as a challenge decision making problem with the goal of ensuring better performance from an enterprise’s suppliers. In the past few years, the development of practical green supplier evaluation and selection (GSES) methods is rapidly evolving (Wetzstein et al. 2016; Zimmer et al. 2016). Some literature reviews on GSCM or green supplier selection have been conducted in prior studies from different aspects. For instance, Koberg and Longoni (2019) proposed a systematic literature review of the papers focused on GSCM in global supply chains. Badi and Murtagh (2019) performed a systematic review of the literature on GSCM in the construction industry. Bastas and Liyanage (2018) undertaken a literature review on the integration of quality management, supply chain management and sustainability management. Maditati et al. (2018) investigated the relationships among GSCM drivers, practice indicators and performance measures via a bibliometric analysis of GSCM articles. Fang and Zhang (2018) explored the overall relationship between GSCM practice and company performance by a meta-analysis of GSCM literature. Fahimnia et al. (2015) analyzed the published studies related to GSCM with the aid of bibliometric and network analysis tools. Mardani et al. (2020) presented a systematic review of the application of structural equation modelling in the assessment of GSCM. Igarashi et al. (2013) provided a literature review on supplier selection and proposed a conceptual model to integrate the different dimensions of green supplier selection. Konys (2019) conducted a meta-analysis of the literature on green-oriented supplier selection and introduced an ontology-based method to synthetize the analyzed selection and evaluation criteria of suppliers. In addition, the quantitative and qualitative decision methodologies in sustainable supplier management were reviewed and analyzed in Zimmer et al. (2016), the multi-criteria decision making (MCDM) methods for designing green supply chains were reviewed in Banasik et al. (2018), and the MCDM approaches for evaluating green supplier performance were analyzed in Govindan et al. (2015). Although the existing literature on GSCM is extensive, no or few researches have been conducted to review the mathematical models used for supporting GSES comprehensively. The reviews of Govindan et al. (2015), Banasik et al. (2018) only

2.1 Introduction

15

focused on the MCDM models for green supplier selection, and the previous study by Zimmer et al. (2016) did not report criteria weighting methods and performance evaluation methods. Moreover, these literature surveys need an update since more than half of related papers have been published after their analysis. Therefore, in this chapter, we systematically review the scientific literature related to GSES models by using the academic database of Scopus. Following a methodological review process, a total of 193 journal articles published between 2009 and 2020 were identified. The main aim of this chapter is to solve the following research questions: (1) What GSES methodologies have been developed in the literature; (2) What are the criteria considered for GSES problems; (3) What are the weighting methods used for deriving criteria weights; and (4) What are the uncertainty methods adopted for managing experts’ evaluation information. Moreover, the statistical analyses on year, journal, country, and application area will be analyzed in order to provide a roadmap to researchers studied in this field. The rest of this chapter is organized as follows. After the introduction, Sect. 2.2 describes the research methodology followed for the literature review. Section 2.3 conducts a detailed review of the selected articles classified into ten categories. The bibliometric analysis results and future research suggestions are presented in Sect. 2.4 and Sect. 2.5, respectively. Finally, we summarize this chapter in Sect. 2.6.

2.2 Research Methodology To perform a systematic review on the literature of GSES, we here followed the PRISMA method (Moher et al. 2009). The PRISMA method mainly includes three stages: Literature search, eligible article selection, and data extraction. First, the electronic database of Scopus was used for literature search since it is the largest abstract and citation database of peer-reviewed literature, allowing in-depth exploration of the literature. Only articles written in English and published in academic peer reviewed journals are considered in this review study. The literature search was conducted by searching the keywords “green supplier selection” and “sustainable supplier selection” in the title, abstract or keywords for identifying pertinent papers comprehensively. In addition, the time span of this literature review is limited to 2009–2020, and the search was completed in May 2020. As consequence, a total of 501 papers were retrieved in line with the search strategy as described above. In the second stage, we choose the scientific literature which is in line with the scope of this review. This review only focuses on the researches which had proposed a method or model to address green supplier evaluation and selection problems. Conversely, the papers that examined the actual practices of green purchasing and green procurement or only incorporated the environmental aspect in supplier selection without quantitative analysis were omitted. Eventually, 193 relevant papers were selected after title (n = 318), abstract (n = 281), and full-text screening (n = 193) based on our inclusion criteria. In the third stage, necessary data were collected from the 193 papers and the included scholarly researches were summarized and analyzed based

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2 Green Supplier Evaluation and Selection …

Fig. 2.1 Article review process based on the PRISMA method

on, e.g., supplier selection model, publication year, and published journal. Figure 2.1 illustrates the entire review procedure of this literature survey. It may be mentioned that this literature review was performed very carefully and presents a comprehensive basis regarding the models, methods and applications of GSES.

2.3 GSES Methods From the collected literature, we can find that multifarious models and methods have been proposed and used to handle the GSES problem. Based on the methods employed in determining the ranking of candidate green suppliers, we construct a classification framework to segregate the literature of the topic to be studied. According to the classification framework, the identified 193 articles are classified into ten categories, including distance-based methods, compromise methods, outranking methods, pairwise comparison methods, mathematical programming methods, aggregation operator-based methods, value and utility methods, combined

2.3 GSES Methods

17

methods, other green supplier selection methods, and supplier selection and order allocation (SSOA) methods. The categories with their related GSES approaches and papers are summarized in Table 2.1. In the following subsections, each of the ten categories is focused and the relevant literature are reviewed in detail with focus on the approaches adopted for GSES. Table 2.1 GSES methods used in the reviewed literature Classification

GSES method

Distance-based TOPSIS methods (31)

GRA

References

Tseng (2011), Tseng and Chiu (2013), Hashemi et al. (2015), Malek et al. (2017), Quan et al. (2018a), Haeri and Rezaei (2019)

6

EDAS

Yazdani et al. (2019), Xu et al. (2020)

2

MABAC

Xu et al. (2019b)

1

Relative-closeness Mousavi et al. (2020) coefficient Compromise methods (19)

Outranking methods (14)

Frequency

Büyüközkan and Ifi (2012), Shen et al. (2013), 21 Kannan et al. (2014), Zhao and Guo (2014), Cao et al. (2015), Freeman and Chen (2015), Wang Chen et al. (2016), Fallahpour et al. (2017), Gupta and Barua (2017), Mousakhani et al. (2017), Abdel-Basset et al. (2018), Van et al. (2018), dos Santos et al. (2019), Hou and Xie (2019), Li et al. (2019), Memari et al. (2019), Tian et al. (2019), Yu et al. (2019a), Yucesan et al. (2019), Chen et al. (2020), Rouyendegh et al. (2020)

1

VIKOR

Datta et al. (2012), Hsu et al. (2014), Kuo et al. 14 (2015), Luthra et al. (2017), Awasthi et al. (2018), Zhou and Xu (2018), Abdel-Baset et al. (2019), Liu et al. (2019a), Meksavang et al. (2019), Phochanikorn and Tan (2019b), Wu et al. (2019b), Fallahpour et al. (2020), Kannan et al. (2020), Peng et al. (2020)

MULTIMOORA

Mohammadi et al. (2017), Liu et al. (2018), Quan et al. (2018b), Liou et al. (2019), Liu et al. (2019c)

5

ELECTRE

Tsui and Wen (2014), Kumar et al. (2017), Gitinavard et al. (2018), Lu et al. (2018), Shojaie et al. (2018), Guarnieri and Trojan (2019)

6

PROMETHEE

Govindan et al. (2017), Abdullah et al. (2019), Roy et al. (2019), Wan et al. (2020)

4

QUALIFLEX

Li and Wang (2017), Wang et al. (2017), Liang and Chong (2019), Liang et al. (2020)

4 (continued)

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2 Green Supplier Evaluation and Selection …

Table 2.1 (continued) Classification

GSES method

References

Pairwise comparison methods (11)

AHP

Lee et al. (2009), Yu and Hou (2016), Pishchulov et al. (2019), Xu et al. (2019c), Ecer (2020)

5

ANP

Hsu and Hu (2009), Büyüközkan and Çifçi (2011), Chung et al. (2016), Faisal et al. (2017), Giannakis et al. (2020)

5

AQM

Liu et al. (2019b)

1

DEA

Kuo et al. (2010), Kuo and Lin (2012), Kumar 18 et al. (2014), Mahdiloo et al. (2015), Shi et al. (2015), Fallahpour et al. (2016), Jain et al. (2016), Jauhar and Pant (2016), Kumar et al. (2016), Jauhar and Pant (2017), Yu and Su (2017), Jafarzadeh Ghoushchi et al. (2018), Wang et al. (2018a), Zarbakhshnia and Jaghdani (2018), Dobos and Vörösmarty (2019a, b), Wu et al. (2019a), Izadikhah and Farzipoor Saen (2020)

MOLP

Yeh and Chuang (2011), Bakeshlou et al. (2017), Pandey et al. (2017), Khalilzadeh and Derikvand (2018)

4

Arshadi Khamseh and Mahmoodi (2014), Sang and Liu (2016), Qin et al. (2017), Wang and Li (2018), Bai et al. (2019), Nie et al. (2019)

6

Prospect theory

Song et al. (2018), Phochanikorn and Tan (2019a), Wu et al. (2019c)

3

Axiomatic design method

Büyüközkan (2012), Kannan et al. (2015), Guo et al. (2017)

3

Possibilistic statistical method

Foroozesh et al. (2018, 2019), Rabbani et al. (2019)

3

Digraph and matrix method

KhanMohammadi et al. (2018), Sinha and Anand (2018)

2

WASPAS

Keshavarz Ghorabaee et al. (2016), Yazdani et al. (2016), Mishra et al. (2019)

3

COPRAS

Mati´c et al. (2019), Kumari and Mishra (2020)

2

MAUT

Shaik and Abdul-Kader (2011)

1

MARCOS

Stevi´c et al. (2020)

1

Range of value

Uluta¸s et al. (2019)

1

Possibility degree

Lu et al. (2019)

1

Fuzzy comprehensive evaluation

Pang et al. (2017)

1

Mathematical programming methods (22)

Value and TODIM utility methods (30)

Frequency

(continued)

2.3 GSES Methods

19

Table 2.1 (continued) Classification

GSES method

References

Fuzzy performance index

Sahu et al. (2014)

1

Fuzzy preference relationship

Sinha and Anand (2017)

1

Piecewise linear value function

Jafarzadeh Ghoushchi et al. (2019)

1

Shahryari Nia et al. (2016), Zhu and Li (2018), Wang et al. (2019), Wu et al. (2019d)

4

Xu et al. (2019a)

1

Prioritized average operator

Liu et al. (2019e)

1

PBM operator

Liu et al. (2019d)

1

HFHPWA operator

Tang (2017)

1

IVIFGWHM operator

Yin et al. (2017)

1

FWA operator

Lin et al. (2017)

1

TOWA operator

Hu et al. (2015)

1

SVTNDPNBM operator

Fan et al. (2019)

1

GRA-TOPSIS

Shi et al. (2018), Chen (2019)

2

TOPSIS, MOORA, GRA

Sen et al. (2018)

1

Aggregation Choquet integral operator-based methods (12) Hybrid aggregation operator

Combined supplier selection methods (14)

Frequency

TOPSIS, VIKOR, Banaeian et al. (2018) GRA

1

MOORA, COPRAS

Yazdani et al. (2017)

1

MOORA, WASPAS

Tavana et al. (2017)

1

MLMCDM, TOPSIS

Sahu et al. (2016)

1

AHP, TOPSIS, IRP

Kaur et al. (2016)

1

VIKOR, ELECTRE

Girubha et al. (2016)

1

ARAS, MOLP

Liao et al. (2016)

1 (continued)

20

2 Green Supplier Evaluation and Selection …

Table 2.1 (continued) Classification

Other supplier selection methods (9)

Supplier selection and order allocation methods (31)

GSES method

References

TOPSIS, ELECTRE

Yu et al. (2019b)

Frequency 1

TOPSIS, TODIM

Mao et al. (2019)

1

TOPSIS, ANFIS

Okwu and Tartibu (2020)

1

TOPSIS, FIS

Jain et al. (2020)

1

Bayesian network, Zhang and Cui (2019) Genetic algorithm

1

Bayesian framework, Monte Carlo Markov Chain

1

Sarkis and Dhavale (2015)

Systems dynamics Orji and Wei (2015)

1

FIS

Amindoust et al. (2012), Amindoust and Saghafinia (2017)

2

Satisfaction degree framework, Regret theory

Qu et al. (2020)

1

Consensus decision making method

Gao et al. (2020)

1

Decision-theoretic Ma et al. (2020) rough set

1

Six sigma quality indices

Chen et al. (2019)

1

TOPSIS, MOLP

Kannan et al. (2013), Govindan and 11 Sivakumar (2016), Hamdan and Cheaitou (2017a, b), Lo et al. (2018), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Mohammed et al. (2019), Yadavalli et al. (2019), Mohammed (2020), Tirkolaee et al. (2020)

AHP, MOLP

Shaw et al. (2012), Almasi et al. (2019), Laosirihongthong et al. (2019), Khoshfetrat et al. (2020)

4

GRA, MOLP

Banaeian et al. (2015)

1

BWM, MOLP

Cheraghalipour and Farsad (2018)

1

QFD, MOLP

Babbar and Amin (2018)

1

MOORA, FMEA, Arabsheybani et al. (2018) MOLP

1

Decision field theory, MOLP

You et al. (2020)

1

AQM, MOLP

Duan et al. (2019)

1 (continued)

2.3 GSES Methods

21

Table 2.1 (continued) Classification

GSES method

References

DEMATEL, Taguchi loss function, MOLP

Gören (2018)

Frequency 1

MOLP model

Tsai and Hung (2009), Kim et al. (2018), Moheb-Alizadeh and Handfield (2018), Park et al. (2018), Torres-Ruiz and Ravindran (2018), Vahidi et al. (2018), Moheb-Alizadeh and Handfield (2019), Rabieh et al. (2019), Jia et al. (2020)

9

2.3.1 Distance-Based Methods First, 31 articles were identified to employ distance-based methods for GSES. Gupta and Barua (2017) proposed a hybrid methodology comprising of best worst method (BWM) and fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) for selecting suppliers among small and medium enterprises based on their green innovation ability. Tian et al. (2019) applied an intuitionistic fuzzy TOPSIS method integrated with BWM for green supplier selection, and Yucesan et al. (2019) combined the BWM with an interval type-2 fuzzy TOPSIS method to solve green supplier selection problems. Wang Chen et al. (2016) developed an integrated fuzzy analytic hierarchy process (AHP)-TOPSIS approach for green supplier selection. Abdel-Basset et al. (2018) presented an integrated interval-valued neutrosophic analytical network process (ANP)-TOPSIS framework to deal with sustainable supplier selection problems. Some researches selected the most suitable supplier regarding the environmental competencies by using the fuzzy TOPSIS (Shen et al. 2013; Kannan et al. 2014), the intuitionistic fuzzy TOPSIS (Memari et al. 2019; Rouyendegh et al. 2020) and the interval type-2 fuzzy TOPSIS (Mousakhani et al. 2017) methods. Dos Santos et al. (2019) integrated fuzzy TOPSIS with entropy method for the evaluation and selection of green suppliers; Yu et al. (2019a) utilized an entropybased TOPSIS method for sustainable supplier selection in the interval-valued Pythagorean fuzzy context. In Hou and Xie (2019), a hesitant fuzzy TOPSIS model was constructed for supplier evaluation in green supply chain, in which evaluation criteria were determined by the decision making trial and evaluation laboratory model (DEMATEL), and criteria weights were obtained using the maximizing deviation method. In Büyüközkan and Ifi (2012), a hybrid MCDM approach based on DEMATEL, ANP and fuzzy TOPSIS was introduced to evaluate green suppliers in fuzzy environment. In Chen et al. (2020), a hybrid rough-fuzzy DEMATELTOPSIS method was proposed to sustainable supplier selection for a smart supply chain. Fallahpour et al. (2017) utilized a hybrid model based on fuzzy preference programing and fuzzy TOPSIS for sustainable supplier selection in a textile company, and Van et al. (2018) adopted an integrated approach based on quality function

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deployment (QFD) and interval neutrosophic TOPSIS for green supplier evaluation in a transportation parts company. Besides, different combination weighting methods (i.e., AHP + entropy method, expert judgement + entropy method, expert judgement + maximizing distance method, and expert judgement + statistical variance method) have been combined with the TOPSIS (Freeman and Chen 2015), the fuzzy TOPSIS (Zhao and Guo 2014), the intuitionistic fuzzy TOPSIS (Cao et al. 2015), and the rough cloud TOPSIS (Li et al. 2019), respectively, for selecting the best green supplier. In Hashemi et al. (2015), an integrated green supplier selection approach was proposed with ANP and an improved grey relational analysis (GRA). In Malek et al. (2017), an enhanced hybrid GRA model was presented for green resilient supply chain network assessment. A GRA-based green supplier selection method was suggested in Haeri and Rezaei (2019), that incorporated BWM and fuzzy grey cognitive map to assign criteria weights. Tseng and Chiu (2013) applied fuzzy GRA approach for evaluating firm’s green supply chain management in linguistic preferences, and Tseng (2011) utilized fuzzy set theory with a grey degree for green supplier selection with linguistic preferences and incomplete information. A weighted grey incidence decision approach was developed by Quan et al. (2018a) to evaluate and choose the best green supplier in the process industry. Based on the EDAS method, Yazdani et al. (2019) developed a hybrid decisionmaking model to deal with the GSES problem of a construction company under legislation and risk factors. In this study, the DEMATEL method was employed to calculate the weight of each evaluation criterion and the failure mode and effect analysis (FMEA) technique was used to determine the risk rating of each alternative supplier. Xu et al. (2020) established an extended EDAS model with single-valued complex neutrosophic sets and applied it for green supplier selection. Xu et al. (2019b) developed a GSES model through the combination of heterogeneous criteria information and an extended multi-attributive border approximation area comparison (MABAC) method. A soft computing approach based on interval type-2 trapezoidal fuzzy sets and relative-closeness coefficients was presented in Mousavi et al. (2020) for green supplier selection problem.

2.3.2 Compromise Methods Nineteen articles in our reviewed literature apply compromise methods to handle the GSES problem. First, the interval-valued fuzzy VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) (Datta et al. 2012), the picture fuzzy VIKOR (Meksavang et al. 2019; Peng et al. 2020) and the interval-valued intuitionistic fuzzy VIKOR (Kuo et al. 2015) were proposed to evaluate and select the best supplier in sustainable supplier management. In Wu et al. (2019b), a green supplier selection method based on BWM and VIKOR was introduced to address the GSES problem in interval type-2 fuzzy environment; in Kannan et al. (2020), a hybrid approach combining fuzzy BWM and interval VIKOR was provided for sustainable circular

2.3 GSES Methods

23

supplier selection. The AHP was coupled with VIKOR (Yazdani et al. 2019) and fuzzy VIKOR (Tseng 2011) for green suppliers’ performance evaluation and selection. The ANP was integrated with VIKOR (Luthra et al. 2017) and neutrosophic VIKOR (Abdel-Baset et al. 2019) for GSES in supply chains. The fuzzy preference programming, a modification of AHP, was integrated with fuzzy VIKOR by Fallahpour et al. (2020) to assess suppliers’ performance with respect to carbon management criteria. In addition, Zhou and Xu (2018) developed an integrated DEMATELANP-VIKOR model for sustainable supplier selection with heterogeneous information, Phochanikorn and Tan (2019b) suggested an integrated DEMATEL-ANPVIKOR approach for sustainable supplier selection under intuitionistic fuzzy environment, and Kuo et al. (2015) proposed a green supplier selection method using DEMATEL-based ANP and VIKOR to evaluate green suppliers in an electronics company. Quan et al. (2018b) proposed a hybrid MCDM approach for the evaluation of suppliers’ environmental performances within the large group environment. Specifically, interval-valued intuitionistic uncertain linguistic sets were used for assessing candidate green suppliers, an extended linear programming technique for multidimension analysis of preference (LINMAP) method was adopted to calculate the objective weights of criteria, and an improved multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) technique was applied to rank green suppliers. Liu et al. (2018) developed a two-stage integrated model for the supplier selection of green fresh product. In the first stage, the relationships of customer requirements, company strategies and selection criteria were analyzed by QFD, and the subjective criteria weights are computed by fuzzy BWM. In the second stage, the objective criteria weights were determined by an entropy method and the most suitable suppliers are obtained using fuzzy MULTIMOORA method. Mohammadi et al. (2017) presented a group decision making method for evaluating and ranking green suppliers, in which the relative preference relation was employed to weight selection criteria and the interval type 2 fuzzy MULTIMOORA method was applied for selecting the best green supplier. Liu et al. (2019c) developed a large-scale green supplier selection approach based on q-rung interval-valued orthopair fuzzy sets and MULTIMOORA method, and Liou et al. (2019) reported a data-driven green supplier evaluation model using random forest algorithm, DEMATEL-based ANP, and multi-objective optimization on the basis of ratio analysis to the aspiration level (MOORA-AS) method.

2.3.3 Outranking Methods Fourteen articles in the data set proposed outranking methods for achieving sustainable supplier selection. Kumar et al. (2017) evaluated the suppliers’ performances based on green practices using fuzzy ELECTRE (elimination and choice translating reality) approach. Lu et al. (2018) evaluated and selected the right suppliers by the use of an integrated method based on rough set theory and ELECTRE approach.

24

2 Green Supplier Evaluation and Selection …

Shojaie et al. (2018) examined the suppliers of a pharmaceutical company by using fuzzy ELECTRE and entropy method in order to achieve a green health supply chain. Gitinavard et al. (2018) investigated the GSES problem in manufacturing systems by using interval-valued hesitant fuzzy ELECTRE and maximizing deviation method. Tsui and Wen (2014) analyzed and prioritized green polarizer suppliers via a hybrid MCDM model, in which AHP and entropy method were used to measure the compromised weights of criteria and the ELECTRE III method was adopted to provide the ranking results for executive managers. Guarnieri and Trojan (2019) proposed a model which combines AHP with the ELECTRE-TRI to support supplier selection based on social, ethical, and environmental criteria. Abdullah et al. (2019) selected the right suppliers by using the preference ranking organization method for enrichment evaluation (PROMETHEE) under the usual criterion preference functions and Govindan et al. (2017) addressed the green supplier selection problem in food supply chain by combining a revised Simos procedure and PROMETHEE method. Based on the fuzzy AHP and PROMETHEE methods, Roy et al. (2019) established a framework for sustainable supplier selection with heterogeneous information. Wan et al. (2020) presented a hesitant fuzzy PROMETHEE method for green supplier selection, in which an entropy-based nonlinear programming model was built to determine criteria weights. The hesitant fuzzy QUALIFLEX method was proposed by Liang and Chong (2019) for green supplier selection in the Hong Kong-Zhuhai-Macau bridge project. The probability hesitant fuzzy QUALIFLEX model was suggested by Li and Wang (2017) for selecting green suppliers in an automobile manufacturing company. In Wang et al. (2017), an integrated decision support framework using cloud model theory and the QUALIFLEX method was developed for the evaluation of qualified green suppliers, and a TOPSIS-based optimization model was constructed to derive criteria weights with unknown or incompletely known weight information. In Liang et al. (2020), a green supplier selection approach for heterogeneous information and dependent criteria based on the QUALIFLEX method and Choquet integral was proposed.

2.3.4 Pairwise Comparison Methods Eleven of the reviewed researches suggested pairwise comparison methods for the selection of optimal green suppliers. The fuzzy AHP (Lee et al. 2009), the interval type-2 fuzzy AHP (Ecer 2020), the voting AHP (Pishchulov et al. 2019), and the multiplicative AHP (Yu and Hou 2016) were used for evaluating the performance and selecting the best green supplier in different areas. Xu et al. (2019c) proposed the use of the sorting method, AHP Sort II, to assess green suppliers in interval type-2 fuzzy environment. The ANP approach was employed in choosing the most suitable sustainable supplier in a white goods manufacturer (Faisal et al. 2017), a bicycle manufacturer (Chung et al. 2016), an electronics company (Hsu and Hu 2009), and multiple manufacturing companies (Giannakis et al. 2020). Büyüközkan and Çifçi

2.3 GSES Methods

25

(2011) developed an approach based on fuzzy ANP within multi-person decisionmaking schema under incomplete preference relations for sustainable supplier selection. Liu et al. (2019b) reported a model by integrating BWM and alternative queuing method (AQM) within the interval-valued intuitionistic uncertain linguistic setting to evaluate and select sustainable suppliers under interval-valued intuitionistic uncertain linguistic environment.

2.3.5 Mathematical Programming Methods The mathematical programming methods have been used by 22 studies for suppliers’ green performance evaluation. Dobos and Vörösmarty (2019a) evaluated and improved the green performance of suppliers using data envelopment analysis (DEA) with incomplete data, and Jafarzadeh Ghoushchi et al. (2018) selected sustainable suppliers in supply chain with a goal programming-DEA model in the presence of imprecise data. Dobos and Vörösmarty (2019b) developed a DEA-type green supplier selection method, in which the effect of inventory ordering and holding costs on the selected supplier was considered. Wang et al. (2018a) integrated fuzzy AHP and DEA to identify the optimal suppliers for edible oil production. Kuo and Lin (2012) provided an approach using ANP and DEA for evaluating green suppliers, and Kuo et al. (2010) built a green supplier selection system by combing artificial neural network and ANP into DEA. Kumar et al. (2014) proposed a green DEA (GDEA) approach to model the supplier selection problem considering both cost cutting and environmental efficiency. Later, two advanced GDEA modes, the carbon market sensitive-GDEA (Jain et al. 2016) and the genetic/immune strategy-GDEA (Kumar et al. 2016), were presented for performance evaluation and selection of sustainable suppliers. A systematic DEA approach was introduced in Shi et al. (2015) to select suppliers for a sustainable supply chain, and a genetic programming-based DEA method was applied in Fallahpour et al. (2016) for green supplier selection under fuzzy environment. In addition, the two-stage DEA model (Zarbakhshnia and Jaghdani 2018), the differential evolution-based DEA models (Jauhar and Pant 2016, 2017), the fuzzy DEA model (Yu and Su 2017), the interval-valued Pythagorean fuzzy DEA (Wu et al. 2019a), the context dependent DEA (Izadikhah and Farzipoor Saen 2020), and the eco-efficiency DEA model (Mahdiloo et al. 2015) have been established for GSES. Pandey et al. (2017) reported a two-phase fuzzy goal programming approach integrating hyperbolic membership function to determine suppliers under the sustainable supply chain environment. Bakeshlou et al. (2017) constructed a multi-objective fuzzy linear programming model to solve the green supplier selection problem. In this study, fuzzy DEMATEL method was used to analyze the interrelations among criteria and fuzzy ANP method was utilized to compute the criteria weights with respect to their dependencies. Yeh and Chuang (2011) suggested an optimum mathematical planning model for selecting suppliers in green supply chain problems and employed two multi-objective genetic algorithms to find the set of Pareto-optimal

26

2 Green Supplier Evaluation and Selection …

solutions. A multi-objective mixed-integer programming model was introduced in Khalilzadeh and Derikvand (2018) to identify optimal suppliers for a green supply chain network considering green factors and stochastic parameters.

2.3.6 Value and Utility Methods From the review, it has been found that 30 articles used various value and utility methods for solving the GSES problems. The TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method has been extended by Qin et al. (2017) and Sang and Liu (2016) for green supplier selection in the context of interval type-2 fuzzy sets. Bai et al. (2019) put forward a grey-based group decisionsupport approach composed of the BWM and TODIM for social GSES, and Arshadi Khamseh and Mahmoodi (2014) presented a fuzzy TOPSIS-TODIM hybrid model to choose the best sustainable supplier using fuzzy time function. In Nie et al. (2019), the TODIM method was combined with continuous interval-valued linguistic term sets to solve green supplier selection problems. In Wang and Li (2018), a GSES approach was suggest based on q-rung orthopair fuzzy sets and TODIM method, and the weights of criteria were computed by a subjective weighting method and a deviation maximization model. Phochanikorn and Tan (2019a) designed an integrated decision-making model based on prospect theory for green supplier selection. It used fuzzy DEMATEL method to consider the cause and effect relationships of relevant criteria and fuzzy ANP to assign their weights; the prospect theory was applied to synthesize procurement’s psychological and behavioral factors in selecting green suppliers. Wu et al. (2019c) provided a sustainable photovoltaic module supplier selection model based on triangular intuitionistic fuzzy numbers and cumulative prospect theory. Further, a method combining AHP and entropy theory was proposed to measure the importance of evaluation criteria. An integrated decision framework based on the third generation prospect theory was given in Song et al. (2018) for sustainable supplier selection under heterogeneous information environment. The fuzzy axiomatic design approach was used by Guo et al. (2017) to address the GSES problem in apparel manufacturing, and by Kannan et al. (2015) to select the best green supplier for an engineering plastic material manufacturer, and combined with fuzzy AHP by Büyüközkan (2012) to evaluate green supplier alternatives for a Turkish automotive company. Rabbani et al. (2019) provided a method for sustainable supplier selection by using interval-valued fuzzy sets and possibilistic statistical reference point systems, and Foroozesh et al. (2019) presented a method for green supplier performance evaluation with interval-valued fuzzy possibilistic statistical model and FMEA. Foroozesh et al. (2018) reported an interval-valued fuzzy sets and possibilistic statistical approach to select the green supplier for manufacturing services with the lowest risk. Sinha and Anand (2018) presented a framework based on graph and matrix method for supplier selection in new product development from sustainability perspective,

2.3 GSES Methods

27

and KhanMohammadi et al. (2018) employed the fuzzy group graph theory and matrix approach for supplier evaluation in sustainable supply chain management. Yazdani et al. (2016) considered customer attitudes in the GSES process and applied step-wise weight assessment ratio analysis (SWARA), QFD and weighted aggregated sum-product assessment (WASPAS) for selecting the optimum green supplier. Keshavarz Ghorabaee et al. (2016) proposed the use of an interval type-2 fuzzy WASPAS method for multi-criteria evaluation of green suppliers, and Mishra et al. (2019) suggested a hesitant fuzzy WASPAS method for the assessment of green suppliers based on exponential information measures. A rough complex proportional assessment (COPRAS) model was developed in Mati´c et al. (2019) for sustainable supplier selection in a construction company. An intuitionistic fuzzy COPRAS method based on parametric measures was proposed in Kumari and Mishra (2020) to solve green supplier selection problem. In addition, the researchers have proposed other green supplier selection methods based on the multiple attribute utility theory (Shaik and Abdul-Kader 2011), the range of value (Uluta¸s et al. 2019), the possibility degree (Lu et al. 2019), the fuzzy comprehensive evaluation (Pang et al. 2017), the fuzzy performance index (Sahu et al. 2014), the fuzzy preference relationship (Sinha and Anand 2017), the piecewise linear value function (Jafarzadeh Ghoushchi et al. 2019), and the measurement of alternatives and ranking according to compromise solution (MARCOS) method (Stevi´c et al. 2020).

2.3.7 Aggregation Operator-Based Methods Twelve studies have proposed a variety of aggregation operator-based methods for evaluating and selecting suppliers in sustainable supply chain. Wu et al. (2019d) selected the optimal green supplier of electric vehicle charging facility based on Choquet integral operator and interval type-2 fuzzy uncertainty. Shahryari Nia et al. (2016) determine the best green supplier for a manufacturing company using intervalvalued intuitionistic fuzzy sets and Choquet integral operator. Zhu and Li (2018) established an integrated framework combining consensus reaching process, prioritized operator, and Choquet integral for green supplier selection under the hesitant fuzzy linguistic environment. Wang and Li (2018) proposed a Choquet integralbased model for sustainable supplier selection which considers the interaction among criteria with heterogeneous information. Xu et al. (2019a) dealt with a GSES problem by using the interval 2-tuple hybrid averaging (ITHA) operator, the interval 2-tuple ordered weighted averagingweighted averaging (ITOWAWA) operator, and the interval 2-tuple hybrid geometric operator. Liu et al. (2019e) addressed a GSES problem with the prioritized average operator under the ordered weighted hesitant fuzzy environment. Liu et al. (2019d) investigated a GSES problem by combining QFD with the partitioned Bonferroni mean operator in the context of interval type-2 fuzzy environment. In addition, the fuzzy weighted average operator (Lin et al. 2017), the 2-tuple ordered weighted averaging (TOWA) operator (Hu et al. 2015), the hesitant fuzzy Hamacher power

28

2 Green Supplier Evaluation and Selection …

weighted average (HFHPWA) operator (Tang 2017), the interval-valued intuitionistic fuzzy geometric weighted Heronian means (IVIFGWHM) operator (Yin et al. 2017), and the single-valued triangular Neutrosophic Dombi prioritized normalized Bonferroni mean (SVTNDPNBM) operator (Fan et al. 2019) were employed for evaluation and selection of the best supplier in green supply chain management.

2.3.8 Combined Supplier Selection Methods It can also be found from the literature review that 14 studies have combined multiple methods to generate green supplier rankings in solving GSES problems. Chen (2019) developed a multi-criteria assessment model based on GRA-TOPSIS for sustainable building materials supplier selection in intuitionistic fuzzy setting, and Shi et al. (2018) put forward an integrated approach using the GRA-TOPSIS for green agrifood supplier selection with interval-valued intuitionistic uncertain linguistic information. Yu et al. (2019b) proposed a hybrid sustainable supplier selection approach integrating TOPSIS and ELECTRE methods, and Mao et al. (2019) presented an integrated interval-valued intuitionistic fuzzy GSES approach based on TOPSIS and TODIM methods. Sen et al. (2018) applied the methods of TOPSIS, MOORA and GRA for evaluating sustainability performance of suppliers under intuitionistic fuzzy context, and Banaeian et al. (2018) used the methods of TOPSIS, VIKOR and GRA for GSES in fuzzy environment. In Okwu and Tartibu (2020), a hybrid model based on adaptive neuro-fuzzy inference system (ANFIS) and TOPSIS was implemented for sustainable supplier selection. In Jain et al. (2020), an integrated method based on fuzzy inference system (FIS) and fuzzy TOPSIS was used to evaluate the supplier’s sustainability performance. Yazdani et al. (2017) developing an integrated approach consisting of DEMATEL, QFD, COPRAS, and MOORA for selecting the best green supplier, Tavana et al. (2017) provided an integrated method combining ANP, QFD, MOORA, and WASPAS to green supplier selection problems. Sahu et al. (2016) explored the application feasibility of the fuzzy multi-level MCDM approach in evaluating green suppliers by comparing with fuzzy TOPSIS method. Kaur et al. (2016) proposed an integer linear programming model toward the appraisement and selection of green suppliers by integrating the ranking results obtained from AHP, TOPSIS, and interpretive ranking process (IRP). Girubha et al. (2016) first used a combination of interpretative structural modelling and ANP for computing the weights of criteria considering their interactions, then applied both VIKOR and ELECTRE algorithms to determine the ranking of available green suppliers. An integrated model was developed in Liao et al. (2016) to facilitate supplier selection in the sustainable supply chain by combining fuzzy AHP, fuzzy additive ratio assessment, and multi-segment goal programming (MSGP) techniques.

2.3 GSES Methods

29

2.3.9 Other Supplier Selection Methods There are nine studies addressing the GSES problem with other methods. Zhang and Cui (2019) designed a model via combining a Bayesian network with an improved genetic algorithm for selecting suppliers of agricultural means of production. Sarkis and Dhavale (2015) put forward a triple-bottom-line approach using a Bayesian framework and Monte Carlo Markov Chain simulation toward the evaluation and selection of suppliers for sustainable operations. Orji and Wei (2015) developed a modeling approach of integrating fuzzy logic and systems dynamics to rank and select green supplier in the manufacturing industry. Amindoust et al. (2012) introduced a ranking model based on FIS for the selection of suppliers considering sustainable perspectives, and Amindoust and Saghafinia (2017) applied a modular model on the basis of FIS for textile supplier selection in sustainable supply chain. In Qu et al. (2020), a stochastic dual hesitant fuzzy linguistic method was proposed based on group satisfaction degree framework and regret theory to rank and select green chain suppliers. In Gao et al. (2020), a group consensus decision making model was developed to help choosing the best green supplier for electronics manufacturing. Ma et al. (2020) proposed a three-way group decision-making approach to address the selection of green supplier by extending decision-theoretic rough set into hesitant fuzzy linguistic environment. Chen et al. (2019) applied six sigma quality indices to the evaluation of suppliers based on their process yields and quality levels.

2.3.10 Supplier Selection and Order Allocation Methods There are still 31 articles in the reviewed literature which not only support the selection of green supplier but also determine order allocation among the potential suppliers. Yadavalli et al. (2019) adopted a modified TOPSIS using Z numbers for selecting green suppliers based on customers’ expectations and developed a biobjective mathematical model for allocating optimal amounts to the best performing suppliers. Duan et al. (2019) used an extended AQM with linguistic Z-numbers for green supplier selection, and established a multi-objective line programming (MOLP) mode to determine the optimal order quantity for the qualified green suppliers. Govindan and Sivakumar (2016) adopted fuzzy TOPSIS for the rating and selection of green suppliers, and used a MOLP model for order allocation among the sleeted suppliers. Tirkolaee et al. (2020) implemented a hybrid approach based on fuzzy ANP, fuzzy DEMATEL, and fuzzy TOPSIS to determine the priority of suppliers considering sustainability aspects, and developed a multi-objective mixedinteger linear programming model to determine the lot size and program the order allocation. Kannan et al. (2013) presented an integrated approach of fuzzy AHP, fuzzy TOPSIS, and MOLP for rating and selecting the best green suppliers according

30

2 Green Supplier Evaluation and Selection …

to economic and environmental criteria and then allocating the optimum order quantities among them. Similar integrated methods based on fuzzy AHP, fuzzy TOPSIS, and MOLP also discussed in Hamdan and Cheaitou (2017a, b), Mohammed et al. (2018, 2019), Mohammed (2020) for green SSOA. Lo et al. (2018) established a model that integrated BWM, fuzzy TOPSIS, and fuzzy MOLP for solving problems in green SSOA, and Nourmohamadi Shalke et al. (2018) proposed a model by using entropy method, TOPSIS, and multi-choice goal programming to evaluate the problem of green SSOA considering quantity discounts. Banaeian et al. (2015) introduced a compound green supplier evaluation and order allocation approach, in which AHP was used to weight green criteria, fuzzy GRA was utilized to determine the best suppliers, and a MOLP was constructed to allocate the orders among them optimally. Almasi et al. (2019) proposed an AHP-based multi-objective and multi-period mathematical model for green SSOA under risk and inflation condition, Khoshfetrat et al. (2020) suggested an AHP-based fuzzy, multiobjective, multi-product and multiperiod mathematical model for green SSOA in the automotive industry, and Cheraghalipour and Farsad (2018) gave a BWM-based bi-objective and multi-period mathematical model for green supplier selection and quota allocation considering quantity discounts under disruption risks. Shaw et al. (2012) developed a sustainable SSOA model using fuzzy AHP and fuzzy MOLP for developing low carbon supply chain. Laosirihongthong et al. (2019) obtained the ranking of green suppliers using fuzzy AHP and determined purchasing order allocation among the ranked suppliers using cost minimization subject to multiple criteria of economic, environmental and social conditions. Babbar and Amin (2018) solved the green SSOA problem by fuzzy QFD and stochastic multi-objective mathematical model. Arabsheybani et al. (2018) considered supplier’s sustainability and order allocation simultaneously on the basis of fuzzy MOORA, FMEA and multi-objective mathematical model. Gören (2018) investigated the green SSOA problem with lost sales by using a decision framework consisting of fuzzy DEMATEL, Taguchi loss function, and bi-objective optimization model. You et al. (2020) developed a model for selecting the most suitable sustainable suppliers and determining the optimal order sizes among them by combining double hierarchy hesitant linguistic term sets, decision field theory, and a MOLP model. In Moheb-Alizadeh and Handfield (2019), the authors developed an inclusive multi-objective mixed integer linear programming model, which accounts for multiple periods, multiple products, and multimodal transportation, to evaluate suppliers and allocate order quantities. In Torres-Ruiz and Ravindran (2018), the authors proposed a multi-objective mixed integer linear program model for selecting critical suppliers in a global supply chain setting and allocate orders incorporating general business and environmental performance objectives. In Vahidi et al. (2018), a bi-objective two-stage mixed possibilistic-stochastic programming model was put forward for sustainable SSOA problem under operational and disruption risks. In Park et al. (2018), a multi-objective integer linear programming model for multiple sourcing and multiple product designs was used to address the green SSOA problem based on regional information. Moheb-Alizadeh and Handfield (2019) considered a multi-objective mixed-integer non-linear programming model for green SSOA

2.3 GSES Methods

31

with stochastic demand. In addition, Kim et al. (2018) established a mixed integer programming model for large-scale green SSOA, Tsai and Hung (2009) constructed a fuzzy goal programming model for optimal green supplier selection and flow allocation, Rabieh et al. (2019) presented a multi-objective mathematical integer programming to select green suppliers and determine their order allocation, and Jia et al. (2020) developed a distributionally robust goal programming model including expected constraints and chance constraints for green SSOA problems.

2.4 Findings and Discussions In this section, the analyses of the selected articles regrading green supplier evaluation criteria, criteria weighting methods, and green supplier evaluation methods are described. Also, we conducted a bibliometric analysis on the frequency of green supplier selection method, citation time, year of publication, journal of publication, country of origin and application field.

2.4.1 Green Evaluation Criteria In traditional supplier selection, only the economic criteria (such as price, quality and delivery) are taken into account to arrive at a prioritization or final selection of green suppliers. Over the past decade, the topic of green supplier selection has received increasing attention as organizations started to focus on issues of environmental performance in purchasing due to stricter regulations and pressure from various stakeholders. As a result, environmental and social criteria have been included by companies nowadays to choose a comprehensive sustainable supplier for improving their sustainable supply chain performance. Thus, it is necessary to analyze the green supplier evaluation criteria employed in the reviewed articles. Taken together, a lot of criteria have been mentioned in the selected researches, but their classification into different groups varies among them. In this chapter, we divided the identified criteria into economic, environmental and social dimensions according to the triple bottom line sustainability framework (Igarashi et al. 2013; Zimmer et al. 2016). The most popular evaluation criteria proposed and used in the literature are shown in Table 2.2. In summary, 2270 criteria have been identified from the reviewed articles. Grouping the criteria having the same or similar labels, 4930 unique criteria were derived. Among them, 47.45% economic, 38.41% environmental and 14.14% social criteria are included. From Table 2.2, we can observe that the most frequently used criteria are Quality, Resource consumption, Price, Green design, Environmental management system, and Greenhouse gas emission. In the economic dimension, Cost, Price, Quality, Delivery, and Technology capability are the most important criteria in the selected studies. In the environmental dimension, Environmental management system, Reduce, Reuse and recycle, Greenhouse gas emission, Green

Criteria

Cost

Dimension

Economic

Kuo et al. (2010), Büyüközkan (2012), Banaeian et al. (2015), Kannan et al. (2015), Govindan and Sivakumar (2016), Shahryari Nia et al. (2016), Fallahpour et al. (2017), Guo et al. (2017), Luthra et al. (2017), Pandey et al. (2017), Pang et al. (2017), Jafarzadeh Ghoushchi et al. (2018), Kim et al. (2018), Moheb-Alizadeh and Handfield (2018), Vahidi et al. (2018), Wang et al. (2018b), Abdel-Baset et al. (2019), Almasi et al. (2019), Duan et al. (2019), Lu et al. (2019), Rabbani et al. (2019), Roy et al. (2019), Wu et al. (2019d), Xu et al. (2019c), Zhang and Cui (2019), Gao et al. (2020), Khoshfetrat et al. (2020)

Transportation cost

(continued)

27

Kuo et al. (2010), Amindoust et al. (2012), Büyüközkan (2012), Kuo and Lin (2012), Kumar et al. (2014), Sahu 58 et al. (2014), Tsui and Wen (2014), Banaeian et al. (2015), Hu et al. (2015), Kannan et al. (2015), Shi et al. (2015), Girubha et al. (2016), Govindan and Sivakumar (2016), Jain et al. (2016), Kumar et al. (2016), Yazdani et al. (2016), Yu and Hou (2016), Gupta and Barua (2017), Jauhar and Pant (2017), Luthra et al. (2017), Pang et al. (2017), Tang (2017), Yazdani et al. (2017), Abdel-Basset et al. (2018), Babbar and Amin (2018), Banaeian et al. (2018), Gören (2018), Kim et al. (2018), Quan et al. (2018a), Sen et al. (2018), Song et al. (2018), Zhu and Li (2018), Abdel-Baset et al. (2019), Almasi et al. (2019), Chen (2019), Dobos and Vörösmarty (2019a, b), Duan et al. (2019), Haeri and Rezaei (2019), Hou and Xie (2019), Jafarzadeh Ghoushchi et al. (2019), Laosirihongthong et al. (2019), Liu et al. (2019c, d), Meksavang et al. (2019), Rabbani et al. (2019), Roy et al. (2019), Tian et al. (2019), Xu et al. (2019b, c), Yadavalli et al. (2019), Zhang and Cui (2019), Gao et al. (2020), Izadikhah and Farzipoor Saen (2020), Khoshfetrat et al. (2020), Stevi´c et al. (2020), Wan et al. (2020), Xu et al. (2020)

Frequency 54

Price

Literature Amindoust et al. (2012), Shaw et al. (2012), Kannan et al. (2013), Hashemi et al. (2015), Sarkis and Dhavale (2015), Fallahpour et al. (2016), Kaur et al. (2016), Liao et al. (2016), Sang and Liu (2016), Shahryari Nia et al. (2016), Yu and Hou (2016), Amindoust and Saghafinia (2017), Bakeshlou et al. (2017), Hamdan and Cheaitou (2017a, b), Kumar et al. (2017), Malek et al. (2017), Mohammadi et al. (2017), Mousakhani et al. (2017), Pandey et al. (2017), Qin et al. (2017), Yin et al. (2017), Yu and Su (2017), Arabsheybani et al. (2018), Awasthi et al. (2018), Cheraghalipour and Farsad (2018), Foroozesh et al. (2018), Gitinavard et al. (2018), Mohammed et al. (2018), Moheb-Alizadeh and Handfield (2018), Nourmohamadi Shalke et al. (2018), Quan et al. (2018b), Torres-Ruiz and Ravindran (2018), Abdullah et al. (2019), Fan et al. (2019), Guarnieri and Trojan (2019), Liang et al. (2019), Liu et al. (2019b, e), Mishra et al. (2019), Mohammed et al. (2019), Moheb-Alizadeh and Handfield (2019), Wu et al. (2019a, d), Yu et al. (2019a, b), Ecer (2020), Jia et al. (2020), Kannan et al. (2020), Mohammed (2020), Mousavi et al. (2020), Okwu and Tartibu (2020), Peng et al. (2020), Tirkolaee et al. (2020)

Cost

Sub-criteria

Table 2.2 Green evaluation criteria frequently used in the literature

32 2 Green Supplier Evaluation and Selection …

Dimension

(continued)

Kuo et al. (2010), Kannan et al. (2013), Freeman and Chen (2015), Kannan et al. (2015), Girubha et al. (2016), 20 Govindan and Sivakumar (2016), Jauhar and Pant (2016), Shahryari Nia et al. (2016), Bakeshlou et al. (2017), Fallahpour et al. (2017), Govindan et al. (2017), Guo et al. (2017), Song et al. (2018), Vahidi et al. (2018), Duan et al. (2019), Uluta¸s et al. (2019), Wu et al. (2019d), Yucesan et al. (2019), Zhang and Cui (2019), Gao et al. (2020)

Frequency

Rejection rate

Literature Tseng (2011), Amindoust et al. (2012), Kuo and Lin (2012), Shaw et al. (2012), Tseng and Chiu (2013), Banaeian 97 et al. (2015), Hashemi et al. (2015), Hu et al. (2015), Orji and Wei (2015), Sarkis and Dhavale (2015), Fallahpour et al. (2016), Girubha et al. (2016), Sang and Liu (2016), Yazdani et al. (2016), Yu and Hou (2016), Amindoust and Saghafinia (2017), Faisal et al. (2017), Govindan et al. (2017), Gupta and Barua (2017), Hamdan and Cheaitou (2017b), Jauhar and Pant (2017), Kumar et al. (2017), Malek et al. (2017), Mohammadi et al. (2017), Mousakhani et al. (2017), Pandey et al. (2017), Pang et al. (2017), Sinha and Anand (2017), Tang (2017), Tavana et al. (2017), Yazdani et al. (2017), Yin et al. (2017), Yu and Su (2017), Arabsheybani et al. (2018), Banaeian et al. (2018), Cheraghalipour and Farsad (2018), Gitinavard et al. (2018), Gören (2018), Lo et al. (2018), Lu et al. (2018), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Quan et al. (2018b), Sen et al. (2018), Shi et al. (2018), Torres-Ruiz and Ravindran (2018), Van et al. (2018), Wang et al. (2018b), Zhou and Xu (2018), Zhu and Li (2018), Abdullah et al. (2019), Chen et al. (2019), Dobos and Vörösmarty (2019a, b), Duan et al. (2019), Fan et al. (2019), Guarnieri and Trojan (2019), Haeri and Rezaei (2019), Hou and Xie (2019), Jafarzadeh Ghoushchi et al. (2019), Laosirihongthong et al. (2019), Li et al. (2019), Liu et al. (2019a, b, c, e), Lu et al. (2019), Mati´c et al. (2019), Meksavang et al. (2019), Mishra et al. (2019), Mohammed et al. (2019), Phochanikorn and Tan (2019b), Pishchulov et al. (2019), Rabieh et al. (2019), Roy et al. (2019), Tian et al. (2019), Wu et al. (2019b, c, d), Xu et al. (2019b, c), Yu et al. (2019a, b), Chen et al. (2020), Gao et al. (2020), Jia et al. (2020), Kannan et al. (2020), Ma et al. (2020), Mohammed (2020), Mousavi et al. (2020), Peng et al. (2020), Qu et al. (2020), Rouyendegh et al. (2020), Stevi´c et al. (2020), Wan et al. (2020), Xu et al. (2020), You et al. (2020)

Sub-criteria

Quality

Criteria

Quality

Table 2.2 (continued)

2.4 Findings and Discussions 33

Dimension

Service

Service quality

Büyüközkan and Çifçi (2011), Tseng (2011), Büyüközkan and Ifi (2012), Tseng and Chiu (2013), Freeman and Chen (2015), Kannan et al. (2015), Sarkis and Dhavale (2015), Liao et al. (2016), Yu and Hou (2016), Jauhar and Pant (2017), Wang et al. (2017), Banaeian et al. (2018), Park et al. (2018), Shi et al. (2018), Zhu and Li (2018), Guarnieri and Trojan (2019), Hou and Xie (2019), Memari et al. (2019), Phochanikorn and Tan (2019a), Yu et al. (2019a), Wan et al. (2020)

Sahu et al. (2014), Freeman and Chen (2015), Hu et al. (2015), Kannan et al. (2015), Sarkis and Dhavale (2015), Sang and Liu (2016), Faisal et al. (2017), Fallahpour et al. (2017), Gupta and Barua (2017), Mohammadi et al. (2017), Jafarzadeh Ghoushchi et al. (2018), KhanMohammadi et al. (2018), Shojaie et al. (2018), Duan et al. (2019), Guarnieri and Trojan (2019), Hou and Xie (2019), Lu et al. (2019), Rabbani et al. (2019), Wu et al. (2019a, c), Zhang and Cui (2019), Izadikhah and Farzipoor Saen (2020), Okwu and Tartibu (2020), Peng et al. (2020), Stevi´c et al. (2020), Tirkolaee et al. (2020)

On time delivery

(continued)

21

26

Büyüközkan (2012), Shaw et al. (2012), Kannan et al. (2013), Kumar et al. (2014), Kannan et al. (2015), Jain et al. 24 (2016), Kaur et al. (2016), Kumar et al. (2016), Shahryari Nia et al. (2016), Wang Chen et al. (2016), Faisal et al. (2017), Fallahpour et al. (2017), Guo et al. (2017), Jauhar and Pant (2017), Luthra et al. (2017), Pandey et al. (2017), Gören (2018), Vahidi et al. (2018), Dobos and Vörösmarty (2019a, b), Liu et al. (2019a), Roy et al. (2019), Wu et al. (2019d), Zhang and Cui (2019)

Frequency

Lead time

Literature Amindoust et al. (2012), Büyüközkan (2012), Kuo and Lin (2012), Tsui and Wen (2014), Fallahpour et al. (2016), 45 Girubha et al. (2016), Kaur et al. (2016), Liao et al. (2016), Amindoust and Saghafinia (2017), Govindan et al. (2017), Luthra et al. (2017), Malek et al. (2017), Mousakhani et al. (2017), Pandey et al. (2017), Tang (2017), Arabsheybani et al. (2018), Cheraghalipour and Farsad (2018), Gitinavard et al. (2018), Liu et al. (2018), Nourmohamadi Shalke et al. (2018), Quan et al. (2018a, b), Song et al. (2018), Torres-Ruiz and Ravindran (2018), Wang et al. (2018b), Zhou and Xu (2018), Abdullah et al. (2019), Guarnieri and Trojan (2019), Haeri and Rezaei (2019), Jafarzadeh Ghoushchi et al. (2019), Laosirihongthong et al. (2019), Liu et al. (2019b, c), Mati´c et al. (2019), Phochanikorn and Tan (2019b), Pishchulov et al. (2019), Rabieh et al. (2019), Roy et al. (2019), Yadavalli et al. (2019), Yu et al. (2019a, b), Chen et al. (2020), Kannan et al. (2020), Rouyendegh et al. (2020), Xu et al. (2020)

Sub-criteria

Delivery

Criteria

Delivery

Table 2.2 (continued)

34 2 Green Supplier Evaluation and Selection …

Dimension

Flexibility

Flexibility

(continued)

Shaik and Abdul-Kader (2011), Amindoust et al. (2012), Shen et al. (2013), Sahu et al. (2014), Tsui and Wen 25 (2014), Kaur et al. (2016), Faisal et al. (2017), Fallahpour et al. (2017), Hamdan and Cheaitou (2017a), Kumar et al. (2017), Luthra et al. (2017), Malek et al. (2017), Mohammadi et al. (2017), Foroozesh et al. (2018), Sen et al. (2018), Guarnieri and Trojan (2019), Mati´c et al. (2019), Mishra et al. (2019), Roy et al. (2019), Xu et al. (2019b), Yadavalli et al. (2019), Yu et al. (2019b), Fallahpour et al. (2020), Kannan et al. (2020), Tirkolaee et al. (2020)

R&D capability Lee et al. (2009), Moher et al. (2009), Tsai and Hung (2009), Shaik and Abdul-Kader (2011), Büyüközkan (2012), 21 Kannan et al. (2013), Tsui and Wen (2014), Kannan et al. (2015), Bakeshlou et al. (2017), Fallahpour et al. (2017), Govindan et al. (2017), Guo et al. (2017), Lin et al. (2017), Pang et al. (2017), Yin et al. (2017), Sen et al. (2018), Hou and Xie (2019), Liang and Chong (2019), Rabbani et al. (2019), Wu et al. (2019c), Wu et al. (2019d)

24

Lee et al. (2009), Kuo et al. (2010), Shaik and Abdul-Kader (2011), Kuo and Lin (2012), Kannan et al. (2013, 2015), Bakeshlou et al. (2017), Guo et al. (2017), Lin et al. (2017), Gören (2018), Vahidi et al. (2018), Abdullah et al. (2019), Almasi et al. (2019), Liu et al. (2019d, e), Phochanikorn and Tan (2019a), Rabieh et al. (2019), Wu et al. (2019d), Xu et al. (2019b), Yu et al. (2019a), Zhang and Cui (2019), Gao et al. (2020), Khoshfetrat et al. (2020), Rouyendegh et al. (2020)

Frequency

Technology level

Literature Büyüközkan and Çifçi (2011), Amindoust et al. (2012), Büyüközkan and Ifi (2012), Tsui and Wen (2014), 48 Banaeian et al. (2015), Kannan et al. (2015), Sarkis and Dhavale (2015), Chung et al. (2016), Kaur et al. (2016), Sang and Liu (2016), Yu and Hou (2016), Govindan et al. (2017), Gupta and Barua (2017), Luthra et al. (2017), Malek et al. (2017), Mohammadi et al. (2017), Mousakhani et al. (2017), Pandey et al. (2017), Sinha and Anand (2017), Wang et al. (2017), Babbar and Amin (2018), Cheraghalipour and Farsad (2018), Gitinavard et al. (2018), Nourmohamadi Shalke et al. (2018), Quan et al. (2018b), Shojaie et al. (2018), Sinha and Anand (2018), Wang et al. (2018b), Zhou and Xu (2018), Abdullah et al. (2019), Bai et al. (2019), Guarnieri and Trojan (2019), Haeri and Rezaei (2019), Jafarzadeh Ghoushchi et al. (2019), Mishra et al. (2019), Mohammed et al. (2019), Tian et al. (2019), Uluta¸s et al. (2019), Wang et al. (2019), Yadavalli et al. (2019), Yu et al. (2019b), Jia et al. (2020), Kannan et al. (2020), Mohammed (2020), Okwu and Tartibu (2020), Peng et al. (2020), Rouyendegh et al. (2020), Tirkolaee et al. (2020)

Sub-criteria

Technology capability

Criteria

Technology

Table 2.2 (continued)

2.4 Findings and Discussions 35

Criteria

Pollution control

Environmental Green image

Dimension

Table 2.2 (continued)

(continued)

Lee et al. (2009), Shaik and Abdul-Kader (2011), Kannan et al. (2015), Kuo et al. (2015), Sahu et al. (2016), 18 Faisal et al. (2017), Gupta and Barua (2017), Lin et al. (2017), Luthra et al. (2017), Pandey et al. (2017), Babbar and Amin (2018), Abdel-Baset et al. (2019), Almasi et al. (2019), Liang and Chong (2019), Phochanikorn and Tan (2019a), Yucesan et al. (2019), Jia et al. (2020), Khoshfetrat et al. (2020)

Pollution prevention

22

Amindoust et al. (2012), Datta et al. (2012), Tsui and Wen (2014), Kannan et al. (2015), Fallahpour et al. (2016), Kumar et al. (2017), Sinha and Anand (2017), Tavana et al. (2017), Sen et al. (2018), Van et al. (2018), Zhou and Xu (2018), Foroozesh et al. (2019), Haeri and Rezaei (2019), Laosirihongthong et al. (2019), Liu et al. (2019a), Mati´c et al. (2019), Rabbani et al. (2019), Uluta¸s et al. (2019), Xu et al. (2019c), Gao et al. (2020), Okwu and Tartibu (2020), Stevi´c et al. (2020)

Pollution control

Hsu and Hu (2009), Tseng (2011), Amindoust et al. (2012), Büyüközkan (2012), Kuo and Lin (2012), Kannan 59 et al. (2013), Shen et al. (2013), Banaeian et al. (2015), Keshavarz Ghorabaee et al. (2016), Sahu et al. (2016), Amindoust and Saghafinia (2017), Bakeshlou et al. (2017), Govindan et al. (2017), Guo et al. (2017), Hamdan and Cheaitou (2017a), Li and Wang (2017), Luthra et al. (2017), Tavana et al. (2017), Arabsheybani et al. (2018), Babbar and Amin (2018), Banaeian et al. (2018), Gören (2018), Jafarzadeh Ghoushchi et al. (2018), KhanMohammadi et al. (2018), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Sen et al. (2018), Shi et al. (2018), Van et al. (2018), Wang et al. (2018b), Zhu and Li (2018), Abdullah et al. (2019), dos Santos et al. (2019), Foroozesh et al. (2019), Guarnieri and Trojan (2019), Jafarzadeh Ghoushchi et al. (2019), Laosirihongthong et al. (2019), Liang and Chong (2019), Liu et al. (2019a), Mati´c et al. (2019), Mishra et al. (2019), Mohammed et al. (2019), Nie et al. (2019), Phochanikorn and Tan (2019a), Rabbani et al. (2019), Rabieh et al. (2019), Roy et al. (2019), Wu et al. (2019a), Yu et al. (2019a, b), Yucesan et al. (2019), Ecer (2020), Jia et al. (2020), Kumari and Mishra (2020), Mohammed (2020), Mousavi et al. (2020), Peng et al. (2020), Stevi´c et al. (2020), Wan et al. (2020)

Environmental management system

Frequency

Shaik and Abdul-Kader (2011), Yeh and Chuang (2011), Datta et al. (2012), Shen et al. (2013), Freeman and Chen 28 (2015), Chung et al. (2016), Girubha et al. (2016), Sahu et al. (2016), Shahryari Nia et al. (2016), Hamdan and Cheaitou (2017b), Li and Wang (2017), Mousakhani et al. (2017), Pang et al. (2017), Qin et al. (2017), Yin et al. (2017), Jafarzadeh Ghoushchi et al. (2018), dos Santos et al. (2019), Fan et al. (2019), Guarnieri and Trojan (2019), Haeri and Rezaei (2019), Hou and Xie (2019), Memari et al. (2019), Nie et al. (2019), Phochanikorn and Tan (2019a, b), Mousavi et al. (2020), Rouyendegh et al. (2020), You et al. (2020)

Literature

Green image

Sub-criteria

36 2 Green Supplier Evaluation and Selection …

Dimension

Criteria

Table 2.2 (continued)

(continued)

46

Hsu and Hu (2009), Kuo et al. (2010), Shaik and Abdul-Kader (2011), Tseng (2011), Yeh and Chuang (2011), 22 Tseng and Chiu (2013), Kannan et al. (2014), Sahu et al. (2014), Cao et al. (2015), Kannan et al. (2015), Kuo et al. (2015), Chung et al. (2016), Shahryari Nia et al. (2016), Fallahpour et al. (2017), Vahidi et al. (2018), Van et al. (2018), Wang and Li (2018), Zarbakhshnia and Jaghdani (2018), Guarnieri and Trojan (2019), Hou and Xie (2019), Gao et al. (2020), Giannakis et al. (2020)

Hazardous waste

Greenhouse gas Lee et al. (2009), Kuo et al. (2010), Shaik and Abdul-Kader (2011), Yeh and Chuang (2011), Amindoust et al. emission (2012), Shaw et al. (2012), Kumar et al. (2014), Hu et al. (2015), Kannan et al. (2015), Kuo et al. (2015), Mahdiloo et al. (2015), Shi et al. (2015), Govindan and Sivakumar (2016), Jain et al. (2016), Kumar et al. (2016), Yu and Hou (2016), Fallahpour et al. (2017), Govindan et al. (2017), Guo et al. (2017), Jauhar and Pant (2017), Lin et al. (2017), Yu and Su (2017), Awasthi et al. (2018), Cheraghalipour and Farsad (2018), Khalilzadeh and Derikvand (2018), Moheb-Alizadeh and Handfield (2018), Nourmohamadi Shalke et al. (2018), Quan et al. (2018a), Sen et al. (2018), Wang et al. (2018b), Zarbakhshnia and Jaghdani (2018), Dobos and Vörösmarty (2019a, b), Duan et al. (2019), Guarnieri and Trojan (2019), Hou and Xie (2019), Liang and Chong (2019), Lu et al. (2019), Meksavang et al. (2019), Moheb-Alizadeh and Handfield (2019), Pishchulov et al. (2019), Yazdani et al. (2019), Fallahpour et al. (2020), Giannakis et al. (2020), Jain et al. (2020), Kannan et al. (2020)

Kannan et al. (2013), Shen et al. (2013), Hashemi et al. (2015), Girubha et al. (2016), Keshavarz Ghorabaee et al. 28 (2016), Bakeshlou et al. (2017), Guo et al. (2017), Li and Wang (2017), Qin et al. (2017), Cheraghalipour and Farsad (2018), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Song et al. (2018), Vahidi et al. (2018), Zhou and Xu (2018), dos Santos et al. (2019), Haeri and Rezaei (2019), Mohammed et al. (2019), Wu et al. (2019b, d), Xu et al. (2019a), Jia et al. (2020), Kannan et al. (2020), Kumari and Mishra (2020), Mohammed (2020), Mousavi et al. (2020), Peng et al. (2020), Tirkolaee et al. (2020)

Pollution production

Frequency

Literature Lee et al. (2009), Tsai and Hung (2009), Yeh and Chuang (2011), Amindoust et al. (2012), Kannan et al. (2014), 41 Cao et al. (2015), Freeman and Chen (2015), Hu et al. (2015), Kannan et al. (2015), Shi et al. (2015), Chung et al. (2016), Govindan and Sivakumar (2016), Jauhar and Pant (2016), Sahu et al. (2016), Yazdani et al. (2016), Yu and Hou (2016), Faisal et al. (2017), Fallahpour et al. (2017), Lin et al. (2017), Wang et al. (2017), Yazdani et al. (2017), Yin et al. (2017), Babbar and Amin (2018), Khalilzadeh and Derikvand (2018), Liu et al. (2018), Sen et al. (2018), Shojaie et al. (2018), Song et al. (2018), Dobos and Vörösmarty (2019a, b), Duan et al. (2019), Foroozesh et al. (2019), Hou and Xie (2019), Liang and Chong (2019), Liu et al. (2019d), Rabbani et al. (2019), Yu et al. (2019a, b), Ecer (2020), Kannan et al. (2020), Stevi´c et al. (2020)

Sub-criteria

Reduce, reuse and recycle

2.4 Findings and Discussions 37

Dimension

Lee et al. (2009), Kuo et al. (2010), Tseng (2011), Yeh and Chuang (2011), Tseng and Chiu (2013), Kannan et al. 30 (2014), Cao et al. (2015), Freeman and Chen (2015), Kannan et al. (2015), Kuo et al. (2015), Girubha et al. (2016), Kaur et al. (2016), Sahu et al. (2016), Shahryari Nia et al. (2016), Wang Chen et al. (2016), Fallahpour et al. (2017), Lin et al. (2017), Pang et al. (2017), Yin et al. (2017), Babbar and Amin (2018), Vahidi et al. (2018), Wang and Li (2018), Almasi et al. (2019), Liang and Chong (2019), Lu et al. (2019), Ecer (2020), Gao et al. (2020), Khoshfetrat et al. (2020), Qu et al. (2020), Stevi´c et al. (2020) Yeh and Chuang (2011), Büyüközkan (2012), Cao et al. (2015), Shahryari Nia et al. (2016), Faisal et al. (2017), Fallahpour et al. (2017), Gupta and Barua (2017), Tavana et al. (2017), Wang et al. (2017), Yin et al. (2017), Lo et al. (2018), Wang and Li (2018), Bai et al. (2019), Guarnieri and Trojan (2019), Li et al. (2019), Liang and Chong (2019), Liu et al. (2019a), Nie et al. (2019), Uluta¸s et al. (2019), Chen et al. (2020), Jain et al. (2020), You et al. (2020)

Green certifications

Green logistics

(continued)

22

Shaik and Abdul-Kader (2011), Freeman and Chen (2015), Kannan et al. (2015), Shahryari Nia et al. (2016), 22 Fallahpour et al. (2017), Hamdan and Cheaitou (2017a), Lin et al. (2017), Pandey et al. (2017), Wang et al. (2017), Abdel-Basset et al. (2018), Awasthi et al. (2018), Babbar and Amin (2018), Abdel-Baset et al. (2019), Abdullah et al. (2019), Guarnieri and Trojan (2019), Liang and Chong (2019), Roy et al. (2019), Yu et al. (2019a), Yucesan et al. (2019), Ecer (2020), Jain et al. (2020), Kannan et al. (2020)

Frequency

Green packing and labeling

Literature Tseng (2011), Amindoust et al. (2012), Büyüközkan (2012), Datta et al. (2012), Arshadi Khamseh and Mahmoodi 30 (2014), Kannan et al. (2015), Gupta and Barua (2017), Luthra et al. (2017), Sinha and Anand (2017), Wang et al. (2017), Yin et al. (2017), Lo et al. (2018), Sen et al. (2018), Zarbakhshnia and Jaghdani (2018), Abdel-Baset et al. (2019), Almasi et al. (2019), Li et al. (2019), Liang and Chong (2019), Liou et al. (2019), Mati´c et al. (2019), Mishra et al. (2019), Wu et al. (2019d), Yucesan et al. (2019), Chen et al. (2020), Ecer (2020), Gao et al. (2020), Khoshfetrat et al. (2020), Ma et al. (2020), Rouyendegh et al. (2020), You et al. (2020)

Sub-criteria

Green Green competencies manufacturing

Criteria

Table 2.2 (continued)

38 2 Green Supplier Evaluation and Selection …

Dimension

Criteria

Table 2.2 (continued)

Lee et al. (2009), Shen et al. (2013), Banaeian et al. (2015), Kannan et al. (2015), Sarkis and Dhavale (2015), Keshavarz Ghorabaee et al. (2016), Liao et al. (2016), Shahryari Nia et al. (2016), Fallahpour et al. (2017), Hamdan and Cheaitou (2017a), Li and Wang (2017), Lin et al. (2017), Pandey et al. (2017), Qin et al. (2017), Wang et al. (2018b), Foroozesh et al. (2019), Liang and Chong (2019), Liu et al. (2019b), Rabbani et al. (2019), Tian et al. (2019), Wu et al. (2019b), Xu et al. (2019a), Kumari and Mishra (2020), Peng et al. (2020) Lee et al. (2009), Shaik and Abdul-Kader (2011), Shen et al. (2013), Banaeian et al. (2015), Freeman and Chen (2015), Kannan et al. (2015), Keshavarz Ghorabaee et al. (2016), Sahu et al. (2016), Fallahpour et al. (2017), Li and Wang (2017), Lin et al. (2017), Pandey et al. (2017), Awasthi et al. (2018), Shojaie et al. (2018), Wang et al. (2018b), dos Santos et al. (2019), Liang and Chong (2019), Liou et al. (2019), Phochanikorn and Tan (2019b), Tian et al. (2019), Kannan et al. (2020), Kumari and Mishra (2020), Peng et al. (2020)

Use of environmentally friendly technology

Use of environmentally friendly materials

(continued)

23

24

Lee et al. (2009), Shaik and Abdul-Kader (2011), Yeh and Chuang (2011), Amindoust et al. (2012), Kannan et al. 54 (2013), Shen et al. (2013), Sahu et al. (2014), Cao et al. (2015), Hashemi et al. (2015), Hu et al. (2015), Mahdiloo et al. (2015), Sarkis and Dhavale (2015), Fallahpour et al. (2016), Girubha et al. (2016), Keshavarz Ghorabaee et al. (2016), Yazdani et al. (2016), Yu and Hou (2016), Bakeshlou et al. (2017), Govindan et al. (2017), Guo et al. (2017), Li and Wang (2017), Lin et al. (2017), Pang et al. (2017), Qin et al. (2017), Tavana et al. (2017), Yazdani et al. (2017), Abdel-Basset et al. (2018), Awasthi et al. (2018), Gören (2018), Liu et al. (2018), Sen et al. (2018), Torres-Ruiz and Ravindran (2018), Vahidi et al. (2018), Wang and Li (2018), Zhou and Xu (2018), dos Santos et al. (2019), Haeri and Rezaei (2019), Hou and Xie (2019), Laosirihongthong et al. (2019), Liang and Chong (2019), Liu et al. (2019a), Mati´c et al. (2019), Mishra et al. (2019), Pishchulov et al. (2019), Wang et al. (2019), Wu et al. (2019b, d), Xu et al. (2019c), Yu et al. (2019b), Zhang and Cui (2019), Ecer (2020), Fallahpour et al. (2020), Giannakis et al. (2020), Kumari and Mishra (2020)

Resource consumption

Frequency

Literature Hsu and Hu (2009), Kuo et al. (2010), Shaik and Abdul-Kader (2011), Tseng (2011), Yeh and Chuang (2011), 52 Amindoust et al. (2012), Büyüközkan (2012), Kannan et al. (2013), Shen et al. (2013), Cao et al. (2015), Kannan et al. (2015), Orji and Wei (2015), Keshavarz Ghorabaee et al. (2016), Yazdani et al. (2016), Gupta and Barua (2017), Hamdan and Cheaitou (2017b), Li and Wang (2017), Luthra et al. (2017), Wang et al. (2017), Yazdani et al. (2017), Yin et al. (2017), Babbar and Amin (2018), Gören (2018), Jafarzadeh Ghoushchi et al. (2018), KhanMohammadi et al. (2018), Liu et al. (2018), Lu et al. (2018), Sen et al. (2018), Shojaie et al. (2018), Song et al. (2018), Van et al. (2018), Zarbakhshnia and Jaghdani (2018), Zhou and Xu (2018), Almasi et al. (2019), dos Santos et al. (2019), Foroozesh et al. (2019), Li et al. (2019), Liou et al. (2019), Liu et al. (2019d), Mati´c et al. (2019), Mishra et al. (2019), Rabbani et al. (2019), Rabieh et al. (2019), Wu et al. (2019a, d), Yu et al. (2019a, b), Chen et al. (2020), Ecer (2020), Khoshfetrat et al. (2020), Kumari and Mishra (2020), Peng et al. (2020)

Sub-criteria

Green design

2.4 Findings and Discussions 39

Social

Information disclosure

Shaik and Abdul-Kader (2011), Shen et al. (2013), Kuo et al. (2015), Sahu et al. (2016), Li and Wang (2017), Malek et al. (2017), Qin et al. (2017), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Torres-Ruiz and Ravindran (2018), Vahidi et al. (2018), Bai et al. (2019), Laosirihongthong et al. (2019), Liang and Chong (2019), Mao et al. (2019), Mati´c et al. (2019), Memari et al. (2019), Pishchulov et al. (2019), Wang et al. (2019), Yucesan et al. (2019), Chen et al. (2020), Ecer (2020), Giannakis et al. (2020), Mousavi et al. (2020), Stevi´c et al. (2020)

Staff training

(continued)

Lee et al. (2009), Büyüközkan and Çifçi (2011), Shaik and Abdul-Kader (2011), Sarkis and Dhavale (2015), Kaur 22 et al. (2016), Shahryari Nia et al. (2016), Govindan et al. (2017), Lin et al. (2017), Tavana et al. (2017), Abdel-Basset et al. (2018), KhanMohammadi et al. (2018), Vahidi et al. (2018), Van et al. (2018), Zhou and Xu (2018), Guarnieri and Trojan (2019), Li et al. (2019), Liang and Chong (2019), Liu et al. (2019a), Moheb-Alizadeh and Handfield (2019), Wang et al. (2019), Yadavalli et al. (2019), Okwu and Tartibu (2020)

Kuo et al. (2010), Amindoust et al. (2012), Hsu et al. (2014), Kannan et al. (2015), Orji and Wei (2015), Shahryari 26 Nia et al. (2016), Luthra et al. (2017), Mohammed et al. (2018), Sen et al. (2018), Wang et al. (2018a), Bai et al. (2019), Foroozesh et al. (2019), Guarnieri and Trojan (2019), Mati´c et al. (2019), Mohammed et al. (2019), Rabbani et al. (2019), Roy et al. (2019), Xu et al. (2019c), Yu et al. (2019a, b), Yucesan et al. (2019), Jia et al. (2020), Kannan et al. (2020), Mohammed (2020), Peng et al. (2020), Stevi´c et al. (2020)

25

Amindoust et al. (2012), Tsui and Wen (2014), Orji and Wei (2015), Amindoust and Saghafinia (2017), Faisal 45 et al. (2017), Fallahpour et al. (2017), Luthra et al. (2017), Abdel-Basset et al. (2018), Arabsheybani et al. (2018), Cheraghalipour and Farsad (2018), Gören (2018), Jafarzadeh Ghoushchi et al. (2018), Mohammed et al. (2018), Nourmohamadi Shalke et al. (2018), Park et al. (2018), Sen et al. (2018), Vahidi et al. (2018), Zarbakhshnia and Jaghdani (2018), Abdel-Baset et al. (2019), Bai et al. (2019), Foroozesh et al. (2019), Laosirihongthong et al. (2019), Li et al. (2019), Mati´c et al. (2019), Memari et al. (2019), Mohammed et al. (2019), Phochanikorn and Tan (2019b), Pishchulov et al. (2019), Rabbani et al. (2019), Rabieh et al. (2019), Roy et al. (2019), Wu et al. (2019a), Yu et al. (2019a, b), Yucesan et al. (2019), Giannakis et al. (2020), Izadikhah and Farzipoor Saen (2020), Jia et al. (2020), Kannan et al. (2020), Mohammed (2020), Okwu and Tartibu (2020), Peng et al. (2020), Qu et al. (2020), Stevi´c et al. (2020), Tirkolaee et al. (2020)

Frequency 33

Health and safety

Literature Kuo et al. (2010), Amindoust et al. (2012), Kannan et al. (2015), Girubha et al. (2016), Fallahpour et al. (2017), Luthra et al. (2017), Arabsheybani et al. (2018), Cheraghalipour and Farsad (2018), Jafarzadeh Ghoushchi et al. (2018), Lu et al. (2018), Mohammed et al. (2018), Torres-Ruiz and Ravindran (2018), Almasi et al. (2019), Bai et al. (2019), Guarnieri and Trojan (2019), Li et al. (2019), Liu et al. (2019a), Mati´c et al. (2019), Mohammed et al. (2019), Phochanikorn and Tan (2019b), Roy et al. (2019), Tian et al. (2019), Wu et al. (2019a), Yu et al. (2019a, b), Chen et al. (2020), Jia et al. (2020), Kannan et al. (2020), Khoshfetrat et al. (2020), Mohammed (2020), Okwu and Tartibu (2020), Stevi´c et al. (2020), Tirkolaee et al. (2020)

Interests and rights

Sub-criteria

Social Social responsibility responsibility

Information

Criteria

Employee

Dimension

Table 2.2 (continued)

40 2 Green Supplier Evaluation and Selection …

Dimension

Criteria

Table 2.2 (continued) Frequency

Literature Shaik and Abdul-Kader (2011), Büyüközkan (2012), Arshadi Khamseh and Mahmoodi (2014), Girubha et al. 24 (2016), Jain et al. (2016), Kaur et al. (2016), Kumar et al. (2016), Sang and Liu (2016), Yu and Hou (2016), Gupta and Barua (2017), Pang et al. (2017), Yin et al. (2017), Jafarzadeh Ghoushchi et al. (2018), Lo et al. (2018), Zhou and Xu (2018), Hou and Xie (2019), Mati´c et al. (2019), Pishchulov et al. (2019), Wu et al. (2019c), Yucesan et al. (2019), Zhang and Cui (2019), Kannan et al. (2020), Peng et al. (2020), Stevi´c et al. (2020), You et al. (2020)

Sub-criteria

Reputation

2.4 Findings and Discussions 41

42

2 Green Supplier Evaluation and Selection …

Fig. 2.2 Co-occurrence analysis of green evaluation criteria

design, and Resource consumption are the most frequently used criteria. Besides, Interests and rights, Health and safety, Social responsibility, and Reputation community are ranked as the top five social criteria in the literature sample. Figure 2.2 shows the whole intellectual landscapes of co-occurrence green evaluation criteria in the considered field. It can be seen that Environmental, Green, Management, Quality, Cost, Capability, and Delivery are the significant green evaluation criteria taking over notable positions.

2.4.2 Criteria Weighting Methods An important step of the GSES process is to determine the weight of each green supplier evaluation criterion. In the reviewed literature, multifarious weighting approaches have been proposed for obtaining appropriate criteria weights. Table 2.3 demonstrates the different types of weighting approaches utilized in the included GSES studies. In general, the current used weighting approaches can be divided into subjective weighing, objective weighing, and combination weighting. As can be seen Table 2.3, the weights of green supplier evaluation criteria are commonly determined according to the judgements of decision makers. The AHP and the ANP are widely acceptable subjective weighting methods and have been used in 23 and 11 papers, respectively. The most frequent used objective weighting method is the DEA method; 15 articles adopted it to evaluate the weights of green supplier evaluation criteria. This was followed by the entropy method, which was employed in nine researches. To integrate the advantages of both subjective and

2.4 Findings and Discussions

43

Table 2.3 Criteria weighting methods used in the literature Classification Weighting methods

References

Subjective weighing methods

Direct given

Hu et al. (2015), Wang Chen et al. (2016), Li and Wang (2017), Liang and Chong (2019), Meksavang et al. (2019), Xu et al. (2019b), Xu et al. (2020)

Frequency

Expert judgement

Shaik and Abdul-Kader (2011), 35 Tseng (2011), Amindoust et al. (2012), Datta et al. (2012), Shen et al. (2013), Tseng and Chiu (2013), Kannan et al. (2014), Sahu et al. (2014), Kannan et al. (2015), Govindan and Sivakumar (2016), Sahu et al. (2016), Sang and Liu (2016), Amindoust and Saghafinia (2017), Guo et al. (2017), Kumar et al. (2017), Lin et al. (2017), Malek et al. (2017), Mousakhani et al. (2017), Pandey et al. (2017), Qin et al. (2017), Banaeian et al. (2018), KhanMohammadi et al. (2018), Lu et al. (2018), Sen et al. (2018), Shi et al. (2018), Abdullah et al. (2019), Foroozesh et al. (2019), Mao et al. (2019), Memari et al. (2019), Rabbani et al. (2019), Yadavalli et al. (2019), Mousavi et al. (2020), Okwu and Tartibu (2020), Rouyendegh et al. (2020), Stevi´c et al. (2020)

AHP

Lee et al. (2009), Büyüközkan 23 (2012), Shaw et al. (2012), Kannan et al. (2013), Banaeian et al. (2015), Liao et al. (2016), Wang Chen et al. (2016), Yu and Hou (2016), Hamdan and Cheaitou (2017a, b), Luthra et al. (2017), Awasthi et al. (2018), Mohammed et al. (2018), Almasi et al. (2019), Guarnieri and Trojan (2019), Laosirihongthong et al. (2019), Mohammed et al. (2019), Pishchulov et al. (2019), Xu et al. (2019c), Ecer (2020), Jain et al. (2020), Khoshfetrat et al. (2020), Mohammed (2020)

7

(continued)

44

2 Green Supplier Evaluation and Selection …

Table 2.3 (continued) Classification Weighting methods

References

Frequency

ANP

Hsu and Hu (2009), Kuo et al. 11 (2010), Büyüközkan and Çifçi (2011), Kuo and Lin (2012), Hashemi et al. (2015), Chung et al. (2016), Faisal et al. (2017), Abdel-Basset et al. (2018), Wang et al. (2018a), Abdel-Baset et al. (2019), Giannakis et al. (2020)

BWM

Banaeian et al. (2015), Gupta and 10 Barua (2017), Cheraghalipour and Farsad (2018), Lo et al. (2018), Bai et al. (2019), Jafarzadeh Ghoushchi et al. (2019), Tian et al. (2019), Wu et al. (2019b), Yucesan et al. (2019), Kannan et al. (2020)

QFD

Babbar and Amin (2018), Van et al. (2018), Liu et al. (2019a), Liu et al. (2019d)

4

Fuzzy AHP

Wang et al. (2018a), Lu et al. (2019), Roy et al. (2019)

3

DEMATEL

Kaur et al. (2016), Yazdani et al. (2019), Chen et al. (2020)

3

Fuzzy preference programming

Fallahpour et al. (2017, 2020)

2

Full consistency method

Mati´c et al. (2019)

1

SWARA

Duan et al. (2019)

1

PIPERECIA

You et al. (2020)

1

Simos method

Govindan et al. (2017)

1

Subjective GRA

Pang et al. (2017)

1

Subjective TOPSIS

Arshadi Khamseh and Mahmoodi (2014)

1

Fuzzy DEMATEL

Gören (2018)

1

DEMATEL, ANP

Kuo et al. (2015), Bakeshlou et al. (2017), Zhou and Xu (2018), Hou and Xie (2019), Liou et al. (2019), Phochanikorn and Tan (2019b), Tirkolaee et al. (2020)

7

Fuzzy DEMATEL, Fuzzy ANP

Phochanikorn and Tan (2019a)

1

ISM, ANP

Girubha et al. (2016)

1

DEMATEL, QFD

Yazdani et al. (2017)

1

ANP, QFD

Tavana et al. (2017)

1 (continued)

2.4 Findings and Discussions

45

Table 2.3 (continued) Classification Weighting methods

Objective weighing methods

References

Frequency

SWARA, QFD

Keshavarz Ghorabaee et al. (2016)

1

BWM, FGCM

Haeri and Rezaei (2019)

1

DEA

Kumar et al. (2014), Mahdiloo 15 et al. (2015), Shi et al. (2015), Fallahpour et al. (2016), Jain et al. (2016), Jauhar and Pant (2016), Kumar et al. (2016), Jauhar and Pant (2017), Yu and Su (2017), Jafarzadeh Ghoushchi et al. (2018), Zarbakhshnia and Jaghdani (2018), Dobos and Vörösmarty (2019a, b), Wu et al. (2019a), Izadikhah and Farzipoor Saen (2020)

Entropy method

Foroozesh et al. (2018), Nourmohamadi Shalke et al. (2018), Shojaie et al. (2018), Chen (2019), dos Santos et al. (2019), Liu et al. (2019c), Yu et al. (2019a, b), Peng et al. (2020)

9

Choquet integral

Shahryari Nia et al. (2016), Zhu and Li (2018), Wang et al. (2019), Wu et al. (2019d), Liang et al. (2020)

5

Maximizing deviation method Gitinavard et al. (2018), Hou and Xie (2019)

2

Ordered weight

Sinha and Anand (2017), Tang (2017)

2

Hesitant fuzzy entropy measure

Wan et al. (2020)

1

Divergence measure method

Kumari and Mishra (2020)

1

Grey incidence entropy

Quan et al. (2018a)

1

Objective GRA

Song et al. (2018)

1

Objective TOPSIS (Incomplete weight)

Wang et al. (2017)

1

LINMAP

Liu et al. (2019d)

1

Relative preference relation

Mohammadi et al. (2017)

1

Preference selection index

Uluta¸s et al. (2019)

1

Time sequence weight

Yin et al. (2017)

1

Delphi method

Rabieh et al. (2019)

1 (continued)

46

2 Green Supplier Evaluation and Selection …

Table 2.3 (continued) Classification Weighting methods

References

Combination weighting methods

AHP and Entropy method

Tsui and Wen (2014), Freeman and Chen (2015), Liu et al. (2018), Wu et al. (2019c)

Frequency 4

Expert judgement and Entropy method

Zhao and Guo (2014), Keshavarz Ghorabaee et al. (2016)

2

Entropy method and Divergence measure method

Mishra et al. (2019)

1

Expert judgement and Maximizing distance method

Cao et al. (2015)

1

Expert judgement and Wang and Li (2018) Maximizing deviation method

1

Expert judgement and Statistical variance method

Wang and Li (2018)

1

Direct given and ordered weight

Xu et al. (2019a)

1

objective weighting methods, combination weighting methods have been gradually utilized to determine the weights of green supplier evaluation criteria in the literature. For instance, the relative weight values of green supplier evaluation criteria were computed by combining AHP and entropy method in Tsui and Wen (2014), Freeman and Chen (2015), Liu et al. (2018), Wu et al. (2019c). Additionally, there is one study which considered the situation with incomplete criteria weighting information and created a TOPSIS-based optimization model to obtain the optimal weights of evaluation criteria for green supplier selection (Wang et al. 2017).

2.4.3 Green Supplier Evaluation Methods Typically, GSES can be seen as an activity performed by a group of decision makers coming from different departments or organizations. During the group GSES process, the evaluation on green suppliers from decision makers are often vague, imprecise, uncertain and hesitant, due to time pressure, lack of data, and human limited information processing capability. To address this issue, a variety of uncertainty theories and methods haven been utilized in the reviewed studies. In Table 2.4, a summarized information from the selected literature regarding green supplier evaluation approaches is showed. As depicted in Table 2.4, fuzzy set theory is the widespread used method to manage the fuzziness of green performance evaluation information from decision makers. Particularly, the fuzzy sets based on TFNs are the most preferred approach adopted in the selected papers. Moreover, the interval type-2 fuzzy sets and the intuitionistic fuzzy sets are also frequently used by researchers to deal with the vagueness and

2.4 Findings and Discussions

47

Table 2.4 Green supplier evaluation methods used in the literature Evaluation methods

References

Fuzzy sets (TFNs)

Lee et al. (2009), Büyüközkan and Çifçi 44 (2011), Tseng (2011), Büyüközkan (2012), Büyüközkan and Ifi (2012), Shaw et al. (2012), Kannan et al. (2013), Shen et al. (2013), Tseng and Chiu (2013), Arshadi Khamseh and Mahmoodi (2014), Kannan et al. (2014), Zhao and Guo (2014), Banaeian et al. (2015), Kannan et al. (2015), Orji and Wei (2015), Kaur et al. (2016), Liao et al. (2016), Sahu et al. (2016), Amindoust and Saghafinia (2017), Fallahpour et al. (2017), Guo et al. (2017), Gupta and Barua (2017), Hamdan and Cheaitou (2017a, b), Kumar et al. (2017), Lin et al. (2017), Yu and Su (2017), Arabsheybani et al. (2018), Awasthi et al. (2018), Banaeian et al. (2018), KhanMohammadi et al. (2018), Mohammed et al. (2018), Shojaie et al. (2018), Chen et al. (2019), dos Santos et al. (2019), Jafarzadeh Ghoushchi et al. (2019), Laosirihongthong et al. (2019), Mohammed et al. (2019), Uluta¸s et al. (2019), Yu et al. (2019b), Chen et al. (2020), Fallahpour et al. (2020), Jain et al. (2020), Mohammed (2020)

Frequency

Fuzzy sets (TrFNs)

Amindoust et al. (2012), Sahu et al. (2014), Fallahpour et al. (2016), Govindan and Sivakumar (2016), Bakeshlou et al. (2017), Pandey et al. (2017), Babbar and Amin (2018), Liu et al. (2018), Lo et al. (2018), Liu et al. (2019e)

Interval type-2 fuzzy sets

Keshavarz Ghorabaee et al. (2016), Sang 10 and Liu (2016), Mohammadi et al. (2017), Mousakhani et al. (2017), Qin et al. (2017), Liu et al. (2019d), Wu et al. (2019b, d), Xu et al. (2019c), Yucesan et al. (2019)

Intuitionistic fuzzy sets

Cao et al. (2015), Sen et al. (2018), Chen (2019), Memari et al. (2019), Phochanikorn and Tan (2019b), Tian et al. (2019), Wu et al. (2019c), Kumari and Mishra (2020), Rouyendegh et al. (2020)

10

9

(continued)

48

2 Green Supplier Evaluation and Selection …

Table 2.4 (continued) Evaluation methods

References

Heterogeneous information

Song et al. (2018), Zhou and Xu (2018), Roy et al. (2019), Wang et al. (2019), Xu et al. (2019b), Liang et al. (2020)

Frequency 6

Hesitant fuzzy sets

Tang (2017), Hou and Xie (2019), Liang and Chong (2019), Mishra et al. (2019), Wan et al. (2020)

5

Interval-valued fuzzy sets

Datta et al. (2012), Foroozesh et al. (2018, 2019), Rabbani et al. (2019)

4

Grey numbers

Hashemi et al. (2015), Malek et al. (2017), Bai et al. (2019), Haeri and Rezaei (2019)

4

Interval-valued intuitionistic uncertain linguistic sets

Banaeian et al. (2015), Shi et al. (2018), Liu et al. (2019d)

3

Interval-valued intuitionistic fuzzy sets

Shahryari Nia et al. (2016), Yin et al. (2017), Mao et al. (2019)

3

Neutrosophic sets

Abdel-Basset et al. (2018), Abdel-Baset et al. (2019)

2

Rough sets

Lu et al. (2018), You et al. (2020)

2

Cloud model theory

Wang et al. (2017), Lu et al. (2019)

2

Interval-valued Pythagorean fuzzy sets

Wu et al. (2019a), Yu et al. (2019a)

2

Picture fuzzy sets

Meksavang et al. (2019), Peng et al. (2020)

2

Interval-valued intuitionistic trapezoidal fuzzy sets

Liu et al. (2019a)

1

Interval type-2 trapezoidal fuzzy sets

Mousavi et al. (2020)

1

2-Tuple linguistic variables

Hu et al. (2015)

1

Interval 2-tuple linguistic variables

Xu et al. (2019a)

1

Hesitant 2-tuple linguistic variables

Zhu and Li (2018)

1

Interval Neutrosophic sets

Van et al. (2018)

1

Probability hesitant fuzzy sets

Li and Wang (2017)

1

Interval-valued hesitant fuzzy sets

Gitinavard et al. (2018)

1

Continuous interval-valued linguistic term set

Nie et al. (2019)

1

Z numbers

Yadavalli et al. (2019)

1

Linguistic Z-numbers

Duan et al. (2019)

1

Rough cloud model

Li et al. (2019)

1

q-rung orthopair fuzzy sets

Wang and Li (2018)

1 (continued)

2.4 Findings and Discussions

49

Table 2.4 (continued) Evaluation methods

References

q-rung interval-valued orthopair fuzzy sets

Liu et al. (2019c)

Frequency 1

Ordered weighted hesitant fuzzy sets

Wang Chen et al. (2016)

1

Single-valued complex neutrosophic sets

Xu et al. (2020)

1

Single-valued triangular neutrosophic sets

Fan et al. (2019)

1

Hesitant fuzzy linguistic term sets

Ma et al. (2020)

1

Double hierarchy hesitant linguistic term sets

You et al. (2020)

1

Hesitant fuzzy linguistic sets

Qu et al. (2020)

1

uncertainty of performance evaluations in GSES, which have appeared in 10 and 9 articles, respectively. Considering that decision makers incline to give their opinions with linguistic expressions, some linguistic computing methods have been utilized in the GSES process recently, which include the interval-valued intuitionistic uncertain linguistic sets (Quan et al. 2018b; Shi et al. 2018; Liu et al. 2019b), the hesitant fuzzy linguistic term sets (Ma et al. 2020; Qu et al. 2020), cloud model theory (Wang et al. 2017; Lu et al. 2019), and interval 2-tuple linguistic variables (Xu et al. 2019a).

2.4.4 Bibliometric Analysis Table 2.1 displays the green supplier selection approaches and their frequency of application in the GSES literature. As shown in Table 2.1, the distance-based methods (31 articles, 16.1%) have been utilized more than other types of green supplier selection methods; the value and utility methods (30 articles, 15.5%) are the second most frequently used category for green supplier selection. Besides, the literature review shows that the TOPSIS approach with 21 articles is the most favored technique for the priority ranking of alternative suppliers in the GSES process, which was followed by the DEA approach with 18 articles. The GRA, VIKOR, ELECTRE, and TODIM methods are also the green supplier selection methods frequently applied to rank green suppliers; these methods were used for GSES more than five times. As for the green SSOA methods, it can be observed that the integration of TOPSIS and MOLP is the most prevalent way to obtain the best green suppliers and allot the optimal order sizes among them. The frequency of the green supplier selection methods employed in the reviewed articles is shown in Fig. 2.3. Table 2.5 lists the top 10 influential researches according to their average citations and total citations extracted from the Scopus database. As reported in Table 2.5, the first influential article is (Qin et al. 2017), which has been cited 75 times in one year.

50

2 Green Supplier Evaluation and Selection …

Fig. 2.3 Green supplier selection methods in the reviewed literature

Table 2.5 Top 10 influential papers

Papers

Average citation

Total citation

Qin et al. (2017)

75

224

Banaeian et al. (2018)

68

135

Hashemi et al. (2015)

44

222

Lee et al. (2009)

41

454

Yazdani et al. (2017)

41

123

Kuo et al. (2010)

34

341

Shen et al. (2013)

34

235

Govindan et al. (2017)

20

61

Tsai and Hung (2009)

15

167

Tseng (2011)

13

113

This study extended the TODIM method for selecting optimal green supplier within an interval type-2 fuzzy context. The second influential article authored by Banaeian et al. (2018) was published in 2018 and cited 135 times. This study applied three popular MCDM methods (TOPSIS, VIKOR and GRA) combined with fuzzy sets for green supplier selection in the agri-food industry. The following influential article is (Hashemi et al. 2015) with its average citation 44. This paper developed a GSES model based on ANP and GRA methods. In addition, the total number of citations

2.4 Findings and Discussions

51

Fig. 2.4 Distribution of articles by publication year

for the research (Lee et al. 2009) was the highest (454 citations), indicating that this study has a high impact in the GSES field. Among the chosen GSES studies, the number of published articles in different years is shown in Fig. 2.4. It can be observed that the approaches for evaluating and selecting green suppliers have growth significantly in the duration from 2009 to 2020, especially after 2015. Note that only five months are considered in this study and thus the publication quantity is 20 in 2020. The frequency of published articles on GSES increased to 60 items in 2019 from 3 items in 2009; 63.2% of the articles in the area are published in the recent three years (2017–2019). This can be attributed to the fact that sustainability has become more and more significant portion in enterprise operation management due to growth of customer environmental consciousness, stringent governmental regulations and stress from inside and outside stakeholders. In addition, some literature reviews of green supply chain management have been published in 2015 focusing on bibliometric and network analysis (Fahimnia et al. 2015), modelling techniques (Igarashi et al. 2013; Malviya and Kant 2015), and theoretical framework development (Malviya and Kant 2015). Nowadays, it is a challenging task for academicians and practitioners to evaluate and select the most appropriate green suppliers in different stages of product life cycle. Thus, it is anticipated that the number of researches on GSES will increase quickly in the next years. Figure 2.5 displays the journals with more than four papers on the GSES. It can be seen that Journal of Cleaner Production is the leading journal in GSES problems with 27 published articles, followed by Sustainability with 21 articles. Besides, Computers and Industrial Engineering, and International Journal of Production Economics have published 8 articles in this field. Figure 2.6 depicts the number of the reviewed publications on the basis of the country of origin. As can be seen from the figure,

52

2 Green Supplier Evaluation and Selection …

Fig. 2.5 Distribution of articles by publication journal

Fig. 2.6 Distribution of articles with respect to country

2.4 Findings and Discussions

53

Fig. 2.7 Distribution of articles by application area

more than 71.5% of the considered publications (138 articles) are derived from four countries or regions (China, Iran, Taiwan, and India), and China with 62 articles is ranked as the first based on the number of articles followed by Iran with 34 articles. Figure 2.7 shows the applied field distribution of the selected articles. The result demonstrates that the proposed GSES methods have been utilized in a variety of fields and the top four application domains are automobile industry (53 articles), electronics industry (25 articles), manufacturing industry (20 articles), and food industry (19 articles), respectively. Furthermore, GSES methods have been commonly used in the construction, energy and chemical, and home appliance industries.

2.5 Future Research Recommendations This review study demonstrates that GSES have attracted a lot of attention from scholars and a variety of GSES models have been proposed from the aspects of performance assessment, evaluation criteria weighting, and alternative suppliers ranking. Based on the results of this review, many opportunities can be identified for the future research, and the following ones are promising directions:

54

(1)

(2)

(3)

(4)

(5)

(6)

(7)

2 Green Supplier Evaluation and Selection …

Considering the performance information of alternative suppliers is usually vague, uncertain or even incomplete, it is suggested to use the latest uncertainty theories to effectively manipulate the uncertainty from human judgements, manage incomplete performance evaluations and heterogeneous evaluation data, and bring an organized method to characterize decision makers’ experience and knowledge for GSES. Decision makers in the GSES may have different experience, backgrounds and interests, and thus conflict opinions are unavoidable in the GSES process. Thus, as another direction for future studies, consensus methods are suggested to be applied to solve conflict judgments of decision makers, which will improve group consistency and lead to efficiency improvement in the GSES process. A variety of weighting methods has been adopted to specify the weights of evaluation criteria in the GSES studies. In the future, it is suggested to explore new subjective weighing, objective weighing and combination weighting methods. Besides, in some situations, the criteria weight information may be incomplete. Therefore, incomplete weighting approaches can be proposed for obtaining the weights of criteria in the future. In addition, in the reviewed articles, criteria weights are often constant for all alternative green suppliers. It is suggested for future study to assign different sets of criteria weights for different alternatives in the GSES. The literature review shows that some scholars focused on how to determine the weights of decision makers (Moher et al. 2009; Kuo et al. 2015; Wang Chen et al. 2016; Luthra et al. 2017; Abdel-Basset et al. 2018). As a result, the techniques to acquire decision makers’ weights are suggested to be studies in the future research. Particularly, it would be very meaningful to dynamically assigning decision makers’ weights based on their evaluation information for alternative suppliers. It is found that MCDM methods are the most popular tool for determining the priority ranking of green suppliers. Future research can be targeted towards apply other MCDM methods such as MACBETH, UTASTAR, and THESEUS, to support decision making in the GSES. Also, to combine the superiorities of different MCDM approaches, future research is suggested to propose GSES models by using multiple or integrated MCDM methods. In recent years, data has started to generate on a large volume in the GSCM field. It has been expected that the amount of data will continue to increase largely due to the complexity of GSES problems. Therefore, with regard to the presentation of large number of criteria and alternatives, we suggest future studies to propose modify methods to handle such data in the GSES. Another possible direction for future work would be to employ techniques such as intelligent algorithms and system dynamics to efficiently solve GSES problems. For instance, deep learning algorithms can be employed to learn criteria weights from the evaluation data of decision makers on every green suppler. Also, MCDM methods can be empowered by neural networks to consider fluctuations in the ranking of alternative suppliers, in the way changes occur in the human brain.

2.6 Chapter Summary

55

2.6 Chapter Summary In this chapter, we conducted a comprehensive review of the publications that concern quantitative models for supporting green supplier selection. A total of 193 articles published in peer-reviewed journals between 2009 and 2020 were identified as relevant to this review from the Scopus database. According to the GSES methods being proposed, the chose articles were classified into ten categories, i.e., distance-based methods, compromise methods, outranking methods, pairwise comparison methods, mathematical programming methods, aggregation operator-based methods, value and utility methods, combined methods, other green supplier selection methods, and SSOA methods. Further, we find that the TOPSIS and the DEA are the two most popular methods applied to determine the ranking of green suppliers. Second, it is discovered that the most frequently used green evaluation criteria are Quality, Resource consumption, Price, Green design, Environmental management system, and Greenhouse gas emission. The analysis of green supplier evaluation methods showed that fuzzy set theory is the most preferred approach employed to handle fuzzy and imprecise performance evaluation information. This review provides academics and practitioners with a guideline and insight into further proposing and applying the GSES approaches to help firms improve environmental sustainability and gain higher competitiveness performance.

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Chapter 3

GSES Based on Intuitionistic Fuzzy VIKOR Method

Considering the fact that it is difficult to precisely determine criteria weights and the ratings of suppliers on each criterion in real-life situations, the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method has been modified for intuitionistic fuzzy data in this chapter for green supplier selection. Further, we take into account both subjective and objective weights of evaluation criteria in the GSES process, as most green supplier selection approaches consider only subjective criteria weights. Finally, two green supplier selection examples are provided to illustrate the proposed intuitionistic fuzzy hybrid VIKOR (IFH-VIKOR) method, and its merits are highlighted by comparing with other relevant approaches.

3.1 Introduction In modern business environment, the green performance of a company largely depends on the competitiveness of its supply chain. Supply chain management is a process that covers raw material procurement, the production of finished products, and distributing the finished good to consumers through distributors and retailers (Fallahpour et al. 2017). Suppliers are the foundation of the supply chain operation, which have a great potential to enhance the competitiveness of supply chain for a focal firm (Rao et al. 2017). In this regard, selecting the most appropriate green supplier can reduce the cost of production, decrease the time for bringing products to the market, improve the quality of products, and increase customer satisfaction and profitability (You et al. 2015; Wang and Cai 2017). Thus, to increase business performance and competitive advantage, green supplier selection is a crucial strategic decision in supply chain management and has become a very fundamental component of the viable benefits of firms and industries. When selecting appropriate green suppliers, various criteria are often involved, including price, quality, delivery time, service, and reputation. It is clear that green supplier selection for an organization is a complex multiple criteria decision-making © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_3

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3 GSES Based on Intuitionistic Fuzzy VIKOR Method

(MCDM) problem due to the presence of conflicting and competing factors, such as quality and cost. The VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje), initially proposed by Opricovic (1998), is an effective MCDM method for handling discrete multi-criteria problems with conflicting and noncommensurable criteria. It focuses on ranking and choosing from a set of alternatives, and determines compromise solutions which can help decision-makers to reach a final decision (Manna et al. 2020; Meksavang et al. 2019; Zhao et al. 2017). In view of its features and capabilities, the VIKOR approach has been successfully implemented in lots of real-world decision-making problems. For example, Qi et al. (2020) proposed an integrated rough VIKOR method for customer-involved design concept evaluation based on customers’ preferences and designers’ perceptions. Demirel et al. (2020) reported a hybrid fuzzy analytic hierarchy process (AHP) and VIKOR methodology that could be applied to select suitable toll stabilizer type for motor yachts. In Li et al. (2020), a machine tool selection method was proposed based on a hybrid MCDM model using fuzzy decision-making trial and evaluation laboratory (DEMATEL), entropy weighting and later defuzzification VIKOR. Rafieyan et al. (2020) suggested an adaptive scheduling approach using a combination of the best-worst method and VIKOR in the cloud computing environment. Samanci et al. (2021) combined the VIKOR method with fuzzy importance, expected performance, and priority analysis to improve the service quality of airline sector. Alemdar et al. (2020) used AHP and VIKOR methods to evaluate pedestrian crossing locations, and Das et al. (2020) extended the VIKOR method in Z-environment for failure mode and effect analysis. Moreover, the use of the VIKOR for supplier selection is practical and has demonstrated satisfactory results (Bahadori et al. 2020; Fallahpour et al. 2020; Kannan et al. 2020; Krishankumar et al. 2020; Wen et al. 2020). Therefore, it is natural to utilize the VIKOR approach to manage green supplier selection problems involving comprehensive criteria. On the other hand, it is often hard to precisely assess the performance of each alternative in the green supplier selection process, as human judgments are imprecise and vague under many circumstances (Herrera-Viedma 2015). As a result, a lot of green supplier selection methods under fuzzy environment have been suggested in the literature (Fallahpour et al. 2020; Kannan et al. 2020; Pourjavad and Shahin 2020; Ecer and Pamucar 2020). In many real-life situations, however, the information obtained is not enough for the exact definition of a membership degree for a certain element (Shahriari 2017). That is, there may be some amount of hesitation degree among membership and non-membership. To address this problem, Atanassov (1986) introduced the concept of intuitionistic fuzzy sets (IFSs) as an extension of fuzzy set theory (Zadeh 1965). Each IFS is described by a membership function and a non-membership function. Because of insufficiency in information availability, the IFS theory has been widely used to solve many MCDM problems. For instance, Wan et al. (2020) introduced a group decision making method with interval-valued Atanassov intuitionistic fuzzy preference relations and applied it to select material suppliers. Zhang et al. (2020) proposed an intuitionistic fuzzy TOPSIS method for complex and changeable bone transplant selection. Wu et al. (2020a) introduced a two-stage method for matching the technology suppliers and

3.1 Introduction

69

demanders based on prospect theory and evidence theory under intuitionistic fuzzy environment. Mishra et al. (2020) extended the evaluation based on distance from average solution (EDAS) approach with IFSs for the assessment of health-care waste disposal technology. Kumar and Kaushik (2020) put forward an approach to evaluate system failure probability using intuitionistic fuzzy fault tree analysis with qualitative failure data of system components. In addition, other intuitionistic fuzzy approaches were proposed by researchers for photovoltaic power coupling hydrogen storage project (Wu et al. 2020b), maritime supply chain management (Sahin and Soylu 2020), and customer requirements discernment (Lou et al. 2020). Therefore, the IFSs are more flexible and precise for tackling imprecise and uncertain decision information in green supplier selection due to the capability of accommodating hesitation in decision-making process. Given the strengths and widespread application of the VIKOR method and IFSs, this chapter extends the classical VIKOR to develop a new method, called intuitionistic fuzzy hybrid VIKOR (IFH-VIKOR), for solving GSES problems. The primary contributions of this chapter are summarized as follows: (1) to deal with the uncertainty and vagueness in green supplier selection, performance ratings of alternatives are taken as linguistic terms denoted by intuitionistic fuzzy numbers (IFNs); (2) to combine the merits of both subjective and objective weighting methods, a combination weighting method is proposed to define criteria weights in solving the green supplier selection problem; and (3) to identify the most appropriate green supplier, an extended VIKOR method is developed for the ranking of the considered alternatives. Furthermore, two empirical examples of green supplier selection are provided to illustrate the applicability and effectiveness of our proposed GSES method. The remaining part of this chapter is set out as follows. In Sect. 3.2, the preliminaries about IFS theory and the objective weighting method are introduced. In Sect. 3.3, we develop the IFH-VIKOR method to solve the green supplier selection problems with intuitionistic fuzzy information. Section 3.4 investigates two practical green supplier selection problems to demonstrate the proposed method. Finally, we conclude this chapter with some observations in Sect. 3.5.

3.2 Preliminaries 3.2.1 Intuitionistic Fuzzy Sets In what follows, some basic concepts of IFSs are introduced. Definition 3.1 (Atanassov 1986) Let X be a fixed set, then an IFS A in X is given as: A = {x, μ A (x), v A (x)|x ∈ X },

(3.1)

where μ A (x) : X → [0, 1] and v A (x) : X → [0, 1] are membership function and non-membership function, respectively, satisfying 0 ≤ μ A (x) +v A (x) ≤ 1, ∀x ∈ X .

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3 GSES Based on Intuitionistic Fuzzy VIKOR Method

The numbers μ A (x) and v A (x) represent, respectively, the membership degree and the non-membership degree of the element x to A, for all x ∈ X . Besides, π A (x) = 1 − μ A (x) − v A (x) denotes the hesitation degree of x ∈ A, which is the degree of indeterminacy or the degree of hesitancy of x to A. It is obvious that 0 ≤ π A (x) ≤ 1, ∀x ∈ X . For an IFS, the pair (μ A (x), v A (x)) is called an intuitionistic fuzzy number (IFN), and each IFN is represented by α = (μα , vα ), where μα ∈ [0, 1], vα ∈ [0, 1] and μα + vα ≤ 1. In addition, S(α) = μα − vα and H (α) = μα + vα are the score and accuracy degrees of α, respectively.   Definition 3.2 (Yazdani et al. 2016, 2017) Given any three IFNs α1 = μα1 , vα1 ,  α2 = μα2 , vα2 , and α = (μα , vα ), the operations of IFNs are shown as follows:   (1) α1 + α2 = μα1 + μα2 − μα1 μα2 , vα1 vα2 ,   (2) α1 × α2 = μα1 μα2 , vα1 + vα2 − vα1 vα2 ,   λ (3) λα = 1 − (1 − μα )λ , vα , λ > 0,   (4) α λ = μλα , 1 − (1 − vα )λ , λ > 0. Definition 3.3 (Xu and Yager 2006; Xu 2007) For comparing any two IFNs α1 and α2 , the method based on score function and accuracy function was proposed as follows: (1) (2)

If S(α1 ) < S(α2 ), then α1 < α2 ; If S(α1 ) = S(α2 ), and (a) (b)

if H (α1 ) < H (α2 ), then α1 < α2 ; if H (α1 ) = H (α2 ), then α1 = α2 .

  Definition  3.4 (Wang and Xin 2005) Suppose that α1 = μα1 , vα1 and α2 =  μα2 , vα2 are two IFNs, then the distance between α1 and α2 is computed by         μα − μα  + να − να  max μα − μα , να − να  1 2 1 2 1 2 1 2 + . (3.2) d(α1 , α2 ) = 4 2   Definition 3.5 (Xia and Xu 2012) For a collection of IFNs αi = μαi , vαi , i = 1, 2, . . . , n, w = (w1 , w2 , . . . , wn )T is the weight vector of αi (i = 1, 2, . . . , n) with n wi = 1, if SIFWA : V n → V , and wi ∈ [0, 1] and Σi=1 SIFWA(α1 , α2 , . . . , αn ) = w1 α1 + w2 α2 + · · · + wn αn

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71

Table 3.1 Linguistic terms for rating alternatives

Linguistic terms

IFNs

Very Poor (VP)

(0.10, 0.90)

Poor (P)

(0.20, 0.65)

Moderately Poor (MP)

(0.35, 0.55)

Fair (F)

(0.50, 0.50)

Moderately Good (MG)

(0.65, 0.25)

Good (G)

(0.80, 0.05)

Very Good (VG)

(0.90, 0.10)

IFN intuitionistic fuzzy number

⎛ ⎜ =⎜ ⎝

n

n

i=1 n

μwαii +

i=1

n

μwαii

vαwii

⎞

⎟ i=1 ⎟, n n  wi ,

 

w ⎠ 1 − μαi 1 − vαi i vαwii +

i=1

i=1

(3.3)

i=1

then the function is called the symmetric intuitionistic fuzzy weighted averaging (SIFWA) operator. The concept of a linguistic variable is of vital importance for dealing with circumstances which are too complex or too ill-defined to be reasonably described via conventional quantitative expressions (Zadeh 1975). In this chapter, the relative weights of criteria and the ratings of alternatives concerning each criterion are taken as linguistic terms represented using IFNs. For instance, these linguistic terms can be denoted by IFNs as depicted in Tables 3.1 and 3.2. Note that the IFNs can be defined based on historical data and/or a questionnaire responded to by domain experts.

Table 3.2 Linguistic terms for rating the importance of criteria

Linguistic Terms

IFNs

Very low (VL)

(0.15, 0.80)

Low (L)

(0.25, 0.65)

Medium Low (ML)

(0.40, 0.50)

Medium (M)

(0.50, 0.50)

Medium High (MH)

(0.60, 0.30)

High (H)

(0.75, 0.15)

Very High (VH)

(0.90, 0.05)

72

3 GSES Based on Intuitionistic Fuzzy VIKOR Method

3.2.2 Objective Weighting Method The entropy concept (Shannon and Weaver 1947) is able to measure information uncertainty formulated in line with probability theory. It is very useful in determining the relative contrast in intensities of criteria to express the average intrinsic information conveyed to a decision-maker. The entropy method utilizes the probabilistic discrimination among data to obtain importance weights of evaluation criteria (Zavadskas and Podvezko 2016; Zavadskas et al. 2017). If all alternatives are the same in relation to a specific criterion, then that criterion should be eliminated because it transmits no information about decision-makers’ preferences. On the opposite, the criterion that discriminates the data more effectively should be given a higher weight. Different from the traditional entropy method, intuitionistic fuzzy entropy (IFE) focuses on the credibility of the input data to determine criteria weights. It measures the extent of separation of the IFSs from fuzzy sets rather than from ordinary sets as in the traditional entropy method. Vlachos and Sergiadis (2007) presented an approach to discrimination measures for IFSs based on information theory, and derived an entropy measure for IFSs as follows: 1  [μ A (xi ) ln μ A (xi ) + v A (xi ) ln v A (xi ) n ln 2 i n

E(A) = −

−(1 − π A (xi )) ln(1 − π A (xi )) − π A (xi ) ln 2].

(3.4)

Here, if μ A (xi ) = 0, v A (xi ) = 0, π A (xi ) = 1, then μ A (xi ) ln μ A (xi ) = 0, v A (xi ) ln v A (xi ) = 0, and (1 − π A (xi )) ln(1 − π A (xi )) = 0, respectively. In this research, the IFE measure is applied to compute objective weights for green supplier evaluation criteria, and the procedural steps are explained as follows: Step 1 Establish the intuitionistic fuzzy decision matrix. Suppose that there are m alternatives Ai (i = 1, 2,…, m) to be performed over n criteria Cj (j = 1, 2,…, n). The intuitionistic fuzzy decision matrix R is constructed as: ⎡

r11 ⎢ r21 ⎢ R=⎢ . ⎣ .. rm1

⎤ r12 · · · r1n r22 · · · r2n ⎥ ⎥ .. .. ⎥, . ··· . ⎦ rm2 · · · rmn

(3.5)

  where ri j = μi j , vi j , i = 1, 2, …, m and j = 1, 2, …, n. Step 2 Calculate the IFE values. The following equaton is applied for the calculation of the IFE value E j for each criterion:

3.2 Preliminaries

73

1  μi j ln μi j + v Ai j ln vi j m ln 2 i      − 1 − πi j ln 1 − πi j − πi j ln 2 , j = 1, 2, . . . , n. m

Ej = −

(3.6)

Step 3 Obtain the objective weights of criteria by 1 − Ej  , j=1 1 − E j

woj = n where 0 ≤ woj ≤ 1 and

n j=1

j = 1, 2, . . . , n,

(3.7)

woj =1.

3.3 The Proposed GSES Method To address a green supplier selection problem, the decision-maker must evaluate alternatives pertaining to each criterion, address criteria weights, and determine the optimum one from the generated set of alternatives. This section extends the VIKOR method to the intuitionistic fuzzy setting for green supplier selection and a combination weighting method is utilized for assigning the weights of evaluation criteria. In the proposed method, the ratings of alternatives are taken as linguistic terms, which can be represented by IFNs as given in Table 3.1. The subjective weights of criteria are evaluated by decision-makers with the linguistic terms shown in Table 3.2. The objective criteria weights are obtained by using the IFE method as presented in Sect. 3.2.2. Thus, the proposed intuitionistic fuzzy hybrid VIKOR (IFH-VIKOR) method can not only benefit from IFSs but also combine the strengths of the two kinds of weighting methods. Suppose that a green supplier selection problem has l decision-makers DMk (k = 1, 2, . . . , l), m alternatives Ai (i = 1, 2, . . . , m) and n evaluation criteria Cj ( j = 1, 2, . . . , n). Each of the  l decision-makers is specified a weight λk > l 0 k = 1, 2, . . . , l; k=1 λk = 1 to reflect his/her relative importance in the green supplier selection process. Then, the steps of the proposed IFH-VIKOR method for the ranking of green suppliers can be defined as follows: Step 1 Aggregate the decision-makers’ individual assessments. In green supplier selection process, the decision-makers’ individual opinions need to be aggregated into group to build a collective intuitionistic fuzzy   evaluations k k k decision matrix. Let ri j = μi j , vi j be the IFN given by DMk on the assessment of Ai with respect to Cj . Then, the aggregated intuitionistic fuzzy ratings (ri j ) of alternatives with regard to each criterion can be acquired through the SIFWA operator as: l    ri j = SIFWA ri1j , ri2j , . . . , ril j = λk rikj , k=1

74

3 GSES Based on Intuitionistic Fuzzy VIKOR Method

⎛ ⎜ ⎜ =⎜ l  ⎝

k=1

l 

μikj

 λk

⎞

λk l 

vikj

⎟ ⎟ k=1 ,  λk  λk

λk λk ⎟ l  l  l  ⎠



μikj 1 − μikj vikj 1 − vikj + + k=1

k=1

k=1

k=1

i = 1, 2, . . . , m; j = 1, 2, . . . , n.

(3.8)

Hence, we can express a green supplier selection problem in a matrix format as seen below: ⎡

r11 ⎢ r21 ⎢ R=⎢ . ⎣ .. rm1

⎤ r12 · · · r1n r22 · · · r2n ⎥ ⎥ .. .. ⎥, . ··· . ⎦ rm2 · · · rmn

  where ri j = μi j , vi j , i = 1, 2,…, m and j = 1, 2,…, n are linguistic terms which can be expressed in IFNs. Step 2 Compute the subjective weights of criteria.   Assume that the weight of the criterion Cj is provided as wkj = μkj , vkj by the decision-maker DMk . Then, the collective intuitionistic fuzzy weights (w j ) of criteria can be computed using the SIFWA operator as: l    λk wkj w j = SIFWA w1j , w2j , . . . , wlj =

⎛ ⎜ ⎜ = ⎜ l  ⎝

k=1

λk l 

μkj

l  λk

vkj

k=1

⎞

⎟ ⎟ k=1 , λk λk

λk ⎟ l  l   λk l  ⎠



μkj 1 − μkj vkj 1 − vkj + + k=1

k=1

k=1

k=1

j = 1, 2, . . . , n,

(3.9)

  where w j = μ j , v j , j = 1, 2, …, n is the importance weight of the jth criterion. Based on the collective weights of criteria w j , the normalized subjective weight of each criterion is obtained by Eq. (3.10) (Boran et al. 2011; Liu et al. 2015).   μj μ j + π j μ j +v j wsj = n    ,  μj μ j + π j μ j +v j

j = 1, 2, . . . , n,

j=1

 where π j = 1 − μ j − v j and nj=1 wsj = 1. Step 3 Calculate the objective weights of criteria.

(3.10)

3.3 The Proposed GSES Method

75

The objective criteria weights can be calculated using the objective weighting method described in Sect. 3.2.2.   Step 4 Determine the intuitionistic fuzzy positive ideal solution f j∗ = μ∗j , v∗j   and the intuitionistic fuzzy negative ideal solution f j− = μ−j , v−j of all criteria ratings, j = 1, 2,…, n. f j∗ =

⎧ ⎫ ⎨ max ri j , for benefit criteria ⎬ i

⎩ min ri j , for cost criteria i

f j− =

⎭

,

⎧ ⎫ ⎨ min ri j , for benefit criteria ⎬ i

⎩ max ri j , for cost criteria i

⎭

,

j = 1, 2, . . . , n,

(3.11)

j = 1, 2, . . . n.

(3.12)

Step 5 Determine the normalized intuitionistic fuzzy differences d¯i j , i = 1, 2, …, m, j = 1, 2, …, n. The normalized intuitionistic fuzzy differences d¯i j are determined as:   d f j∗ , ri j , d¯i j =  d f j∗ , f j−

(3.13)

where   d f j∗ , ri j = 



d f j∗ , f j− =

     ∗    μ j − μi j  + v∗j − vi j  4      ∗    μ j − μ−j  + v∗j − v−j  4

+

+

        max μ∗j − μi j , v∗j − vi j  2

,

        max μ∗j − μ−j , v∗j − v−j  2

.

(3.14)

(3.15)

Step 6 Obtain the values S i and Ri , i = 1, 2, …, m, by using the formulas: Si = ϕ

n 

wsj d¯i j + (1 − ϕ)

j=1

n 

woj d¯i j

j=1

n n    s  o ¯ ϕw j + (1 − ϕ)w j di j = = wcj d¯i j , j=1

(3.16)

j=1

  Ri = max wcj d¯i j . j

(3.17)

where wcj = ϕwsj +(1 − ϕ)woj are the combination weights of criteria, and ϕ ∈ [0, 1] denotes the relative importance between subjective weights and objective weights.

76

3 GSES Based on Intuitionistic Fuzzy VIKOR Method

The value of ϕ can be taken to be any value from 0 to 1 and it set as 0.5 in this chapter for simplicity. Step 7 Determine the values Qi , i = 1, 2, …, m, with Eq. (3.18). Qi = v

Si − S ∗ Ri − R ∗ + (1 − v) − , − ∗ S −S R − R∗

(3.18)

where S ∗ = min Si , S − = max Si , R ∗ = min Ri , R − = max Ri ; v and 1-v are i

i

i

i

the weights for the strategy of maximum group utility and the individual regret, respectively. Usually, the value of v can be assumed to be 0.5. Step 8 Rank the alternative green suppliers according to the values of S, R, and Q in increasing order. The results are three ranking lists. Step 9 Propose a compromise solution, the alternative (A(1) ), which is the best ranked by the measure Q (minimum) if the following   two conditions are satisfied:  C1 Acceptable advantage: Q A(2) − Q A(1) ≥ 1/(m − 1), where A(2) is the alternative with second position in the ranking list by Q. C2 Acceptable stability: The alternative A(1) must also be in the first place by S or/and R. This compromise solution is stable within the green supplier selection process, which could be: “voting by majority rule” (when v > 0.5 is needed), or “by consensus” v ≈ 0.5, or “with veto” (v < 0.5). The following compromise solutions can be proposed if one of the above conditions is not fulfilled: • Alternatives A(1) and A(2) if only condition C2 is not satisfied; or (2) (M) • Alternatives A(1) , A ,…, condition C1 is not satisfied; A(M) is calculated  A  if (1)   (M) −Q A < 1/(m − 1) for maximum M. by the equation Q A

3.4 Illustrative Examples Two practical examples are presented in this section for illustrating the applicability of the proposed IFH-VIKOR method for GSES.

3.4.1 Supplier Selection for a General Hospital A university teaching hospital located in Shanghai, China intends to buy a new information management system in order to increase work productivity. After preelimination, four software companies A1 , A2 , A3 , and A4 have been determined as alternatives for further assessment. To perform the evaluation, a group composed of four decision-makers DM1 , DM2 , DM3 , and DM4 has been established. Five evaluation criteria for the system are considered, which include Functionality (C1 ), Reliability (C2 ), Usability (C3 ), Maintainability (C4 ), and Price (C5 ).

3.4 Illustrative Examples

77

The expert committee employ the linguistic terms expressed in Tables 3.1 and 3.2 to assess the importance weights of criteria and the suppliers with regard to each criterion. The evaluation results obtained are shown in Tables 3.3 and 3.4. In the supplier selection process, the following weights are given to the four decision makers: λ1 = 0.15, λ2 = 0.20, λ3 = 0.30, and λ4 = 0.3 owing to their different domain knowledge backgrounds and expertise. Table 3.3 Assessed information on the four alternatives Criteria

Decision makers

A1

A2

A3

A4

C1

DM1

MP

G

MG

F

DM2

MP

G

F

F

DM3

F

MG

F

F

DM4

F

G

MG

F

DM1

F

MG

MG

MG

DM2

MG

MG

G

F

DM3

MG

MG

MG

MG

DM4

MG

MG

G

F

DM1

F

F

F

MG

DM2

F

MG

F

F

DM3

MP

MG

MP

MG

DM4

F

F

MP

F

DM1

MG

VG

MG

F

DM2

F

G

VG

F

DM3

MG

G

G

MG

DM4

F

VG

MG

MP

DM1

G

MG

G

MG

DM2

G

G

MG

MG

DM3

MG

G

VG

F

DM4

MG

MG

G

F

C2

C3

C4

C5

Alternatives

Table 3.4 Importance weights of criteria Criteria

Decision makers DM1

DM2

DM3

DM4

C1

H

MH

MH

H

C2

H

H

H

VH

C3

VH

H

VH

VH

C4

M

M

MH

MH

C5

ML

M

ML

M

78

3 GSES Based on Intuitionistic Fuzzy VIKOR Method

Table 3.5 Collective intuitionistic fuzzy decision matrix and the subjective weights of criteria Alternatives

C1

C2

C3

C4

C5

A1

(0.446,0.518)

(0.629,0.282)

(0.454,0.515)

(0.569,0.379)

(0.708,0.149)

A2

(0.761,0.084)

(0.650,0.250)

(0.577,0.366)

(0.857,0.071)

(0.732,0.117)

A3

(0.577,0.366)

(0.739,0.108)

(0.401,0.533)

(0.762,0.133)

(0.814,0.087)

A4

(0.500,0.500)

(0.569,0.379)

(0.569,0.379)

(0.492,0.436)

(0.554,0.405)

wj

(0.680,0.216)

(0.815,0.104)

(0.878,0.063)

(0.566,0.366)

(0.455,0.500)

Next, we use the IFH-VIKOR method being proposed to provide a solution for the supplier selection problem, and the computational process is described as follows: Step 1 After quantifying the linguistic evaluations by corresponding IFNs, the collective intuitionistic fuzzy decision matrix can be created using the SIFWA operator as given in Eq. (3.8). The results are shown in Table 3.5. Step 2 The assessments of decision-makers on criteria weights are fused by Eq. (3.9) as listed in the last row of Table 3.5. Then, using Eq. (3.10), the normalized subjective weights of criteria are obtained as displayed in Table 3.6. Step 3 Based on the objective weighting method, the IFE value of each criterion is obtained by Eq. (3.6) and the objective criteria weights are calculated based on Eq. (3.7). The results of these calculations are displayed in Table 3.7. Step 4 Functionality, reliability, usability, and maintainability are benefit criteria, and price is a cost criterion. Hence, we can determine the intuitionistic fuzzy positive ideal solution and the intuitionistic fuzzy negative ideal solution of all criteria ratings as seen below: f 1∗ = (0.761, 0.084), f 2∗ = (0.739, 0.108), f 3∗ = (0.577, 0.366), f 4∗ = (0.857, 0.071), Table 3.6 Normalized intuitionistic fuzzy differences and normalized subjective weights of criteria Alternatives

C1

C2

C3

C4

C5

A1

1.000

0.642

0.822

0.830

0.760

A2

0.000

0.524

0.000

0.000

0.859

A3

0.639

0.000

1.000

0.238

1.000

A4

0.933

1.000

0.069

1.000

0.000

w Sj

0.207

0.242

0.255

0.166

0.130

Table 3.7 Calculated intuitionistic fuzzy entropy (IFE) values and objective weights of criteria Weights

C1

C2

C3

C4

C5

Ej

0.816

0.742

0.929

0.688

0.604

w Oj

0.151

0.211

0.058

0.256

0.324

3.4 Illustrative Examples

79

Table 3.8 Values of S, R, and Q for the four alternatives Indexes

A1

A2

A3

A4

S

0.801

0.314

0.548

0.616

R

0.179

0.195

0.227

0.227

Q

0.500

0.166

0.740

0.810

Table 3.9 Ranking of the four alternatives by S, R, and Q Indexes

A1

A2

A3

A4

By S

4

1

2

3

By R

1

2

3

3

By Q

2

1

3

4

f 5∗ = (0.554, 0.405);

f 1− = (0.446, 0.518), f 2− = (0.569, 0.379), f 3− = (0.401, 0.533), f 4− = (0.492, 0.436), f 5− = (0.814, 0.087). Step 5 The normalized intuitionistic fuzzy differences are calculated by applying Eq. (3.13) and outlined in Table 3.6. Step 6 The values of S, R, and Q are calculated by Eqs. (3.16)–(3.18) for the four alternatives and summarized in Table 3.8. Step 7 The rankings of the four alternatives by the S, R, and Q values in increasing order are presented in Table 3.9. Step 8 Based on Table 3.9, the ranking of the four alternatives is A2  A1  A3  A4 in accordance with the values of Q. Thus, A2 is the most suitable company among the alternatives to provide the required information management system for this hospital. To validate the effectiveness of the method being proposed, the intuitionistic fuzzy TOPSIS (IF-TOPSIS) suggested by Boran et al. (2011) is applied for the given case study. With the use of the evaluation of criteria weights and the ratings of alternative suppliers in Tables 3.3 and 3.4, the four alternatives are ranked as A2  A3  A4  A1 . It is found that the most desirable supplier obtained by the IFH-VIKOR and the IF-TOPSIS is exactly the same. This demonstrates the validity of our proposed method.

3.4.2 Supplier Selection for a Car Manufacturer To further demonstrate the proposed IFH-VIKOR method, an example of resilient supplier selection from (Sahu et al. 2016) is considered. An automobile manufacturer desires to develop a proactive resiliency strategy for selecting suppliers as

80

3 GSES Based on Intuitionistic Fuzzy VIKOR Method

its commitment to the global market. Five potential suppliers, denoted as A1 , A2 , …, A5 , are identified for the analysis. For assessing the suppliers, five decisionmakers, i.e., DM1 , DM2 , …, DM5 , from different departments are invited. The following criteria have been considered in the supplier evaluation and selection: Quality (C1 ), Reliability (C2 ), Functionality (C3 ), Customer satisfaction (C4 ), and Cost (C5 ). By using the seven-member linguistic term set in Table 3.1, the assessments of alternative suppliers given by the decision-makers are shown in Table 3.10. Similarly, the decision-makers are asked to use another seven-member linguistic term set (Table 3.2) to rate the importance weights against individual criteria. The linguistic assessments regarding criteria weights are given in Table 3.11. Note that Table 3.10 Assessed information of alternatives for Example 2 Alternatives

Criteria

DM1

DM2

DM3

DM4

DM5

A1

C1

MG

F

G

MG

VG

C2

F

G

MG

F

G

C3

F

G

G

G

F

C4

F

G

G

G

G

C5

G

MG

F

VG

MG

C1

VG

VG

G

G

G

C2

MG

VG

G

F

G

C3

G

VG

MG

VG

VG

C4

MG

G

MG

G

VG

C5

F

VG

F

MP

VG

C1

G

MG

MG

MG

G

C2

VG

MG

MG

MG

MG

C3

G

MP

MG

MP

G

C4

VG

G

MG

VG

VG

C5

F

G

G

MP

MP

C1

G

MP

F

F

MP

C2

G

G

VG

G

VG

C3

VG

VG

VG

G

G

C4

VG

G

VG

VG

VG

C5

VG

MG

G

G

G

C1

G

G

VG

VG

G

C2

MG

VG

MG

VG

MG

C3

MG

VG

MG

G

VG

C4

G

G

F

MG

MG

C5

G

G

MG

VG

MG

A2

A3

A4

A5

Decision makers

3.4 Illustrative Examples

81

Table 3.11 Importance weights of criteria for Example 2 Criteria

Decision makers DM1

DM2

DM3

DM4

DM5

C1

H

H

M

H

H

C2

VH

VH

VH

H

H

C3

H

H

MH

H

MH

C4

M

VH

H

H

H

C5

VH

H

VH

H

H

Table 3.12 Values of S, R, and Q for Example 2 Indexes

A1

A2

A3

A4

A5

S

0.643

0.326

0.433

0.375

0.556

R

0.202

0.119

0.199

0.192

0.224

Q

0.895

0.000

0.551

0.424

0.862

λ1 = λ2 = ··· = λ5 = 0.2 in this case, since the same weights are allocated to the five decision-makers. With the help of the proposed IFH-VIKOR model, the values of S, R, and Q acquired for the five suppliers are presented in Table 3.12. It is clear that the ranking order for the five alternatives is A2  A4  A3  A5  A1 and A2 is the most suitable supplier. The above supplier selection problem was also solved by the fuzzy VIKOR (Sahu et al. 2016) and the fuzzy TOPSIS (Haldar et al. 2014) methods. The ranking results of the candidate suppliers as derived via the application of these methods and the proposed IFH-VIKOR method are shown in Fig. 3.1. The ranking results show that the first choice of supplier remains the same, i.e., A2 , using the proposed approach and the fuzzy VIKOR method. Nevertheless, according to the fuzzy TOPSIS method, A4 has a higher priority as compared to A2 , and is the best option for the considered supplier selection case. The ranking orders of the other alternatives (A1 , A3 , A5 ,) obtained by the proposed IFH-VIKOR method are different from those produced by the fuzzy VIKOR and the fuzzy TOPSIS approaches. The main reasons that brought about the inconsistencies are as follows: (1) fuzzy set theory is used by the two compared methods to handle the ambiguity information that arises in supplier selection process. However, there is no means to incorporate the hesitation or uncertainty in fuzzy sets. In contrast, the theory of IFSs adopted in this chapter is helpful for addressing the uncertainty of supplier evaluation and for quantifying the ambiguous nature of subjective assessments in a convenient way; (2) only subjective weights of criteria are taken into account in the fuzzy VIKOR and the fuzzy TOPSIS methods. In the proposed IFH-VIKOR approach, both subjective and objective criteria weights are considered in the prioritization of alternative suppliers, which makes the method here proposed more realistic and more flexible; and (3) the ranking lists determined by using the proposed model and the fuzzy TOPSIS

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3 GSES Based on Intuitionistic Fuzzy VIKOR Method

Fig. 3.1 Comparative ranking of the candidate suppliers

method are greatly different. This is mainly because the aggregation approaches employed in the two approaches are dissimilar. The IFH-VIKOR approach is based on an aggregating function which represents the distance from the ideal solution. The fuzzy TOPSIS method, in contrast, is based on the idea that the optimum alternative should have the shortest distance from the positive ideal solution and the farthest from the negative ideal solution.

3.5 Chapter Summary In this chapter, we presented an IFH-VIKOR approach to deal with green supplier selection problems in which the preference ratings of alternatives and the importance of criteria are given as linguistics terms characterized by IFNs. The SIFWA operator was used to aggregate the ratings of decision-makers into collective assessments. In particular, both subjective and objective weights of criteria were considered during the GSES process, which can avoid the subjectivity in decision-makers’ knowledge and is helpful to reflect the essential characteristics of a green supplier selection problem. To illustrate the feasibility and effectiveness of the proposed IFH-VIKOR method, two application examples were examined, and the obtained results were demonstrated. Moreover, comparative analyses with relevant representative methods were made to indicate the advantages of our developed GSES methodology.

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Pourjavad E, Shahin A (2020) Green supplier development programmes selection: a hybrid fuzzy multi-criteria decision-making approach. Int J Sustain Eng 13(6):463–472 Qi J, Hu J, Peng YH (2020) Integrated rough VIKOR for customer-involved design concept evaluation combining with customers’ preferences and designers’ perceptions. Adv Eng Inf 46:101138 Rafieyan E, Khorsand R, Ramezanpour M (2020) An adaptive scheduling approach based on integrated best-worst and VIKOR for cloud computing. Comput Ind Eng 140:106272 Rao C, Xiao X, Goh M, Zheng J, Wen J (2017) Compound mechanism design of supplier selection based on multi-attribute auction and risk management of supply chain. Comput Ind Eng 105:63–75 Sahin B, Soylu A (2020) Intuitionistic fuzzy analytical network process models for maritime supply chain. Appl Soft Comput J 96:106614 Sahu A, Datta S, Mahapatra S (2016) Evaluation and selection of resilient suppliers in fuzzy environment: exploration of fuzzy-VIKOR. Benchmarking 23:651–673 Samanci S, Didem Atalay K, Bahar Isin F (2021) Focusing on the big picture while observing the concerns of both managers and passengers in the post-COVID era. J Air Transp Manage 90:101970 Shahriari M (2017) Soft computing based on a modified MCDM approach under intuitionistic fuzzy sets. Iran J Fuzzy Syst 14:23–41 Shannon C, Weaver W (1947) A mathematical theory of communication. The University of Illinois Press, Urbana Vlachos I, Sergiadis G (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28:197–206 Wan SP, Xu GL, Dong JY (2020) An Atanassov intuitionistic fuzzy programming method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Appl Soft Comput 95:106556 Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069 Wang X, Cai J (2017) A group decision-making model based on distance-based VIKOR with incomplete heterogeneous information and its application to emergency supplier selection. Kybernetes 46:501–529 Wen TC, Chang KH, Lai HH (2020) Integrating the 2-tuple linguistic representation and soft set to solve supplier selection problems with incomplete information. Eng Appl Artif Intell 87:103248 Wu A, Li H, Dong M (2020a) A novel two-stage method for matching the technology suppliers and demanders based on prospect theory and evidence theory under intuitionistic fuzzy environment. Appl Soft Comput 95:106553 Wu Y, Wu C, Zhou J, He F, Xu C, Zhang B, Zhang T (2020b) An investment decision framework for photovoltaic power coupling hydrogen storage project based on a mixed evaluation method under intuitionistic fuzzy environment. J Energy Storage 30:101601 Xia M, Xu Z (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13:31–47 Xu Z (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187 Xu Z, Yager R (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433 Yazdani M, Chatterjee P, Zavadskas E, Hashemkhani Zolfani S (2017) Integrated QFD-MCDM framework for green supplier selection. J Clean Prod 142:3728–3740 Yazdani M, Hashemkhani Zolfani S, Zavadskas E (2016) New integration of MCDM methods and QFD in the selection of green suppliers. J Bus Econ Manage 17:1097–1113 You X, You J, Liu H, Zhen L (2015) Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Expert Syst Appl 42:1906–1916 Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353 Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

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Zavadskas E, Cavallaro F, Podvezko V, Ubarte I, Kaklauskas A (2017) MCDM assessment of a healthy and safe built environment according to sustainable development principles: a practical neighborhood approach in Vilnius. Sustainability 9:702 Zavadskas E, Podvezko V (2016) Integrated determination of objective criteria weights in MCDM. Int J Inf Technol Dec Making 15:267–283 Zhang L, Zhan J, Yao Y (2020) Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf Sci 517:315–339 Zhao J, You XY, Liu HC, Wu SM (2017) An extended VIKOR method using intuitionistic fuzzy sets and combination weights for supplier selection. Symmetry 9(9):169

Chapter 4

GSES Based on Picture Fuzzy VIKOR Method

This chapter aims to develop a modified VIKOR technique for GSES, that uses ordered weighted distance operators in the aggregation of picture fuzzy information. Concretely, we first propose the picture fuzzy ordered weighted standardized distance (PFOWSD) operator and the picture fuzzy Euclidean ordered weighted standardized distance (PFEOWSD) operator, and extended them by using the hybrid average operator. Then, we develop a green supplier selection approach by combining the picture fuzzy distance operators and the VIKOR method. The new approach can manipulate attitudinal character of the classical VIKOR method, so that a decision maker can take decisions according to his or her preference. Further, by using the PFOWSD operator, one can parametrize the VIKOR method from the maximum to the minimum result. Thus, the information obtained using the new green supplier selection approach is much more complete. Finally, a practical case example in the beef supply chain is given to explain the proposed picture fuzzy-ordered weighted distance (PFOWD)-VIKOR model.

4.1 Introduction In the competitive global marketplace, companies have started to look after sustainability issues throughout their supply chain activities because of strict environmental legislation, scarcity of natural resources, and growing consumer awareness of environmental issues (Gören 2018; Zhu and Li 2018). Organizations are expecting their suppliers or partners to boost up sustainability in their collective work. These also lead manufacturers to practice the integration of environmental, economic, and social factors in production and supply chain activities. Sustainability refers to the ability of an enterprise to make present decisions without negatively affecting the future circumstances of the natural environment, societies and business viability (Giannakis and Papadopoulos 2016; Lu et al. 2018). The aim of green supply chain management (GSCM) is to cut down environmental pollution caused by the supply chain © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_4

87

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4 GSES Based on Picture Fuzzy VIKOR Method

activities of an organization (Tseng et al. 2018). In GSCM, supplier selection plays a significant role and has great influence on the competitive advantage of a company. It is a process of selecting the most appropriate green supplier with the right price and quality at the right time and quantity (Arabsheybani et al. 2018). Supplier selection based on green criteria represents a strategic decision and is regarded as a crucial concern in the implementation of GSCM. Unsuitable suppliers will increase the production and inventory costs, lower product quality, and ultimately decrease profitability and customer satisfaction (Quan et al. 2018; Van et al. 2018). Therefore, in recent years, ranking and selecting green suppliers has achieved a considerable amount of attention among researchers and practitioners who are attempting to move towards sustainable production (Stevi´c et al. 2020; Kilic and Yalcin 2020; Hoseini et al. 2020; You et al. 2020). Green supplier selection is generally modelled as a type of multi-criteria decisionmaking (MCDM) problem that includes a wide variety of alternatives and conflicting assessment criteria. Hence, researchers considered the MCDM methods as a suitable and effective methodology for selecting green suppliers in the literature (Shi et al. 2018; Ecer and Pamucar 2020; Hendiani et al. 2020). The VIKOR method (Opricovic 1998) is a famous MCDM tool to improve the quality of decision making. It has been developed for MCDM and takes into account contradictory and non-commensurable criteria to determine a compromise solution that is acceptable for all decision makers (Opricovic and Tzeng 2007). Due to its characteristics and potential benefits in compromise ranking, the VIKOR approach has been used in many of fields in recent years (Abdel-Basset et al. 2020; Qi et al. 2020; Das et al. 2020; Samanci et al. 2021). The detailed literature reviews regarding the VIKOR approach and its applications can be found in Gul et al. (2016) and Mardani et al. (2016). Although it is popular application, one limitation with the VIKOR technique is that it is neutral regarding the attitudinal character of a decision maker. In the real world, there are many situations in which decisions should be underestimated or overestimated in order to be more or less pessimistic against indefinite issues affecting the future (Merigó and GilLafuente 2010, 2011). But no or few researches have been carried out focusing on this issue in the application of the VIKOR method. On the other hand, in realistic green supplier selection processes, it is common that evaluation criteria data are vague and ambiguous because of a lack of information and knowledge. Some valuable theories and methods (e.g., intuitionistic fuzzy sets (IFSs) (Atanassov 1986)) were suggested to represent the uncertainty in applied green supplier evaluation situations (Kumari and Mishra 2020; Kilic and Yalcin 2020; Rouyendegh et al. 2020). Picture fuzzy sets (PFSs), first proposed by Cuong (2014), are a valuable extension of IFSs, which are characterized by membership degree and non-membership degree. In contrast, the PFSs are described by positive membership, neutral membership, and negative membership functions (Wei 2018; Jana and Pal 2019). Because of the consideration of new parameters, PFSs can represent imprecise assessments that IFSs can otherwise handle, and, moreover, they can depict more complex and uncertain information for decision makers (Arya and Kumar 2020; Xu et al. 2019). Recently, the PFS theory has been increasingly used

4.1 Introduction

89

as an ideal method for modelling uncertainty in real MCDM problems (Ding et al. 2020; Lin et al. 2020; Ping et al. 2020; Joshi 2020; Yue 2020). Against the above background, this chapter aims to present a new green supplier selection model by extending the VIKOR method with ordered weighted distance operators and PFSs. To achieve this target, we first introduce two new distance operators: the picture fuzzy ordered weighted standardized distance (PFOWSD) operator and the picture fuzzy Euclidean ordered weighted standardized distance (PFEOWSD) operator. Then, we suggest applying the picture fuzzy ordered weighted distance (PFOWD) operators to calculate separation measures in the VIKOR method. The fundamental characteristic of the PFOWD-VIKOR technique is that it calculates the separation measures from the best and the worst values with the developed distance operators, and consequently, the GSES problem can be addressed by a decision maker according to more complete information. In addition, an empirical case is given for illustrating the efficiency of the PFOWD-VIKOR model for choosing the optimal green suppliers in the beef industry. The remainder of this chapter is structured as follows. Section 4.2 provides the basic notions and definitions of PFSs briefly. In Sect. 4.3, we introduce the PFOWSD and the PFEOWSD operators and present extensions by the hybrid average (HA) operator (Xu and Da 2003). Section 4.4 develops the green supplier selection model with the aid of the PFOWD operators and VIKOR technique. In Sect. 4.5, the proposed approach is applied to green supplier selection in the beef supply chain. Finally, conclusions of this chapter are discussed in Sect. 4.6.

4.2 Preliminaries 4.2.1 Picture Fuzzy Sets On the basis of IFSs (Atanassov 1986), the concept of PFSs was proposed by Cuong (2014) to model complex and uncertain assessments of experts in real decisionmaking problems. Definition 4.1 A PFS P on the universe X is expressed by P = { x, μ P (x), η P (x), ν P (x)|x ∈ X },

(4.1)

where μ P (x) is the positive membership degree of x in P, η P (x) is the neutral membership degree of x in P, and ν P (x) is the negative membership degree of x in P; μ P (x), η P (x), and ν P (x) satisfy the conditions that 0 ≤ μ P (x), η P (x), ν P (x) ≤ 1 and 0 ≤ μ P (x) + η P (x) + ν P (x) ≤ 1. For each PFS P in X, the parameter π P (x) = 1−μ P (x) − η P (x) − ν P (x) is called the refusal membership degree of x in P. For convenience, the three-tuple

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4 GSES Based on Picture Fuzzy VIKOR Method

p˜ = (μ, η, v) is referred to as a picture fuzzy number (PFN), where 0 ≤ μ+η+ν ≤ 1 and 0 ≤ μ, η, ν ≤ 1. Definition 4.2 (Liu and Zhang 2018; Wei 2018) For any two PFNs p˜ 1 = (μ1 , η1 , v1 ) and p˜ 2 = (μ2 , η2 , v2 ), the basic operational rules of PFNs are defined as follows: (1) (2) (3) (4)

p˜ 1 ⊕ p˜ 2 = (μ1 + μ2 − μ1 μ2 , η1 η2 , v1 v2 ); p˜ 1 ⊗ p˜ 2 = (μ1 μ2 , η1 + η2 − η1 η2 ,v1 + v2 − v1 v2 ); λ p˜ 1 = 1 − (1 − μ1 )λ , (η1 )λ , (v1 )λ , λ > 0;   p˜ 1λ = (μ1 )λ , 1 − (1 − η1 )λ , 1 − (1 − v1 )λ , λ > 0.

Definition 4.3 (Li et al. 2017; Wei 2018) Let Φ be the set of all PFNs in X. The score function of a PFN p˜ = (μ, η, v) is computed by S( p) ˜ =

1 (1 + μ − v). 2

(4.2)

  where S( p) ˜ ∈ [0, 1]. The accuracy function of a PFN p˜ = μ p , ν p is defined by H ( p) ˜ = μ + η + v,

(4.3)

where H ( p) ˜ ∈ [0, 1]. Using the score function S and the accuracy function H, the comparison laws of PFNs are defined below. Definition 4.4 Supposing there are two PFNs p˜ 1 = (μ1 , η1 , v1 ) and p˜ 2 = (μ2 , η2 , v2 ), then (1) (2) (3)

If S( p˜ 1 ) > S( p˜ 2 ), then p˜ 1 > p˜ 2 ; If S( p˜ 1 ) = S( p˜ 2 ) and H ( p˜ 1 ) > H ( p˜ 2 ), then p˜ 1 > p˜ 2 ; If S( p˜ 1 ) = S( p˜ 2 ) and H ( p˜ 1 ) = H ( p˜ 2 ), then p˜ 1 = p˜ 2 .

Motivated by the distance measure between IFSs (Wang and Xin 2005), Dutta (2018) proposed a distance formula for PFSs taking into account the parameters of positive membership, neutral membership, and negative membership. Definition 4.5 (Dutta 2018) Let p˜ 1 = (μ1 , η1 , ν1 ) and p˜ 2 = (μ2 , η2 , v2 ) be any two PFNs. The distance of p˜ 1 and p˜ 2 is calculated by 1 (|μ1 − μ2 | + |η1 − η2 | + |v1 − v2 | + |ρ1 − ρ2 |) 4 1 + max(|μ1 − μ2 |, |η1 − η2 |, |v1 − v2 |, |ρ1 − ρ2 |). 2

d( p˜ 1 , p˜ 2 ) =

(4.4)

Based on the basic operational rules of PFNs, Wei (2017) developed the picture fuzzy-weighted averaging (PFWA) operator for decision making.

4.2 Preliminaries

91

Definition 4.6 (Wei 2017) Suppose p˜ i = (μi , ηi , νi )(i = 1, 2, . . . , n) is a collection of PFNs in . The PFWA operator can be computed by using the following formula:  n

PFWA( p˜ 1 , p˜ 2 , . . . , p˜ n ) = ⊕ wi p˜ i = 1 − i=1

n 

(1 − μi ) , wi

i=1

n  i=1

(ηi ) , wi

n 

 (vi )

wi

,

i=1

(4.5) where w = (w1 , w2 , . . . ,  wn )T is the associated weights of p˜ i (i = 1, 2, . . . , n), n wi = 1. satisfying wi ∈ [0, 1] and i=1

4.2.2 The OWAD Operator The ordered weighted averaging distance (OWAD) operator (Merigó and GilLafuente 2010, 2011) is an extension of the traditional Hamming distance by using the ordered weighted average (OWA) operator (Yager 1988). An important feature of the OWAD operator is the reordering of the arguments of the individual distances according to their values. It can be defined as follows for two sets of X = {x1 , x2 , . . . , xn } and Y = {y1 , y2 , . . . , yn }. Definition 4.7 An OWAD operator of dimension n is a mapping OWAD: R n × R n → T R that nhas an associated weighting vector ω = (ω1 , ω2 , . . . , ωn ) , with ω j ∈ [0, 1] and j=1 ω j = 1, such that: OWAD(x1 , y1 , . . . , xn , yn ) =

n 

ωjdj,

(4.6)

j=1

where d j denotes the jth largest of the individual distance |xi − yi |, and xi and yi represent the ith elements of the sets X and Y. Similarly, the Euclidean ordered weighted averaging distance (EOWAD) operator, an extension of the traditional Euclidean distance, was defined in Merigó and GilLafuente (2008).

4.3 Picture Fuzzy Distance Operators 4.3.1 The PFOWSD Operator This section gives the definition of the PFOWSD operator for green supplier selection 

∗ = r˜1∗ , r˜2∗ , . . . , r˜n∗ , using the VIKOR method. Suppose that the three PFSs R

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4 GSES Based on Picture Fuzzy VIKOR Method



i = {˜ri1 , r˜i2 , . . . , r˜in } denote, respectively, the ideal − = r˜1− , r˜2− , . . . , r˜n− , and R R solution, the nadir (negative ideal) solution, and the ith considered alternative in a GSES problem with n evaluation criteria. Then, the PFOWSD operator can be explained as follows. Definition 4.8 For the related weighting vector ω = (ω1 , ω2 , . . . , ωn )T , with ωk ∈ [0, 1] and nk=1 ωk = 1, we define the PFOWSD operator as follows: n

∗ −

   ∗ − ωk d k , PFOWSD r˜1 , r˜1 , r˜i1 , . . . , r˜n , r˜n , r˜in =

(4.7)

k=1

where d k represents the kth largest of the individual picture fuzzy standardized  distance

d r˜ ∗j ,˜ri j ,  d r˜ ∗j ,˜r − j

r˜ ∗j and r˜ − j represent the ideal value and the nadir value of the jth

criterion, respectively, and r˜i j is the picture fuzzy value of ith alternative regarding Cj , i = 1, 2, . . . , m. ∗ = {0.9, 0.1, 0, 1, 0, 0, 0.8, 0.1, 0.1, 1, 0, 0}, R − = Example 4.1 Let R i = {0.7, 0.2, 0.1, 0.4, 0.1, 0.5, {0, 1, 0, 0, 0.9, 0.1, 0, 1, 0, 0, 0.8, 0.1}, R 0.3, 0.1, 0.5, 0.6, 0.1, 0.2} be three PFS, and the associated weighting vector is ω = (0.4, 0.3, 0.2, 0.1). Then, we can obtain the PFOWSD operator as: d(0.9, 0.1, 0, 0.7, 0.2, 0.1) d(0.9, 0.1, 0, 0.4, 0.1, 0.5) + 0.3 × d(1, 0, 0, 0, 0.9, 0.1) d(0.9, 0.1, 0, 0, 1, 0) d(0.9, 0.1, 0, 0.6, 0.1, 0.2) d(0.9, 0.1, 0, 0.3, 0.1, 0.5) + 0.1 × + 0.2 × d(0.8, 0.1, 0.1, 0, 1, 0) d(1, 0, 0, 0, 0.8, 0.1) = 0.339.

PFOWSD = 0.4 ×

Note that the PFOWSD operator is commutative, monotonic, idempotent, and bounded. The proofs of these properties are straightforward and thus omitted here. Like the OWAD operator, the PFOWSD operator includes a parameterized family of picture fuzzy distance operators by changing the weights, such as the descending PFOWSD operator, the picture fuzzy maximum, the picture fuzzy minimum, the picture fuzzy normalized Hamming standardized distance (PFNHSD) operator, and the picture fuzzy-weighted Hamming standardized distance (PFWHSD). Bedsides, we can obtain other families of PFOWSD operators referring to the OWAD operator, e.g., the step-PFOWASD operator, the window-PFOWASD, the olympic-PFOWASD, the PFOWASD-median, the centered-PFOWASD, the SPFOWASD, and the non-monotonic-PFOWASD. The formulation of these families is straightforward, as indicated in Merigó and Gil-Lafuente (2010, 2011), Liu and Liu (2017), and Merigó et al. (2017).

4.3 Picture Fuzzy Distance Operators

93

4.3.2 The PFEOWSD Operator ∗ , R − , and R i denote, respectively, the ideal solution, Suppose that the three PFSs R the nadir solution, and the ith considered alternative in a GSES problem with n evaluation criteria. Then, the definition of the PFEOWSD operator is given as follows. T Definition 4.9 For n the related weighting vector ω = (ω1 , ω2 , . . . , ωn ) satisfying ωk ∈ [0, 1] and k=1 ωk = 1, we define the PFEOWSD operator by the formula:

 n 1/2   ∗ −

∗ −

 2 PFEOWSD r˜1 , r˜1 , r˜i1 , . . . , r˜n , r˜n , r˜in = ωk d k ,

(4.8)

k=1

where d k represents the kth largest of the individual picture fuzzy standardized  distance

d r˜ ∗j ,˜ri j ,  d r˜ ∗j ,˜r − j

r˜ ∗j and r˜ − j denote the idea value and the nadir value of the jth

criterion, respectively, and r˜i j is the picture fuzzy value of ith alternative regarding Cj , i = 1, 2, . . . , m. ∗ , R − , and R i , and the weighting vector ω given Example 4.2 For the three PFSs R in Example 4.1, the PFEOWSD operator is determined by 



PFEOWSD = 0.4 ×  +0.2 ×

d(0.9, 0.1, 0, 0.4, 0.1, 0.5) d(1, 0, 0, 0, 0.9, 0.1)

d(0.9, 0.1, 0, 0.3, 0.1, 0.5) d(0.8, 0.1, 0.1, 0, 1, 0)

2

 + 0.3 ×

2

 + 0.1 ×

d(0.9, 0.1, 0, 0.7, 0.2, 0.1) d(0.9, 0.1, 0, 0, 1, 0)

d(0.9, 0.1, 0, 0.6, 0.1, 0.2) d(1, 0, 0, 0, 0.8, 0.1)

2

2 1/2

= 0.340.

It should be noted that the PFEOWSD operator is commutative, monotonic, idempotent, and bounded. By using different weighting vectors, we can determine different types of picture fuzzy distance operators, which include the picture fuzzy maximum, the picture fuzzy minimum, the picture fuzzy-normalized Euclidean standardized distance (PFNESD), and the picture fuzzy-weighted Euclidean standardized distance (PFWESD). Like the EOWAD operator, we can determine other families of PFEOWSD operators (e.g., the step-PFEOWSD operator, the window-PFEOWSD, the olympicPFEOWSD, the PFEOWSD-median, the centered-PFEOWSD, the S-PFEOWSD, and the non-monotonic-PFEOWSD).

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4 GSES Based on Picture Fuzzy VIKOR Method

4.3.3 The HPFOWSD Operator Motivated by the HA operator (Xu and Da 2003), the hybrid PFOWSD (HPFOWSD) − , and R i denote, ∗ , R operator is introduced in this part. Suppose that the three PFSs R respectively, the ideal solution, the nadir solution, and the ith considered alternative in a GSES problem with n evaluation criteria. Then, the HPFOWSD operator is explained as below. Definition 4.10 For the related weighting vector ω = (ω1 , ω2 , . . . , ωn )T , with ωk ∈ [0, 1] and nk=1 ωk = 1, we define the HPFOWSD operator as: n

∗ −

   ∗ − ωk dˆk , HPFOWSD r˜1 , r˜1 , r˜i1 , . . . , r˜n , r˜n , r˜in =

(4.9)

k=1

where dˆk represents the kth largest of the nw j d j , d j

=

  d r˜ ∗j ,˜ri j ,  d r˜ ∗j ,˜r − j

w =

T Cj with w j ∈ [0, 1] and (w 1n , w2 , . . . , wn ) is the weighting vector of the − ∗ j=1 w j = 1, n is the balancing coefficient, and r˜ j and r˜ j denote the idea value and the nadir value of the jth criterion, respectively; r˜i j is the picture fuzzy value of ith alternative regarding Cj , i = 1, 2, . . . , m.

∗ , R − , and R i be three PFSs and the weighting vector ω is the Example 4.3 Let R same as Example 4.1. According to Eq. (4.9), we have d(0.9, 0.1, 0, 0.7, 0.2, 0.1) d(0.9, 0.1, 0, 0.4, 0.1, 0.5) = 0.342, d 2 = = 0.350, d(0.9, 0.1, 0, 0, 1, 0) d(1, 0, 0, 0, 0.9, 0.1) d(0.9, 0.1, 0, 0.3, 0.1, 0.5) d(0.9, 0.1, 0, 0.6, 0.1, 0.2) = 0.333, d 4 = = 0.300. d3 = d(0.8, 0.1, 0.1, 0, 1, 0) d(1, 0, 0, 0, 0.8, 0.1) d1 =

Then, we have dˆ1 = 4 × 0.3 × 0.342 = 0.420, dˆ2 = 4 × 0.2 × 0.350 = 0.274, dˆ3 = 4 × 0.1 × 0.333 = 0.133, dˆ4 = 4 × 0.4 × 0.300 = 0.480. Finally, the HPFOWSD operator can be calculated as follows: HPFOWSD = 0.4 × 0.480 + 0.3 × 0.420 + 0.2 × 0.274 + 0.1 × 0.133 = 0.386. It can be observed that if ωk = 1/n, for all k, the PFWHSD operator is derived and if wk = 1/n, for all k, the PFOWSD operator is determined. If ωk = 1/n and w j = 1/n, for all k and j, we get the PFNHSD operator. The HPFOWSD operator has similar properties than the PFOWSD operator. But it is not idempotent nor

4.3 Picture Fuzzy Distance Operators

95

commutative. Besides, a wide range of families of the HPFOWSD operator can be obtained following the method given in the PFOWSD operator.

4.3.4 The HPFEOWSD Operator Similarly, the hybrid PFEOWSD (HPFEOWSD) operator is a generalization of the − , and R i denote, respec ∗ , R PFEOWSD operator. Suppose that the three PFSs R tively, the ideal solution, the nadir solution, and the ith considered alternative in a GSES problem with n evaluation criteria. Then, the definition of the HPFEOWSD operator is given below. Definition 4.11  For an associated weighting vector ω = (ω1 , ω2 , . . . , ωn )T , with ωk ∈ [0, 1] and nk=1 ωk = 1, we define the HPFEOWSD operator as:  n 1/2   2  ∗ −

∗ −

 HPFEOWSD r˜1 , r˜1 , r˜i1 , . . . , r˜n , r˜n , r˜in = ωk dˆk ,

(4.10)

k=1

where dˆk represents the kth largest of the nw j d j , d j

=

  d r˜ ∗j ,˜ri j  , d r˜ ∗j ,˜r − j n j=1 w j

w =

= 1, n (w1 , w2 , . . . , wn )T is the weight of the Cj with w j ∈ [0, 1] and − ∗ is the balancing coefficient, and r˜ j and r˜ j are the ideal value and the nadir value of the jth criterion, respectively; r˜i j is the picture fuzzy value of ith alternative regarding Cj , i = 1, 2, . . . , m. ∗ , R − , and R˜ i be three PFSs, the weighting vector ω is the same Example 4.4 Let R as Example 4.1, and the weighting vector w = (0.3, 0.2, 0.1, 0.4). Similar to Example 4.3, we have dˆ1 = 0.480, dˆ2 = 0.420, dˆ3 = 0.274, dˆ4 = 0.133. Thus, the HPFEOWSD operator is determined as below: 1/2  HPFEOWSD = 0.4 × 0.4802 + 0.3 × 0.4202 + 0.2 × 0.2742 + 0.1 × 0.1332 = 0.402. In this case, when ωk = 1/n, for all k, we get the PFWESD operator, and when wk = 1/n, for all k, we get the PFEOWSD operator. When ωk = 1/n and w j = 1/n, for all k and j, the PFNESD operator is obtained. It can be seen that the HPFEOWSD operator accomplishes similar properties than the HPFOWSD operator.

96

4 GSES Based on Picture Fuzzy VIKOR Method

4.4 The Proposed GSES Approach In what follows, we present an ordered weighted distance-based VIKOR method for solving GSES problems with conflicting criteria and picture fuzzy information. The proposed green supplier selection approach, called PFOWD-VIKOR, can be useful in many of situations such as in those where a decision maker wants to underestimate the results so as to take a more prudent selection than in normal cases. The process to follow in evaluating green suppliers with the PFOWD-VIKOR approach is based on the procedure developed in Opricovic (1998) and Merigó and Gil-Lafuente (2008), with the differences that the criteria values are given in the form of PFNs and the separation measures are calculated with the PFOWSD operator. Let us consider a GSES problem, which contains m alternatives (potential suppliers) Ai (i = 1, 2, . . . , m) and n evaluation criteria C j ( j = 1, 2, . . . , n). Each alternative is evaluated against the n criteria. The decision makers Dk (k = 1, 2, . . . , l) utilize linguistic terms to score the ratings of alternatives with respect to each criterion. Thus, the performance ratings of decision makers Dk (k = 1, 2, . . . , l) assigned   for k . each alternative form a linguistic evaluation matrix denoted by Z = z ikj m×n

The importance weights of the l decision makers are denoted by λk (k = 1, 2, . . . , l)  with λk ≥ 0 and lk=1 λk = 1. Then, by using the PFOWD-VIKOR algorithm, the multi-criteria green supplier selection problem can be approached with the following steps:   k = r˜ikj of each decisionStep 1 Obtain the picture fuzzy evaluation matrix R m×n

maker. The first step is to convert the decision makers’ linguistic expressions for k = alternatives into PFNs to establish the picture fuzzy evaluation matrixes R    r˜ikj (k = 1, 2, . . . , l), where r˜ikj = μikj , ηikj , νikj for i = 1, 2, . . . , m; j = m×n

1, 2, . . . , n and k = 1, 2, . . . , l. For example, the linguistic terms illustrated in Table 4.1 can be used by decision makers for sustainability evaluation of alternative suppliers.   = r˜i j by Step 2 Determine the collective picture fuzzy evaluation matrix R m×n using the PFWA operator. Table 4.1 Linguistic terms for assessing the alternatives

Linguistic terms

Picture fuzzy numbers (PFNs)

Very poor (VP)

Poor (P)

Moderately poor (MP)

Fair (F)

Moderately good (MG)

Good (G)

Very good (VG)

4.4 The Proposed GSES Approach

97

k (k = 1, 2, . . . , l) are aggregated with The picture fuzzy evaluation matrixes R the PFWA operator, as the formula in Eq. (4.11) to obtain the matrix R.   l r˜i j = PFWA r˜i1j , r˜i2j , . . . , r˜il j = ⊕ λi r˜ikj k=1   l l l     k wk   k  wk k wk = 1− 1 − μi j , ηi j , vi j . k=1

k=1

(4.11)

k=1

Step 3 Find the best r˜ ∗j and the worst r˜ − j values of all criteria ratings using Eqs. (4.12) and (4.13), for j = 1, 2, …, n. ⎧ ⎫ ⎨ max r˜i j , for benefit criteria ⎬ i r˜ ∗j = , ⎩ min r˜i j , for cost criteria ⎭

j = 1, 2, . . . , n,

(4.12)

j = 1, 2, . . . , n.

(4.13)

i

r˜ − j =

⎧ ⎫ ⎨ min r˜i j , for benefit criteria ⎬ i

⎩ max r˜i j , for cost criteria ⎭

,

i

Step 4 Obtain the values S i and Ri , i = 1, 2, …, m, by employing the below equations: n



   ωk d k , Si = PFOWSD r˜1∗ , r˜1− , r˜i1 , . . . , r˜n∗ , r˜n− , r˜in =

(4.14)

k=1

  Ri = max ωk d k ,

(4.15)

k

where ωk is the ordered weights of criteria. It may be mentioned here that we can use the picture fuzzy distance operators presented in the last section in the above equations. Step 5 Obtain the values Qi , i = 1, 2, …, m, by the following equation: Qi = v

Si − S ∗ Ri − R ∗ + − v) , (1 S− − S∗ R− − R∗

(4.16)

where S ∗ = min Si , S − = max Si , R ∗ = min Ri , R − = max Ri . In addition, v i

i

i

i

means the weight for the strategy of maximum group utility, and 1 − v is the weight of the individual regret. In the real application, we can take the value of v as 0.5. Step 6 Based on the ascending orders of the values S, R, and Q, all the alternatives can be acquired. As a result, three ranking lists can be yielded. Step 7 This step is to determine a compromise solution (A(1) ), which is best ranked by the measure Q (minimum) and, at the same time, the following two conditions should be satisfied:

98

4 GSES Based on Picture Fuzzy VIKOR Method

    C1 Acceptable advantage: Q A(2) − Q A(1) ≥ 1/(m − 1), where A(2) ranks the second according to the values of Q. C2 Acceptable stability in decision making: The alternative A(1) should be the first alternative by S or/and R. The compromise solution is stable in a green supplier selection process, which could be “voting by majority rule” (v > 0.5), or “by consensus” v ≈ 0.5, or “with veto” (v < 0.5). If one of the conditions is not fulfilled, then we can obtain a set of compromise solutions in line with the following rules: • Alternatives A(1) and A(2) if only C2 is not fulfilled or (1) (2) (M) • Alternatives if C1 is not fulfilled; A(M) is determined by the , A ,…,(1)A   A (M) −Q A < 1/(m − 1) for maximum M. relation Q A

4.5 Case Study In this section, we applied the PFOWD-VIKOR methodology to an empirical green supplier selection case in the beef supply chain (Singh et al. 2018) to demonstrate its applicability and effectiveness. In what follows, the background information and the implementation process are discussed in detail.

4.5.1 Background Description In recent years, carbon footprint reduction has received great attention from researchers and practitioners around the world. Apart from the manufacturing and transportation industries, the agriculture sector is one of the main contributors to global carbon emission. Compared to other agri-food products, beef has the uppermost carbon footprint, and the majority of its emissions takes place at beef farms (Singh et al. 2018). This is particularly true in developing countries where the majority of global cattle are raised, but farmers in these areas are often not aware of modern technology to curtail carbon emissions from their farms. Furthermore, there is an increasing pressure on the beef industry from the government and clients to reduce carbon emissions in its supply chain. Therefore, it is of vital importance to increase consciousness of beef farmers and, thus, incorporate sustainable criteria in selecting the best cattle supplier by abattoir and processor. To mitigate carbon emission, the proposed approach was applied for the selection of a supplier for a beef abattoir and processor company. After premilitary screening, ten potential alternatives (beef farmers) of this company were considered, which are denoted as Ai (i = 1, 2, . . . , 10). The green performance of these suppliers was evaluated according to the following seven criteria: quality of meat (C1 ), age of cattle (C2 ), diet fed to cattle (C3 ), average weight (C4 ), traceability (C5 ), carbon footprint (C6 ), and price (C7 ). An expert group consisting of three decision makers (DM1 , DM2 , and DM3 ) was established to conduct the performance rating of each supplier.

4.5 Case Study

99

Table 4.2 Linguistic evaluation matrixes of the decision makers Criteria C1

C2

C3

C4

C5

C6

C7

Decision makers

Alternatives A1

A2

DM1

VG

F

P

MG

F

G

MP

P

P

MG

DM2

VG

MG

MG

MG

MG

G

F

VG

MG

MG

DM3

VG

F

G

MG

VG

G

G

VG

F

G

DM1

MP

G

P

F

VG

F

MP

G

F

MP

DM2

MP

G

MP

F

VG

MP

MP

MG

MP

F

DM3

MP

G

F

F

VG

P

MP

F

P

MG

DM1

VG

F

MG

VG

VG

G

MP

F

MP

MG

DM2

VG

F

G

G

G

G

F

MG

F

MG

DM3

VG

F

VG

MG

G

G

MG

G

MG

MG

DM1

G

MG

MG

P

P

G

P

P

MG

VG

DM2

G

G

MG

P

P

G

MP

MP

G

VG

DM3

G

VG

MG

P

MP

G

F

F

VG

VG

DM1

G

VG

G

VG

VP

VG

P

P

MG

VG

DM2

VG

VG

MG

G

P

VG

P

P

MG

VG

DM3

VG

VG

F

VG

MP

VG

MP

P

MG

VG

DM1

MP

G

MG

VG

G

F

MP

VG

F

VG

DM2

F

MG

MG

G

G

MG

F

G

F

VG

DM3

MG

F

MG

VG

G

G

MG

MG

F

VG

DM1

F

F

P

MP

F

F

F

F

F

P

DM2

F

F

MP

F

F

MP

MP

MP

F

F

DM3

F

MP

F

MP

P

F

F

F

F

F

A3

A4

A5

A6

A7

A8

A9

A10

The decision makers’ weights were assumed as λ1 = 0.3, λ2 = 0.4, and λ3 = 0.3 since they had different levels of technical knowledge and expertise. According to the linguistic terms defined in Table 4.1, evaluation results of the three decision makers for the ten suppliers are listed in Table 4.2.

4.5.2 Implementation Results To identify the supplier that performed the best on sustainability requirements, the proposed PFOWD-VIKOR framework was implemented. The obtained results are given as follows: Step 1 The linguistic evaluation data of decision makers are transformed into PFNs according to Table  For example, for DM1 , the obtained picture fuzzy  4.1. 1 = r˜i1j is demonstrated as in Table 4.3. evaluation matrix R 10×7

100

4 GSES Based on Picture Fuzzy VIKOR Method

Table 4.3 Picture fuzzy evaluation matrix of DM1 Alternatives

Criteria C1

C2

C3

C4

C5

C6

C7

A1









A2









A3









A4









A5









A6









A7









A8









A9









A10









  = r˜i j Step 2 The collective picture fuzzy evaluation matrix R of suppliers m×n is obtained by Eq. (4.11). Table 4.4 displays the aggregated picture fuzzy evaluations of alternatives. and Eqs. (4.12) and (4.13), the best r˜ ∗j and the worst Step 3 Based on the matrix R − r˜ j values for the seven criteria are determined as listed in Table 4.4. Steps 4 and 5 Now we need to determine the values S i , Ri , and Qi for the ten alternative suppliers with Eqs. (4.14)–(4.16). Note that it is possible to employ different picture fuzzy distance operators to calculate the S i index. In the case study, we considered the PFNHSD, the PFWHSD, the PFOWSD, the PFHOWSD, the PFNESD, the PFWESD, the PFEOWSD, and the HPFEOWSD operators. The following weighting

4.5 Case Study

101

Table 4.4 Collective picture fuzzy evaluation matrix R Alternatives Criteria C1

C2

C3

C4

A1





A2

A3

A4

A5

A6

A7

A8

A9





A10







r˜ ∗j





r˜ − j





C5

C7





C6









vectors were selected: ω = (0.15, 0.15, 0.10, 0.10, 0.15, 0.15, 0.20) and w = (0.170, 0.103, 0.129, 0.116, 0.140, 0.171, 0.171). The results of these calculations are shown in Tables 4.5 and 4.6. Steps 6 and 7 All the alternative suppliers are ranked in ascending order based on the values of S i , Ri , and Qi . The lowest value of Qi in each method is the optimal result. As a result, the ranking results are displayed in Table 4.7.

0.157 0.401

R

Q

Hybrid picture fuzzy-ordered weighted standardized distance (HPFOWSD)

Picture fuzzy-ordered weighted standardized distance (PFOWSD)

Picture fuzzy-weighted Hamming standardized distance (PFWHSD)

0.489

0.468 0.180 0.392

R

Q

Q

S

0.165 0.383

R

Q 0.449

0.171 0.389

R

S

0.494

S

A1

S

Picture fuzzy normalized Hamming standardized distance (PFNHSD)

Alternatives

Ranking indexes

Distance operators

Table 4.5 Results with picture fuzzy Hamming operators A2

0.428

0.183

0.491

0.393

0.162

0.477

0.425

0.174

0.518

0.390

0.154

0.497

A3

0.347

0.163

0.489

0.349

0.150

0.507

0.349

0.156

0.521

0.357

0.143

0.539

A4

0.286

0.153

0.468

0.517

0.179

0.493

0.285

0.146

0.497

0.528

0.170

0.527

A5

0.281

0.147

0.489

0.497

0.174

0.50

0.294

0.140

0.533

0.506

0.166

0.532

A6

0.000

0.108

0.368

0.227

0.15

0.391

0.000

0.103

0.392

0.227

0.143

0.41

A7

0.782

0.180

0.853

0.822

0.165

0.866

0.762

0.171

0.882

0.822

0.157

0.905

A8

0.222

0.141

0.454

0.331

0.150

0.490

0.218

0.135

0.478

0.339

0.143

0.521

A9

1.000

0.231

0.862

0.964

0.193

0.832

1.000

0.220

0.913

0.971

0.183

0.877

A10

0.143

0.126

0.436

0.029

0.115

0.418

0.151

0.120

0.472

0.054

0.109

0.464

102 4 GSES Based on Picture Fuzzy VIKOR Method

A3

A4

A5

A6

A7

A8

A9

A10

0.560

0.658 0.605 0.607 0.625 0.442 0.901 0.558 0.997 0.553 0.471 0.422 0.396 0.380 0.279 0.464 0.365 0.595 0.326

0.706 0.464 0.529

Hybrid picture fuzzy Euclidean-ordered weighted S standardized distance (HPFEOWSD) R Q

0.498 0.372 0.333 0.323 0.000 0.706 0.240 1.000 0.175

0.454 0.370 0.591 0.576 0.227 0.810 0.367 1.000 0.043

0.387 0.426 0.387 0.497 0.296

0.518

0.418 0.387 0.461 0.45

0.426

Q

0.624 0.617 0.649 0.659 0.495 0.912 0.615 0.922 0.531

0.439 0.322 0.398 0.399 0.060 0.697 0.263 1.000 0.090

0.422 0.377 0.405 0.396 0.321 0.414 0.360 0.531 0.292

0.640 0.616 0.632 0.654 0.468 0.922 0.592 0.98

0.422 0.343 0.585 0.560 0.199 0.792 0.340 1.000 0.068

0.408 0.378 0.450 0.439 0.378 0.415 0.378 0.485 0.307

0.560

R

0.471

Q

A2

0.625 0.629 0.664 0.669 0.498 0.940 0.626 0.95

0.663

0.414

R

0.510

Q 0.69

0.415

R S

0.685

S

A1

Ranking indexes Alternatives

S

picture fuzzy Euclidean-ordered weighted standardized distance (PFEOWSD)

Picture fuzzy-weighted Euclidean standardized distance (PFWESD)

Picture fuzzy-normalized Euclidean standardized distance (PFNESD)

Distance operators

Table 4.6 Results with picture fuzzy Euclidean operators

4.5 Case Study 103

Distance operators PFNESD PFWESD PFEOWSD HPFEOWSD

Ranking

A10 ∼ A6 A8 A3 A2 A1 A5 A4 A7 A9

A6 ∼ A10 A8 A4 A5 A3 A1 A2 A7 A9

A10 ∼ A6 A8 A3 A1 A2 A5 A4 A7 A9

A6 ∼ A10 A8 A5 A4 A3 A1 A2 A7 A9

Distance operators

PFNHSD

PFWHSD

PFOWSD

HPFOWSD

Table 4.7 Ranking results with the PFOWD-VIKOR model

A6 ∼ A10 A8 A5 A4 A3 A1 A2 A7 A9

A10 ∼ A6 A8 A3 A2 A1 A5 A4 A7 A9

A6 ∼ A10 A8 A3 A4 A5 A2 A1 A7 A9

A10 ∼ A6 A8 A3 A2 A1 A5 A4 A7 A9

Ranking

104 4 GSES Based on Picture Fuzzy VIKOR Method

4.5 Case Study

105

As one can note, depending on the particular type of picture fuzzy distance operators, the priority of alternative suppliers is dissimilar. For some situations, the most suitable supplier is A10 because it has the lowest distance to the ideal alternative. For other circumstances, we can observe that the optimal choice is A6 . However, according to the related rules in Sect. 4.5, both A10 and A6 are compromise solutions since only the acceptability condition C1 is valid. Besides, by using the dominance theory (Brauers and Zavadskas 2010), an aggregated ranking of the alternatives can be acquired based on the considered picture fuzzy distance operators (i.e., A10 ∼ A6 A8 A3 A5 A4 A1 ∼ A2 A7 A9 ). Therefore, in the given application, the focal abattoir and processor company can select A10 or A6 as the best beef cattle supplier for procurement.

4.5.3 Comparative Analysis In this section, to show the effectiveness of the proposed GSES model, we made a comparison analysis using the same case study in the beef supply chain, with the fuzzy TOPSIS (Singh et al. 2018), the IF-VIKOR (Zhao et al. 2017), and the IF-GRA (Sen et al. 2018) methods. Figure 4.1 shows the order results of the suppliers that were produced by using the listed methods. It can be seen that A10 is rated first among the four methods. Especially, the top two and the last two suppliers determined by

Fig. 4.1 Rankings of suppliers by the compared methods

106

4 GSES Based on Picture Fuzzy VIKOR Method

the proposed model agree with the ones using the fuzzy TOPSIS and the IF-VIKOR methods. This confirms the efficiency of the proposed PFOWD-VIKOR method. On the other hand, there is a difference in the ranking orders of other suppliers derived with the four methods. For example, A8 ranks third and is better than A4 when using the proposed approach. However, the third highest ranking supplier is A4 and A8 has a lower priority when the fuzzy TOPSIS and the IF-VIKOR methods are used. According to the IF-GRA method, A3 is ranked behind A5 . In reality, the former is more important, and, thus, the result of the proposed approach suggests that A3 has a higher priority in comparison with A5 . This is also validated by the fuzzy TOPSIS and the IF-VIKOR methods. Besides, when balancing all the criteria, the two suppliers A1 and A2 should be given the same priority for selection, as derived by the proposed approach. But the other three methods produce the opposite results: A1 is better than A2 by the fuzzy TOPSIS and the IF-GRA, and A2 ranks higher than A1 using the IF-VIKOR method. Thus, a more reasonable ranking can be achieved by the use of the PFOWD-VIKOR algorithm. In addition, the inconsistency in the rankings of suppliers can be explained by different features of the compared methods. The proposed approach employs PFSs to handle the inherent lack of precision of the data gathered in the GSES problem, unlike the fuzzy TOPSIS approach on the basis of fuzzy sets and the IF-VIKOR and IF-GRA methods using IFSs. Moreover, another reason for the different ranking results from the presented approach and the fuzzy TOPSIS method is that the VIKOR method ranks sustainable alternatives based on the closeness to the ideal solution. The TOPSIS method selects the optimum alternative, which should have the “shortest distance” from the idea solution and the “farthest distance” from the “negative-idea” solution. The proposed approach and the IF-GRA method produce vastly different priority results for the suppliers. This is, in part, due to the fact that the GRA method uses only one “reference” point in determining the ranking of alternative suppliers.

4.5.4 Managerial Implications This chapter presented a new decision-making approach for purchase managers to select the best green supplier to increase the competitiveness and economic level of an enterprise. The proposed GSES approach is unique in its integration of ordered weighted distance operators and the VIKOR approach in picture fuzzy environment. The case example showed that the proposed approach led to superior results, compared to other methods. In summary, the new approach proposed for green supplier selection has several implications for practitioners and academicians in the green supplier management field. First, by using PFSs, the proposed approach is more appropriate to address the challenge of decision makers in assessing the green performance of suppliers. It incorporates a complete degree of confidence in experts’ opinions and can easily represent the uncertainty of evaluation information in solving GSES problems. Second, by using picture fuzzy distance operators in the green supplier selection process, various methods can be provided for managers. In

4.5 Case Study

107

real-word cases, we often do not know which scenario is the correct one by reason of uncertainty. Hence, representing different specific cases that might occur is valuable for gaining the whole picture of a different, future status quo. Finally, the proposed approach determines the ranking of alternative suppliers following the basic procedure of VIKOR method. The ranking result or compromise solution obtained is more accurate and reliable and can be easily accepted by decision makers since it offers a maximum group utility of the “majority” and a minimum individual regret of the “opponent”. Therefore, our study provides practical and theoretical guidance for the organizations that are implementing or will implement GSCM.

4.6 Chapter Summary In this chapter, a PFOWD-VIKOR framework was established to solve GSES problems under picture fuzzy environment. We first introduced the PFOWSD and the PFEOWSD operators as new types of picture fuzzy distance operators. Then, the normal VIKOR technique was modified using the developed distance operators to obtain the performance ranking of green suppliers. The key benefit of the proposed approach is that we can manipulate the neutrality of results according to the optimism degree of a decision maker. Therefore, a decision maker is able to choose the optimal supplier according to his or her attitudinal character and thus, obtain a more comprehensive view of a GSES problem. Finally, the PFOWD-VIKOR approach was applied in beef supply chain management concerning the selection of eco-friendly cattle suppliers. Further, through comparison with existing methods, the advantages and practicalities of the presented approach were illustrated.

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Chapter 5

GSES Using Interval 2-Tuple Linguistic Distance Operators

With respect to multi-criteria GSES problems with interval 2-tuple linguistic information, a new approach that uses distance measures is proposed in this chapter. Motivated by the ordered weighted distance (OWD) measures, we develop some interval 2-tuple linguistic distance operators such as the interval 2-tuple weighted distance (ITWD), the interval 2-tuple ordered weighted distance (ITOWD), and the interval 2-tuple hybrid weighted distance (ITHWD) operators. These aggregation operators are very useful for the treatment of input data in the form of interval 2-tuple linguistic variables. We study some desirable properties of the ITOWD operator and further generalize it by using the generalized and the quasi-arithmetic means. Finally, the new approach is utilized to complete a green supplier selection study for an actual hospital from the healthcare industry.

5.1 Introduction The ordered weighted averaging (OWA) operator (Yager 1988) is a very well-known aggregation operator, providing a parameterized family of aggregation operators that includes the maximum, the minimum and the average, among others. The prominent characteristic of the OWA operator is reordering step. An interesting extension of the OWA is the use of distance measures in the OWA operator. In this respect, Xu and Chen (2008) developed the ordered weighted distance (OWD) measure, which is the generalization of a variety of well-known distance measures, such as the normalized Hamming distance, the normalized Euclidean distance, and the normalized geometric distance. The prominent characteristic of the OWD measure is that it can relieve (or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low (or high) weights. Merigó and Gil-Lafuente (2010) proposed a technique for decision making using the OWA operator to calculate Hamming distance and introduced the ordered weighted averaging distance (OWAD) operator. The main advantage of this operator is that it can © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_5

111

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take into account the attitudinal character of a decision maker in the aggregation process; thus, the decision maker is able to consider a decision problem more clearly according to his or her interests. Merigó et al. (2013) introduced the probabilistic ordered weighted averaging distance (POWAD) operator, which uses a unified model between the probability and the OWA operator considering the degree of importance that each concept has in the aggregation. Zeng et al. (2013) further extended the POWAD operator to deal with uncertain environments represented in the form of interval numbers and proposed the uncertain probabilistic ordered weighted averaging distance (UPOWAD) operator. Merigó et al. (2014) studied the use of distance measures and heavy aggregations in the OWA operator and presented the heavy ordered weighted averaging distance (HOWAD) operator. It is a new aggregation operator that provides a parameterized family of aggregation operators between the minimum distance and the total distance operator. In addition, Merigó and Casanovas (2010) introduced the linguistic ordered weighted averaging distance (LOWAD) operator for linguistic decision making. Zeng and Su (2011) and Zeng (2013) considered the situations with intuitionistic fuzzy and interval-valued intuitionistic information, and developed some intuitionistic fuzzy weighted distance measures. Xu (2012) developed some fuzzy ordered distance measures for group decision making with linguistic, interval, triangular or trapezoidal fuzzy preference information. Xian and Sun (2014) developed the fuzzy linguistic induced Euclidean ordered weighted averaging distance (FLIEOWAD) operator for group linguistic decision making, in which criteria values take the form of fuzzy linguistic information. More recently, other types of distance measures have been proposed in the literature, such as the hesitant fuzzy psychological distance measure operator (Song et al. 2020), the q-rung orthopair fuzzy distance measure (Pinar and Boran 2020), the type 2 hesitant fuzzy distance operator (Özlü and Karaaslan 2020), the hesitant fuzzy psychological distance operator (Li et al. 2020), the single valued neutrosophic distance measure (Ero˘glu and Sahin ¸ 2020), the modified Pythagorean fuzzy distance measure (Ejegwa 2020), and so on (Rezaei and Rezaei 2019, 2020; Mahanta and Panda 2020; Zhou and Chen 2020). In many situations, however, the input arguments may take the form of interval 2-tuple linguistic variables (Zhang 2013; Liu et al. 2014a; Xue et al. 2016) because of time pressure, lack of knowledge or data, and decision makers’ limited attention and information processing capabilities. Furthermore, decision makers may use different linguistic term sets to express their evaluations on the established selection criteria considering their personal backgrounds, preferences and different understanding levels to alternatives. Therefore, it is necessary to extend the ordered weighted distance measures to accommodate the interval 2-tuple linguistic environment (Liu et al. 2014b; You et al. 2015; Shan et al. 2016), which is also the focus of this paper. For doing so, we will develop some interval 2-tuple linguistic distance operators such as the interval 2-tuple weighted distance (ITWD), the interval 2tuple ordered weighted distance (ITOWD), and the interval 2-tuple hybrid weighted distance (ITHWD) operators. These aggregation operators are very effective to deal with the situations where the input data are expressed in interval 2-tuple linguistic variables. We study some desirable properties of the ITOWD operator and further

5.1 Introduction

113

generalize it by using the generalized and the quasi-arithmetic means obtaining the generalized interval 2-tuple ordered weighted distance (GITOWD) and the quasiarithmetic interval 2-tuple ordered weighted distance (Quasi-ITOWD) operators. Finally, based on the GITOWD operator, we develop an approach for GSES with interval 2-tuple linguistic information and illustrate it with a numerical example. The remainder of this chapter is set out as follows. In Sect. 5.2, we introduce some basic concepts and operation laws of interval 2-tuple linguistic variables. In Sect. 5.3, we develop the ITWD, the ITOWD and the ITHWD operators, and investigate some desirable properties of the ITOWD operator. In Sect. 5.4, we present a GSES approach based on the developed interval 2-tuple linguistic distance operators. A supplier selection example is given in Sect. 5.5 to verify the proposed approach and to demonstrate its feasibility and practicality. Finally, conclusions are provided in Sect. 5.6.

5.2 Preliminaries 5.2.1 2-Tuple Linguistic Variables The 2-tuple linguistic representation model was firstly presented in (Herrera and Martínez 2000) based on the concept of symbolic translation. It is used to represent linguistic information by means of a linguistic 2-tuple (s, α), where s is a linguistic term from the predefined linguistic term set S and α is a numerical value representing the symbolic translation. In the classical 2-tuple linguistic approach, the range of β is between 0 and g, which is relevant to the granularity of a linguistic term set. Here, β is the result of an aggregation of the indices of a set of labels assessed in the linguistic term set S. To overcome this restriction, Tai and Chen (2009) proposed a generalized 2-tuple linguistic model and translation functions.   Definition 5.1 (Tai and Chen 2009) Let S = s0 , s1 , . . . , sg be a linguistic term set and β ∈ [0, 1] is a value representing the result of a symbolic aggregation operation. Then the generalized translation function  used to obtain the 2-tuple linguistic variable equivalent to β is defined as follows:   1 1  : [0, 1] → S × − , 2g 2g  si , i = round(β ·g)  (β) = (si , α), with 1 1 α = β − gi , α ∈ − 2g , 2g

(5.1)

(5.2)

where round(·) is the usual rounding operation, si has the closest index label to β and α is the value of the symbolic translation.

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  Definition 5.2 (Tai and Chen 2009) Let S = s0 , s1 , . . . , sg be a linguistic term set and (si , α) be a 2-tuple. There exists a function −1 which is able to convert a 2-tuple linguistic variable into its equivalent numerical value β ∈ [0, 1]. The reverse function −1 is defined as follows:   1 1 → [0, 1], (5.3) −1 : S × − , 2g 2g −1 (si , α) =

i + α = β. g

(5.4)

Particularly, it is necessary to point out that the conversion of a linguistic term into a linguistic 2-tuple consists of adding a value 0 as symbolic translation (Herrera and Martínez 2000): si ∈ S ⇒ (si , 0).

(5.5)

The comparison of linguistic information represented by 2-tuples is carried out according to an ordinary lexicographic order. Definition 5.3 (Herrera and Martínez 2000, 2001) Let (sk , α1 ) and (sl , α2 ) be two 2-tuples, then: (1) (2)

If k < l then (sk , α1 ) is smaller than (sl , α2 ); If k = l then (a) (b) (c)

if α 1 = α 2 , then (sk , α1 ) is equal to (sl , α2 ); if α 1 < α 2 then (sk , α1 ) is smaller than (sl , α2 ); if α 1 > α 2 then (sk , α1 ) is bigger than (sl , α2 ).

5.2.2 Interval 2-Tuple Linguistic Variables Motivated by the uncertain linguistic variables (Xu 2004b) and based on the definitions of (Tai and Chen 2009), Zhang (2012) proposed an interval 2-tuple linguistic representation model as a generalization of the 2-tuple linguistic variables. Due to its characteristics and advantages, the interval 2-tuple linguistic representation model has been widely applied for dealing with uncertainty in various multi-criteria decision making problems (Liu et al. 2015a; Liu et al. 2015b; Liu et al. 2016a; Liu et al. 2016b). It can be defined as follows.   Definition 5.4 (Zhang 2012, 2013) Let S = s0 , s1 , . . . , sg be a linguistic term set. 2-tuple linguistic variable of two 2-tuples, denoted by  is composed

 An interval



(si , α1 ), sj , α2 , where (si , α1 ) ≤ sj , α2 ,si sj and α1 (α2 ) represent the linguistic label of S and symbolic translation, respectively. The interval 2-tuple that expresses

5.2 Preliminaries

115

the equivalent information to an interval value [β1 , β2 ](β1 , β2 ∈ [0, 1], β1 ≤ β2 ) is derived by the following function:



with [β1 , β2 ] = (si , α1 ), sj , α2

⎧ si , i = round(β1 · g) ⎪ ⎪ ⎪ ⎪ ⎨ sj , j = round(β2 · g)

 1 1 α1 = β1 − gi , α1 ∈ − 2g , 2g ⎪ ⎪   ⎪ ⎪ ⎩ α2 = β2 − j , α2 ∈ − 1 , 1 . g 2g 2g

(5.6)

On the contrary, there is always a function −1 such that an interval 2-tuple can be converted into an interval value [β1 , β2 ](β1 , β2 ∈ [0, 1], β1 ≤ β2 ) as follows: 

−1 (si , α1 ), sj , α2 =



 i j + α1 , + α2 = [β1 , β2 ]. g g

(5.7)

Specially, if si = sj and α1 = α2 , then the interval 2-tuple linguistic variable reduces to a 2-tuple linguistic variable. Based on the operations of uncertain linguistic variables (Xu 2004), Zhang (2012) further gave some basic operational laws of interval 2-tuples and proposed the interval 2-tuple weighted average (ITWA) operator. Definition 5.5 (Zhang 2012) Consider any three interval 2-tuples a˜ = [(r, α), (t, ε)] a˜ 1 = [(r1 , α1 ), (t1 , ε1 )] and a˜ 2 = [(r2 , α2 ), (t2 , ε2 )], and let λ ∈ [0, 1], then their operations are defined as follows: (1) a˜ 1 ⊕ a˜ 2 = [(r1 , α1 ), (t1 , ε1 )] ⊕ [(r2 , α2 ), (t2 , ε2 )] =  −1 (r1 , α1 ) + −1 (r2 , α2 ), −1 (t1 , ε1 ) + −1 (t2 , ε2 ) ; (2) λ˜a = λ[(r, α), (t, ε)] =  λ−1 (r, α), λ−1 (t, ε) . Definition 5.6 (Zhang 2012) Let a˜ i = [(ri , αi ), (ti , εi )](i = 1, 2, . . . , n) be a set T of interval 2-tuples n and w = (w1 , w2 , . . . , wn ) be their associated weights, with wi ∈ [0, 1]and i=1 wi = 1. Then, the ITWA operator is defined as: n

ITWAw (˜a1 , a˜ 2 , . . . , a˜ n ) = ⊕ (wi a˜ i ) i=1  n  n   −1 −1 = wi  (ri , αi ), wi  (ti , εi ) . i=1

i=1

(5.8)

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Inspired by the distance measure in uncertain linguistic environment (Xu 2014), the distance between interval 2-tuples can be defined below. Definition 5.7 Let a˜ 1 = [(r1 , α1 ), (t1 , ε1 )] and a˜ 2 = [(r2 , α2 ), (t2 , ε2 )] be any two interval 2-tuples, then        1  −1  (r1 , α1 ) − −1 (r2 , α2 ) + −1 (t1 , ε1 ) − −1 (t2 , ε2 ) d a˜ , b˜ =  2 (5.9) ˜ Especially, if the interval is called the interval 2-tuple distance between a˜ and b. 2-tuples a˜ 1 = [(r1 , α1 ), (t1 , ε1 )] and a˜ 2 = [(r2 , α2 ), (t2 , ε2 )] are degenerated to 2tuples aˆ = (r1 , α1 ) and bˆ = (r2 , α2 ), then the interval 2-tuple distance will become the 2-tuple distance (Wei 2010).

5.3 Interval 2-Tuple Linguistic Distance Operators The OWAD operator (Merigó and Gil-Lafuente 2010) is an extension of the traditional Hamming distance by using the OWA operator, which provides a parameterized family of aggregation operators ranging from the minimum to the maximum distance. For two real numbers sets A={a1 , a2 , . . . , an } and B={b1 , b2 , . . . , bn }, the OWAD operator is defined as follows. Definition 5.8 An OWAD operator of dimension n is a mapping OWAD : Rn ×Rn → R that has an associated weighting vector ω=(ω1 , ω2 , . . . , ωn )T , with ωj ∈ [0, 1] and n ωj = 1, such that j=1 OWAD(a1 , b1 , a2 , b2 , . . . , an , bn ) =

n 

ωj dj ,

(5.10)

j=1

where dj represents the jth largest of the individual distance |ai − bi |. Further, Xu and Chen (2008) developed an ordered weighted distance (OWD) measure, which generalizes a variety of well-known distance measures and aggregation operators. Definition 5.9 An OWD measure of dimension n is a mapping OWD : Rn ×Rn → R that has an associated weighting vector ω=(ω1 , ω2 , . . . , ωn )T , with ωj ∈ [0, 1] and n ωj = 1, such that j=1 ⎛ OWD(a1 , b1 , a2 , b2 , . . . , an , bn ) = ⎝

n  j=1

⎞1/λ ωj djλ ⎠

,

(5.11)

5.3 Interval 2-Tuple Linguistic Distance Operators

117

where dj is the jth largest of the individual distance |ai − bi |. If λ = 1, then the OWD measure is reduced to the OWAD operator; if λ = 1 and ω = (1/n, 1/n, . . . , 1/n)T , then the OWD measure is reduced to the normalized Hamming distance.

5.3.1 Interval 2-Tuple Linguistic Distance Operators The OWAD and the OWD operators have only been used in the situations in which the input arguments are exact values. However, the judgments of people depend on personal psychological aspects such as experience, learning, situation, state of mind, and so forth. It is more suitable for decision makers to provide their preferences by means of linguistic variables rather than numerical ones. For convenience, let S˜ be the set of all ˆ be the set of all 2-tuples, A={˜ ˜ a1 , a˜ 2 , . . . , a˜ n } and interval 2-tuples, S   ˜ b˜ 1 , b˜ 2 , . . . , b˜ n be two sets of interval 2-tuples. Based on Eq. (5.9), we B= define the ITWD operator as follows. ˆ Definition 5.10 An ITWD operator of dimension n is a mapping ITWD:S˜ n ×S˜ n → S, T , w , . . . , w with w ∈ 1] and that has an associated weight vector w = [0, (w ) 1 2 n i n i=1 wi = 1, such that n          ˜ ˜ ˜ ITWD a˜ 1 , b1 , a˜ 2 , b2 , . . . , a˜ n , bn = wi dITD a˜ i , b˜ i ,

(5.12)

i=1

  where dITD a˜ i , b˜ i is the interval 2-tuple distance between a˜ i and b˜ i . Especially, if w = (1/n, 1/n, . . . , 1/n)T , then the ITWD becomes the interval 2-tuple normalized distance (ITND) operator: n      1     dITD a˜ i , b˜ i . ITND a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = n i=1

(5.13)

  ˜ a1 , a˜ 2 , . . . , a˜ n } and B= ˜ b˜ 1 , b˜ 2 , . . . , b˜ n are If the sets of interval 2-tuples A={˜     ˆ aˆ 1 , aˆ 2 , . . . , aˆ n and B= ˆ bˆ 1 , bˆ 2 , . . . , bˆ n , then degenerated to the sets of 2-tuples A= the ITWD is reduced to the 2-tuple weighted distance (TWD) operator: n          TWD aˆ 1 , bˆ 1 , aˆ 2 , bˆ 2 , . . . , aˆ n , bˆ n = wi dTD aˆ i , bˆ i , i=1

  where dTD aˆ i , bˆ i is the 2-tuple distance between aˆ i and bˆ i .

(5.14)

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Based on the OWA and the ITWD operators, we define an interval 2-tuple ordered weighted distance (ITOWD) operator as follows. Definition 5.11 An ITOWD operator of dimension n is a mapping ITOWD:S˜ n × ˆ that has an associated weight vector ω=(ω1 , ω2 , . . . , ωn )T , with ωj ∈ [0, 1] S˜ n → S, n and j=1 ωj = 1, such that n          ITOWD a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = ωj dITD a˜ σ (j) , b˜ σ (j) ,

(5.15)

j=1

    where dITD a˜ σ (j) , b˜ σ (j) is the jth largest of the interval 2-tuple distance dITD a˜ i , b˜ i .     Especially, if there is a tie between dITD a˜ i , b˜ i and dITD a˜ j , b˜ j ,     then we replace each of dITD a˜ i , b˜ i and dITD a˜ j , b˜ j by their average      dITD a˜ i , b˜ i + dITD a˜ j , b˜ j /2 in the process of aggregation. If k items are tied, T then we replace these by k replicas of their average. If ω = (1/n, 1/n,   . . . , 1/n) , then the ITOWD becomes the ITND; if the position of the dITD a˜ i , b˜ i is the same as   the ordered position of the dITD a˜ σ (j) , b˜ σ (j) , then the ITWD is obtained. Moreover, ˆ then the ITOWD is reduced to the 2-tuple if A˜ and B˜ are degenerated to Aˆ and B, ordered weighted distance (TOWD) operator: n          TOWD aˆ 1 , bˆ 1 , aˆ 2 , bˆ 2 , . . . , aˆ n , bˆ n = ωj dTD aˆ σ (j) , bˆ σ (j) ,

(5.16)

j=1

    where dTD aˆ σ (j) , bˆ σ (j) is the jth largest of the 2-tuple distance dTD aˆ i , bˆ i . Similar to the OWAD operator, the ITOWD operator is commutative, monotonic, idempotent and bounded. These properties can be shown with the following theorems. Theorem5.1 (Commutativity-OWA aggregation). Assume f is the ITOWD oper     ˜ ˜ ˜ be any permutation of the arguments ator. If a˜ 1 , b1 , a˜ 2 , b2 , . . . , a˜ n , bn       a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n , then f

            a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n .

Theorem 5.2 (Commutativity-distance measure). Assume f is the ITOWD operator, then             f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = f b˜ 1 , a˜ 1 , b˜ 2 , a˜ 2 , . . . , b˜ n , a˜ n .

5.3 Interval 2-Tuple Linguistic Distance Operators

119

  Theorem 5.3 (Monotonicity). Assume f is the ITOWD operator. If dITD a˜ i , b˜ i ≥   dITD a˜ i , b˜ i for all i, then            a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n ≥ f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n .

 f

  Theorem 5.4 (Idempotency). Assume f is the ITOWD operator. If dITD a˜ i , b˜ i = d for all i, then       f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = d . The proofs of the above theorems are straightforward and thus omitted. Theorem 5.5 (Bounded). Assume f is the ITOWD operator, then             min dITD a˜ i , b˜ i ≤ f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n ≤ max dITD a˜ i , b˜ i .       Proof Let max dITD a˜ i , b˜ i = t, and min dITD a˜ i , b˜ i = r, then  f

n n n           a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = ωj dITD a˜ σ (j) , b˜ σ (j) ≤ ωj t = t ωj = t, j=1

j=1

j=1

n n n            f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = ωj dITD a˜ σ (j) , b˜ σ (j) ≥ ωj r = r ωj = r. j=1

j=1

j=1

Therefore             min dITD a˜ i , b˜ i ≤ f a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n ≤ max dITD a˜ i , b˜ i . Another important issue is the determination of the weighting vector associated with the ITOWD operator. In the literature, various methods have been suggested for the OWA weights, which can also be implemented for the ITOWD operator, such as the normal distribution-based method (Xu 2005), the maximum Bayesian entropy method (Yari and Chaji 2012), and the least squares-based method (Ahn and Park 2008). Inspired by (Xu and Xia 2011; Zeng and Su 2011), in the following, we give three ways to determine the ITOWD weights.

120

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

(1) Let   dITD a˜ σ (j) , b˜ σ (j)  , ωj =  1 ˜ σ (j) a ˜ d , b ITD σ (j) j=1 then ωj+1 ≥ ωj ≥ 0, j = 1, 2, . . . , n − 1, and

j = 1, 2, . . . , n, 1 j=1

(5.17)

ωj = 1.

(2) Let ωj =

e 1

  −dITD a˜ σ (j) ,b˜ σ (j)

j=1

e

 , −dITD a˜ σ (j) ,b˜ σ (j)

then 0 ≤ ωj+1 ≤ ωj , j = 1, 2, . . . , n − 1, and

j = 1, 2, . . . , n, 1 j=1

(5.18)

ωj = 1.

(3) Let   1 1   d˙ ITD a˜ σ (j) , b˜ σ (j) = dITD a˜ σ (j) , b˜ σ (j) , j=1 n and             d¨ dITD a˜ σ (j) , b˜ σ (j) , d˙ ITD a˜ σ (j) , b˜ σ (j) = dITD a˜ σ (j) , b˜ σ (j) − d˙ ITD a˜ σ (j) , b˜ σ (j) ,

then we define      1 − d¨ dITD a˜ σ (j) , b˜ σ (j) , d˙ ITD a˜ σ (j) , b˜ σ (j)      , ωj =   1 ¨ dITD a˜ σ (j) , b˜ σ (j) , d˙ITD a˜ σ (j) , b˜ σ (j) 1 − d j=1

j = 1, 2, . . . , n, (5.19)

 from which we get ωj ≥ 0, j = 1, 2, . . . , n, and 1j=1 ωj = 1. Note that the weight vector derived from Eq. (5.17) is a monotonic decreasing sequence, the weight vector derived from Eq. (5.18) is a monotonic increasing sequence, and the weight vector derived fromEq. (5.19) combine   the above two ˙ ˜ cases, i.e., the closer the value dITD a˜ σ (j) , bσ (j) to the mean dITD a˜ σ (j) , b˜ σ (j) , the larger the weight ωj . Clearly, the fundamental characteristic of the ITWD operator is that it considers the importance of each given interval 2-tuple distance, whereas the fundamental characteristic of the ITOWD operator is the reordering step, and it weights all the ordered positions of the interval 2-tuple distances instead of weighting the given interval 2-tuple distances themselves. Motived by the idea of the linguistic hybrid

5.3 Interval 2-Tuple Linguistic Distance Operators

121

geometric averaging (LHGA) operator (Xu 2005), in the following, we develop an ITHWD operator that weights both the given interval 2-tuple distances and their ordered positions. Definition 5.12 An ITHWD operator of dimension n is a mapping ITHWD:S˜ n × ˆ that has an associated weight vector ω=(ω1 , ω2 , . . . , ωn )T , with ωj ∈ [0, 1] S˜ n → S, n and j=1 ωj = 1, such that n          ωj dITD a˙˜ σ (j) , b˙˜ σ (j) , ITHWD a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n =

(5.20)

j=1

  where dITD a˙˜ σ (j) , b˙˜ σ (j) is the jth largest of the weighted interval 2       tuple distance dITD a˙˜ i , b˙˜ i dITD a˙˜ i , b˙˜ i = nwi dITD a˜ i , b˜ i , i = 1, 2, . . . , n , w =   (w1 , w2 , . . . , wn )T is the weight vector of dITD a˜ i , b˜ i (i = 1, 2, . . . , n), with wi ∈  [0, 1] and ni=1 wi = 1, and n is the balancing coefficient. Especially, if w = (1/n, 1/n, . . . , 1/n)T , then the ITHWD is reduced to the ITOWD operator; if ω = (1/n, 1/n, . . . , 1/n)T , then the ITHWD is reduced to the ˆ then the ITHWD ITWD operator. Moreover, if A˜ and B˜ are degenerated to Aˆ and B, is reduced to the 2-tuple hybrid weighted distance (THWD) operator: n          ˙ ωj dTD a˙ˆ σ (j) , bˆ σ (j) , THWD aˆ 1 , bˆ 1 , aˆ 2 , bˆ 2 , . . . , aˆ n , bˆ n =

(5.21)

j=1

  ˙ dTD a˙ˆ σ (j) , bˆ σ (j) is the jth largest of the weighted 2-tuple        ˙ ˙ distance dTD a˙ˆ j , bˆ j dTD a˙ˆ j , bˆ j = nwi dTD aˆ i , bˆ i , i = 1, 2, . . . , n , w =   ˙ T (w1 , w2 , . . . , wn ) is the weight vector of dTD a˙ˆ j , bˆ j (i = 1, 2, . . . , n), with  wi ∈ [0, 1] and ni=1 wi = 1, and n is the balancing coefficient.

where

5.3.2 Generalizations of the ITOWD Operator In what follows, generalizations of the ITOWD operator are presented by using the generalized and the quasi-arithmetic means. Definition 5.13 A GITOWD operator of dimension n is a mapping GITOWD:S˜ n × ˆ that has an associated weight vector ω=(ω1 , ω2 , . . . , ωn )T , with ωj ∈ [0, 1] S˜ n → S, n and j=1 ωj = 1, such that

122

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

⎛ ⎞1/λ n         λ a˜ σ (j) , b˜ σ (j) ⎠ , GITOWD a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = ⎝ ωj dITD 

j=1

(5.22)     where dITD a˜ σ (j) , b˜ σ (j) is the jth largest of the interval 2-tuple distance dITD a˜ i , b˜ i , and λ is a parameter such that λ ∈ (−∞, +∞) − {0}. Similar to the OWA and the GOWA operators (Yager 1988, 2004), the GITOWD operator has many desirable properties, such as commutativity, monotonicity, boundedness and idempotency. Especially, if there are ties between interval 2-tuple distances, as in the case of the ITOWD operator, we replace each of the tied arguments by their generalized mean in the process of aggregation. If A˜ and B˜ are degenˆ then we can get the generalized 2-tuple ordered weighted distance erated to Aˆ and B, (GTOWD) operator. The GITOWD operator provides a parameterized family of aggregation operators. In order to study this family, we can analyze the weighting vector ω or the parameter λ. By choosing a different manifestation of the weighting vector in the GITOWD operator, we are able to obtain different types of distance operators: • The interval 2-tuple maximum distance is found if ω1 = 1 and ωj = 0, for all j = 1. • The interval 2-tuple minimum distance if ωn = 1 and ωj = 0, for all j = n. • The generalized interval 2-tuple normalized distance (GITND) operator is formed when ωj = 1/n for all j. • The generalized interval 2-tuple distance (GITWD) operator is obtained  weighted  ˜ when the position of the dITD a˜ i , bi is the same as the ordered position of the   dITD a˜ σ (j) , b˜ σ (j) . Some special cases can also be obtained as the change of the parameter λ: • If λ = 1, then the GITOWD is reduced to the ITOWD operator. • If λ → 0, then the GITOWD is reduced to the interval 2-tuple ordered weighted geometric distance (ITOWGD) operator. • If λ = −1, then the GITOWD is reduced to the interval 2-tuple ordered weighted harmonic distance (ITOWHD) operator. • If λ = 2, then the GITOWD is reduced to the interval 2-tuple ordered weighted Euclidean distance (ITOWED) operator. • If λ = 3, then the GITOWD is reduced to the interval 2-tuple ordered weighted cubic distance (ITOWCD) operator. Definition 5.14 A Quasi-ITOWD operator of dimension n is a mapping Quasiˆ that has an associated weight vector ω=(ω1 , ω2 , . . . , ωn )T , ITOWD:S˜ n × S˜ n → S, n ωj = 1, such that with ωj ∈ [0, 1] and j=1

5.3 Interval 2-Tuple Linguistic Distance Operators

123

⎛ ⎞ n           −1 Quasi - ITOWD a˜ 1 , b˜ 1 , a˜ 2 , b˜ 2 , . . . , a˜ n , b˜ n = g ⎝ ωj g dITD a˜ σ (j) , b˜ σ (j) ⎠, j=1

(5.23)     where dITD a˜ σ (j) , b˜ σ (j) is the jth largest of the interval 2-tuple distance dITD a˜ i , b˜ i , andg is a general continuous strictly monotone function. As we can see, the GITOWD operator is a particular case of the Quasi-ITOWD ˆ then we can get the operator when g(x) = xλ . If A˜ and B˜ are degenerated to Aˆ and B, quasi-arithmetic 2-tuple ordered weighted distance (Quasi-TOWD) operator. Note that all properties and particular cases commented in the GITOWD operator can also be discussed in this generalization.

5.4 The Proposed GSES Method In this section, we develop an approach based on the proposed interval 2-tuple linguistic distance operators for solving multi-criteria group GSES problems. Suppose that a green supplier selection problem has l decision makers DMk (k = 1, 2, . . . , l), m alternatives Ai (i = 1, 2, . . . , m), and n decision criteria Cj (j = 1, 2, . . . , n). Each decision maker DMk is given a weight vk >  0(k = 1, 2, . . . , l) satisfying lk=1  vk = 1 to reflect his/her relative importance in the GSES process. Let Dk = dijk

m×n

be the linguistic decision matrix of the

kth decision maker, where dijk is the linguistic information provided by DMk on the assessment of Ai with respect to Cj . In addition, decision makers may use different linguistic term sets to express their assessment values. Next, we apply the ITWA and the GITOWD operators for multi-criteria group green supplier selection under interval 2-tuple linguistic environment.   into the interval Step 1 Convert the linguistic decision matrix Dk = dijk     m×n    2-tuple linguistic decision matrix R˜ k = r˜ijk = rijk , 0 , tijk , 0 , where m×n m×n   k k k k rij , tij ∈ S, S = s0 , s1 , . . . , sg and rij ≤ tij . Suppose that DMk provides his assessments in a set of five linguistic terms S S = {s0 = V ery poor, s1 = Poor, s2 = Medium , s3 = Good , s4 = V ery good }. The linguistic information provided in the decision matrix Dk can be converted into corresponding interval 2-tuple linguistic assessments according to the following ways: • A certain grade such as Poor, which can be written as [(s1 , 0), (s1 , 0)]; • An interval such as Poor-Medium, which means that the assessment of an alternative concerning the criterion under consideration is between Poor and Medium. This can be expressed as [(s1 , 0), (s2 , 0)].

124

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

In particular GSES problems, there exist many situations where information may be unquantifiable due to its nature, or the precise quantitative information may be unavailable or the cost for its computation is too high. Thus, it is more reasonable and nature for decision makers to make their judgments by using linguistic expressions. Generally, three main methods have been introduced for dealing with qualitative assessments (Herrera and Martínez 2000; Martínez and Herrera 2012; Wang et al. 2016). The first method is based on membership functions (Zadeh 1975), which converts linguistic information into fuzzy numbers by means of a membership function. However, this method led to a certain degree of information loss in the transformation process. The second method is based on linguistic symbols (Xu and Xia 2011) that made computations on the subscripts of linguistic terms and was easy to operate. However, this approach may lead to inflexibility for different semantics. The third method is based on linguistic 2-tuples (Shan et al. 2016), which can avoid the information distortion and loss in linguistic information processing and has been widely utilized for managing linguistic MCDM problems. Therefore, to deal with linguistic information more reasonably and accurately, the decision maskers’ assessments on alternative suppliers are first transformed into interval 2-tuples in the proposed approach. Step 2 Utilize the ITWA operator   



rij , αij , tij , εij = ITWA r˜ij1 , r˜ij2 , . . . , r˜ijl  l  l       −1 k −1 k = vk  rij , 0 , vk  tij , 0 , i = 1, 2, . . . , m, j = 1, 2, . . . , n,

r˜ij =

k=1

k=1

(5.24) to aggregate the interval 2-tuple linguistic decision matrices R˜ k (k  = 1, 2, . . . , l) into a collective interval 2-tuple linguistic decision matrix R˜ = r˜ij m×n . Step 3 Determine the ideal level of each criterion in order to characterize the 

collective ideal alternative r˜ ∗ = r˜1∗ , r˜2∗ , . . . , r˜n∗ , where r˜j∗ =

    rj∗ , αj∗ , tj∗ , εj∗ ,

j = 1, 2, . . . , n.

(5.25)

Step 4 Calculate the separation measure Si+ of each alternative from the ideal alternative by using the GITOWD operator:   ! " ! " Si+ = GITOWD r˜i1 , r˜1∗ , r˜i2 , r˜2∗ , . . . , r˜ij , r˜j∗ ⎛ ⎞1/λ n    λ =⎝ r˜iσ (j) , r˜σ∗ (j) ⎠ , i = 1, 2, . . . , m, ωj dITD j=1

(5.26)

5.4 The Proposed GSES Method

125

  λ r˜iσ (j) , r˜σ∗ (j) is the jth largest of the interval 2-tuple distance where dITD   dITD r˜ij , r˜j∗ ,ω = (ω1 , ω2 , . . . , ωn )T is the weighting vector of the GITOWD oper ator such that ωj ∈ [0, 1] and nj=1 ωj = 1. Note that it is possible to consider a wide range of GITOWD operators such as those described in the previous section. Step 5 Rank all the alternatives Ai (i = 1, 2, . . . , m) and select the best one(s) according to the increasing order of their separation measures.

5.5 An Illustrative Example 5.5.1 Example Illustration In this section, we develop an illustrative example of the new approach in a group decision making problem of green supplier selection. Suppose that a tertiary care hospital desires to select the most appropriate green supplier for one of the key medical devices in the general anesthesia process. After preliminary screening, six suppliers,Ai (i = 1, 2, . . . , 6), have remained as alternatives for further evaluation. In order to evaluate the alternative suppliers and select the best one, an expert committee of three decision makers, DM1 , DM2 and DM3 , has been formed. The selection decision is made on the basis of one objective and five criteria Cj (j = 1, 2, . . . , 5). These criteria, which are critical for the supplier selection, are defined below: C1 : Technical capability; C2 : Delivery performance; C3 : Product quality; C4 : Flexibility; C5 : Price/Cost. The three decision makers employ different linguistic term sets to assess the suitability of the suppliers with respect to the above selection criteria. Specifically, DM1 provides his assessments by using the linguistic term set A; DM2 provides his assessments using B; DM3 provides her assessments using C. These linguistic term sets are denoted as follows: A = {a0 = V ery poor(V P), a1 = Poor(P), a2 = Medium(M ), a3 = Good (G)} a4 = V ery good (V G)}, B = {b0 = V ery poor(V P), b1 = Poor(P), b2 = Medium poor(MP), b3 = Medium(M ), b4 = Medium good (MG), b5 = Good (G), b6 = V ery good (V G)}. C = {c0 = Extra poor(EP), c1 = V ery poor(V P), c2 = Poor(P), c3 = Medium poor(MP), c4 = Medium(M ), c5 = Medium good (MG), c6 = Good (G), c7 = V ery good (V G), c8 = Extra good (EG)},

126

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

The linguistic assessments of the six alternatives on each criterion provided by the three decision makers are presented in Table 5.1. With this information, we can make an aggregation in order to make a decision. First, we convert the linguistic decision  matrix shown   in Table  5.1 into the interval k k ˜ rij , 0 , tij , 0 , which is depicted 2-tuple linguistic decision matrix Rk = 6×5

in Table 5.2. Then, we aggregate the information of the three experts to obtain a collective interval 2-tuple linguistic decision matrix. We use the ITWA operator to obtain this matrix while assuming that v = (0.3, 0.4, 0.3)T . The results are shown in Table 5.3. According to their objectives, the group of experts establishes a collective ideal supplier as shown in Table 5.4. It is now possible to develop different methods based on the GITOWD operator for the selection of the optimum green supplier. In this example, we consider the interval 2-tuple maximum distance, the interval 2-tuple minimum distance, the ITND, the ITWD, the ITHWD, the ITOWD, the ITOWGD, the ITOWHD, the ITOWED and the ITOWCD operators. For convenience, we assume the following weighting vector ω = (0.112, 0.236, 0.304, 0.236, 0.112)T , which is derived by the normal distribution-based method (Xu 2005). The aggregated results are presented Table 5.1 Linguistic assessments of the suppliers Decision makers DM1

DM2

DM3

Alternatives

Criteria C1

C2

C3

C4

C5

A1

G-VG

M-G

G

M

G

A2

VG

G

VG

M-G

G

A3

M

M

P-M

G-VG

M

A4

G

G-VG

M

G

G-VG

A5

M

VG

G

VG

G

A6

G

M-G

VG

G

M-G

A1

VG

M

G-VG

M

G

A2

MG

VG

G

MG

MG

A3

M-G

MG

M

MG

G

A4

G

VG

G

MG-G

M

A5

M-G

M

G

VG

VG

A6

MG

M-G

G

G

VG

A1

M-MG

G

MG

G

M

A2

VG

VG

MG

VG

G

A3

VG

M

G

MG

VG

A4

EG

VG

G

G

VG

A5

G

MG

G-VG

G

MG

A6

M

M-G

G

G

MG

5.5 An Illustrative Example

127

Table 5.2 Interval 2-tuple linguistic decision matrix Decision makers

Alternatives

DM1

DM2

DM3

Criteria C1

C2

C3

C4

C5

A1

[(a3 ,0), (a4 ,0)]

[(a2 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

[(a2 ,0), (a2 ,0)]

[(a3 ,0), (a3 ,0)]

A2

[(a4 ,0), (a4 ,0)]

[(a3 ,0), (a3 ,0)]

[(a4 ,0), (a4 ,0)]

[(a2 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

A3

[(a2 ,0), (a2 ,0)]

[(a2 ,0), (a2 ,0)]

[(a1 ,0), (a2 ,0)]

[(a3 ,0), (a4 ,0)]

[(a2 ,0), (a2 ,0)]

A4

[(a3 ,0), (a3 ,0)]

[(a3 ,0), (a4 ,0)]

[(a2 ,0), (a2 ,0)]

[(a3 ,0), (a3 ,0)]

[(a3 ,0), (a4 ,0)]

A5

[(a2 ,0), (a2 ,0)]

[(a4 ,0), (a4 ,0)]

[(a3 ,0), (a3 ,0)]

[(a4 ,0), (a4 ,0)]

[(a3 ,0), (a3 ,0)]

A6

[(a3 ,0), (a3 ,0)]

[(a2 ,0), (a3 ,0)]

[(a4 ,0), (a4 ,0)]

[(a3 ,0), (a3 ,0)]

[(a2 ,0), (a3 ,0)]

A1

[(b6 ,0), (b6 ,0)]

[(b3 ,0), (b3 ,0)]

[(b5 ,0), (b6 ,0)]

[(b3 ,0), (b3 ,0)]

[(b5 ,0), (b5 ,0)]

A2

[(b5 ,0), (b5 ,0)]

[(b6 ,0), (b6 ,0)]

[(b5 ,0), (b5 ,0)]

[(b4 ,0), (b4 ,0)]

[(b4 ,0), (b4 ,0)]

A3

[(b3 ,0), (b5 ,0)]

[(b4 ,0), (b4 ,0)]

[(b3 ,0), (b3 ,0)]

[(b4 ,0), (b4 ,0)]

[(b5 ,0), (b5 ,0)]

A4

[(b5 ,0), (b5 ,0)]

[(b6 ,0), (b6 ,0)]

[(b5 ,0), (b5 ,0)]

[(b4 ,0), (b5 ,0)]

[(b3 ,0), (b3 ,0)]

A5

[(b3 ,0), (b5 ,0)]

[(b3 ,0), (b3 ,0)]

[(b5 ,0), (b5 ,0)]

[(b6 ,0), (b6 ,0)]

[(b6 ,0), (b6 ,0)]

A6

[(b4 ,0), (b4 ,0)]

[(b3 ,0), (b5 ,0)]

[(b5 ,0), (b5 ,0)]

[(b5 ,0), (b5 ,0)]

[(b6 ,0), (b6 ,0)]

A1

[(c4 ,0), (c5 ,0)]

[(c6 ,0), (c6 ,0)]

[(c5 ,0), (c5 ,0)]

[(c6 ,0), (c6 ,0)]

[(c4 ,0), (c4 ,0)]

A2

[(c7 ,0), (c7 ,0)]

[(c7 ,0), (c7 ,0)]

[(c5 ,0), (c5 ,0)]

[(c7 ,0), (c7 ,0)]

[(c6 ,0), (c6 ,0)]

A3

[(c7 ,0), (c7 ,0)]

[(c4 ,0), (c4 ,0)]

[(c6 ,0), (c6 ,0)]

[(c5 ,0), (c5 ,0)]

[(c7 ,0), (c7 ,0)]

A4

[(c8 ,0), (c8 ,0)]

[(c7 ,0), (c7 ,0)]

[(c6 ,0), (c6 ,0)]

[(c6 ,0), (c6 ,0)]

[(c7 ,0), (c7 ,0)]

A5

[(c6 ,0), (c6 ,0)]

[(c5 ,0), (c5 ,0)]

[(c6 ,0), (c7 ,0)]

[(c6 ,0), (c6 ,0)]

[(c5 ,0), (c5 ,0)]

A6

[(c4 ,0), (c4 ,0)]

[(c4 ,0), (c6 ,0)]

[(c6 ,0), (c6 ,0)]

[(c6 ,0), (c6 ,0)]

[(c5 ,0), (c5 ,0)]

128

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

Table 5.3 Collective interval 2-tuple linguistic decision matrix C1

C2

C3

C4

C5

A1

[0.775, 0.888] [0.575, 0.650] [0.746, 0.813] [0.575, 0.575] [0.708, 0.708]

A2

[0.896, 0.896] [0.888, 0.888] [0.821, 0.821] [0.679, 0.754] [0.717, 0.717]

A3

[0.613, 0.746] [0.567, 0.567] [0.500, 0.575] [0.679, 0.754] [0.746, 0.746]

A4

[0.858, 0.858] [0.888, 0.963] [0.708, 0.708] [0.717, 0.783] [0.688, 0.763]

A5

[0.575, 0.708] [0.688, 0.688] [0.783, 0.821] [0.925, 0.925] [0.813, 0.813]

A6

[0.642, 0.642] [0.500, 0.783] [0.858, 0.858] [0.783, 0.783] [0.738, 0.813]

Table 5.4 Collective ideal supplier r˜ ∗

C1

C2

C3

C4

C5

[0.8, 0.9]

[0.9, 1]

[0.8, 0.9]

[0.9, 1]

[0.8, 0.9]

in Tables 5.5 and 5.6 and the rankings of the alternative suppliers for each particular case are shown in Table 5.7. As we can see, depending on the distance operator used, the ranking orders of the six suppliers are different. Due to the fact that each particular type of the GITOWD operator may lead to different results, a decision maker can select for his decision the one that is in closest accordance with his interests. However, in this example, Table 5.5 Aggregated results 1 Alternatives

Max

Min

ITND

ITWD

ITHWD

A1

[0.375]

[0.019]

[0.189]

[0.208]

[0.196]

A2

[0.233]

[0.050]

[0.106]

[0.106]

[0.092]

A3

[0.383]

[0.104]

[0.241]

[0.271]

[0.273]

A4

[0.200]

[0.025]

[0.108]

[0.116]

[0.109]

A5

[0.263]

[0.048]

[0.124]

[0.117]

[0.101]

A6

[0.308]

[0.050]

[0.162]

[0.159]

[0.145]

Table 5.6 Aggregated results 2 Alternatives

ITOWD

ITOWGD

ITOWHD

ITOWED

ITOWCD

A1

[0.184]

[0.131]

[0.080]

[0.224]

[0.252]

A2

[0.094]

[0.080]

[0.071]

[0.111]

[0.128]

A3

[0.240]

[0.224]

[0.208]

[0.253]

[0.265]

A4

[0.108]

[0.091]

[0.072]

[0.121]

[0.130]

A5

[0.111]

[0.084]

[0.068]

[0.140]

[0.162]

A6

[0.158]

[0.136]

[0.115]

[0.176]

[0.191]

5.5 An Illustrative Example

129

Table 5.7 Rankings of the alternative suppliers Operators

Ranking

Operators

Ranking

Max

A4  A2  A5  A6  A1  A3

ITOWD

A2  A4  A5  A6  A1  A3

Min

A1  A4  A5  A6 = A2  A3

ITOWGD

A2  A5  A4  A1  A6  A3

ITND

A2  A4  A5  A6  A1  A3

ITOWHD

A5  A2  A4  A1  A6  A3

ITWD

A2  A4  A5  A6  A1  A3

ITOWED

A2  A4  A5  A6  A1  A3

ITHWD

A2  A5  A4  A6  A1  A3

ITOWCD

A2  A4  A5  A6  A1  A3

it is clear that the best choice is A2 , although in some exceptional situations the alternative suppliers such as A1 , A4 or A5 could be optimal.

5.5.2 Comparative Discussion To further evaluate the proposed GSES method, we conduct a comparative analysis with some previous linguistic decision making methods, which include the one based on the uncertain linguistic weighted averaging (ULWA) and the uncertain linguistic hybrid aggregation (ULHA) operators (Xu 2004), the one based on the uncertain linguistic weighted geometric mean (ULWGM) and the uncertain linguistic hybrid geometric mean (ULHGM) operators (Wei 2009), and the one based on the uncertain linguistic weighted harmonic mean (ULWHM) and the uncertain linguistic hybrid harmonic mean (ULHHM) operators (Park et al. 2011). The ranking results of the six alternatives derived by using these methods are presented in Table 5.8. Note that the linguistic term set S = {s0 , s1 , . . . , s6 } is used for evaluating alternative suppliers in the compared methods. From Table 5.8, it can be observed that the ranking orders of the alternatives obtained by the methods of Xu (2004) and Wei (2009) are exactly the same as those determined by the proposed approach when the ITND, the ITWD, the ITOWD, the ITOWED and the ITOWCD operators are applied. Further, the ranking of Park et al. Table 5.8 Ranking comparisons Alternatives

Xu (2004)’s method

Wei (2009)’s method

Park et al. (2011)’s method

r˜j

Ranking

r˜j

Ranking

r˜j

A1

[s4.13 , s4.29 ]

5

[s3.98 , s4.11 ]

5

[s3.88 , s3.99 ] 5

A2

[s5.00 , s5.00 ]

1

[s4.85 , s4.85 ]

1

[s4.82 , s4.82 ] 1

A3

[s3.86 , s3.98 ]

6

[s3.67 , s3.76 ]

6

[s3.49 , s3.56 ] 6

A4

[s4.83 , s4.97 ]

2

[s4.67 , s4.81 ]

2

[s4.54 , s4.67 ] 3

A5

[s4.80 , s4.93 ]

3

[s4.61 , s4.75 ]

3

[s4.55 , s4.67 ] 2

A6

[s4.53 , s4.72 ]

4

[s4.37 , s4.59 ]

4

[s4.28 , s4.50 ] 4

Ranking

130

5 GSES Using Interval 2-Tuple Linguistic Distance Operators

(2011)’s approach is in line with the proposed method using the ITHWD operator. Thus, the proposed GSES method is validated. However, compared with the listed methods, the proposed approach using interval 2-tuple linguistic distance operators is more reasonable and flexible for solving green supplier selection problems because: • It has exact characteristic in linguistic information processing and can effectively avoid the loss and distortion of information in traditional linguistic computational models. • The linguistic term sets with different granularity of uncertainty can be used by decision makers for assessing alternatives. This enables decision makers to express their judgments more realistically. • By using a wide range of distance operators, we can take different potential situations into consideration and provide a more complete picture for GSES. Thus, it is easier to select the alternative that better fits the interests of a decision maker.

5.6 Chapter Summary In this chapter, we developed some interval 2-tuple linguistic distance operators including the ITWD, the ITOWD, and the ITHWD operators. These distance operators are very suitable to deal with the decision information represented in interval 2-tuple arguments under multi-granular linguistic context. We gave three ways to determine the associated weighting vectors and studied some desired properties of the ITOWD operator. Moreover, further generalizations of the ITOWD operator were presented by using the generalized and the quasi-arithmetic means. The results are the GITOWD and the Quasi-ITOWD operators. Finally, we applied the developed interval 2-tuple linguistic distance operators to multi-criteria group green supplier selection with interval 2-tuple linguistic information. A case example from the healthcare industry was given to verify the developed GSES method and to demonstrate its practicality and effectiveness. The results showed that the proposed approach provides more complete information for decision making because it can consider a wide range of future scenarios according to the interests of a decision maker.

References Ahn BS, Park H (2008) Least-squared ordered weighted averaging operator weights. Int J Intell Syst 23(1):33–49 Ejegwa PA (2020) Modified Zhang and Xu’s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems. Neural Comput Appl 32:10199–10208 Ero˘glu H, Sahin ¸ R (2020) A neutrosophic VIKOR method-based decision-making with an improved distance measure and score function: case study of selection for renewable energy alternatives. Cogn Comput 12(6):1338–1355 Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752

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Chapter 6

GSES Using Interval 2-Tuple Linguistic VIKOR Method

Green supplier selection can be regarded as a complex group multiple criteria decision making problem requiring consideration of a number of alternative suppliers and quantitative and qualitative criteria. Additionally, decision makers cannot easily express their judgments on the alternatives with exact numerical values in many practical situations, and there usually exists uncertain and incomplete assessments. In response, this chapter proposes an extended VIKOR method for GSES with interval 2-tuple linguistic information. The feasibility and practicability of the proposed interval 2-tuple linguistic VIKOR (ITL-VIKOR) method are demonstrated through two realistic examples and comparisons with the existing approaches. Results show that the ITL-VIKOR method being proposed is more suitable and effective to handle the green supplier selection problems under vague, uncertain and incomplete information environment.

6.1 Introduction Supply chain management is the strategic coordination of supply chain for the purpose of integrating supply and demand management (Chu and Varma 2012; Lee et al. 2015). It aims to reduce supply chain risk and uncertainty, diminish production costs, and optimize inventory levels, business processes, and cycle times, thus resulting in increased competitiveness, customer satisfaction and profitability (Boran et al. 2009). A supply chain is a network of suppliers, manufacturing plants, warehouses, and distribution channels organized to extract raw materials, convert these raw materials into intermediate and finished products, and distribute the finished products to customers (Bidhandi et al. 2009). With the competition between companies evolved to competition between supply chains, green supplier selection has received a great deal of attention of both researchers and practitioners nowadays (Bektur 2020; Çalık 2020; Ecer 2020; Ecer and Pamucar 2020; Zhang et al. 2020).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_6

133

134

6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

In the literature, a variety of approaches have been suggested to construct effective green supplier systems. A detailed review and classification of the GSES methods can be found in Chap. 2. Under many conditions, however, exact data are inadequate to model real-life situations because of the complexity of GSES problems. Therefore, fuzzy set theory (Zadeh 1965) was incorporated to deal with the vagueness and ambiguity in GSES process (Ecer and Pamucar 2020; Jain and Singh 2020; Pourjavad and Shahin 2020). Previous studies have made significant contributions to green supplier selection; however, the majority of researchers concentrated on the methods applying linguistic value by using fuzzy logic to handle the uncertainty in real situations. As a result, an approximation process must be developed to express the results in the initial expression domain, which produces a loss of information and hence a lack of precision in the final results (Herrera and Martínez 2000; Liu et al. 2013). Furthermore, decision makers are often unsure of their preferences during the GSES process because of the reasons such as time pressure, lack of experience and data. They often demonstrate different evaluations or opinions from one to another and produce different types of assessment information for a certain alternative concerning a given criterion, some of which may be imprecise, uncertain and incomplete. These different types of information are very hard to incorporate into the green supplier selection by using the crisp and fuzzy logic approaches. Whereas, the interval 2-tuple linguistic representation model (Zhang 2012; Liu et al. 2014) overcomes the above-mentioned weaknesses. The advantages of this model are that decision makers can express their preferences by the use of linguistic term sets with different granularity of uncertainty and/or semantics (multigranular linguistic contexts), and their judgments can be expressed with an interval 2-tuple from the predefined linguistic term set. Therefore, the interval 2-tuple linguistic representation model will be more flexible and precise to deal with linguistic terms in solving the GSES problems. In other way, many quantitative and qualitative criteria (or factors) should be taken into consideration when selecting green suppliers for an organization, including price, quality, delivery, service, reputation, and so on (Hemmati and Pasandideh 2020; Hoseini et al. 2020; Krishankumar et al. 2020; You et al. 2020). In order to select the optimum suppliers, it is necessary to make balance among these tangible and intangible factors some of which may conflict and compete like low price versus high quality. Moreover, there may be multiple decision makers taking part in the evaluation of alternatives together during the green supplier selection process. Therefore, GSES is a kind of group multiple criteria decision making (MCDM) problem (Deng et al. 2014) and MCDM techniques can be utilized to solve the green supplier selection problem of an organization. The VIKOR method, a very useful technique for MCDM, was first developed by Opricovic (1998) to solve a discrete decision problem with noncommensurable and conflicting criteria. This method focuses on ranking and selecting from a set of alternatives, and determines compromise solutions for a problem with conflicting criteria, which can help the decision makers to reach a final decision (Opricovic and Tzeng 2007, 2004). The main advantages of the VIKOR method are that it introduces a multi-criteria ranking index based on the particular measure of “closeness” to the ideal solution and the obtained compromise

6.1 Introduction

135

solution provides a maximum group utility for the “majority” and a minimum individual regret for the “opponent” (Arya and Kumar 2020; Ero˘glu and Sahin ¸ 2020; Zhou et al. 2020). Due to its characteristics and capabilities, the VIKOR method has been widely studied and applied in group decision making problems in recent years (Das et al. 2020; Ero˘glu and Sahin ¸ 2020; Khorram 2020; Krishankumar et al. 2020; Xu et al. 2020; Samanci et al. 2021). The background introduced above shows that it may be inappropriate to use fuzzy logic-based methods for evaluation and selection of green suppliers because of the loss of information in the linguistic information processing. Moreover, decision makers tend to use different linguistic term sets to express their judgments on the subjective criteria, and there usually exists uncertain and incomplete assessments. In response, this chapter develops a new group MCDM model using interval 2-tuple linguistic variables and extended VIKOR method to solve GSES problems under uncertain and incomplete information environment. The proposed method can not only avoid information distortion and loss which occur formerly in the linguistic information processing, but also model the diversity and uncertainty of the assessment information provided by decision makers in green supplier selection. Furthermore, both conflicting quantitative and qualitative criteria in real-life applications can be considered simultaneously in the developed method. The rest of this chapter is organized as follows. In Sect. 6.2, some basic concepts of interval 2-tuple linguistic variables are briefly reviewed. In Sect. 6.3, an extended VIKOR approach is proposed to solve the green supplier selection problem with interval 2-tuple linguistic information. Two numerical examples are provided in Sect. 6.4 to illustrate the proposed GSES approach and finally, some conclusions are summarized in Sect. 6.5.

6.2 Preliminary The basic concepts of 2-tuple linguistic variables (Chen and Tai 2005) and interval 2-tuple linguistic variables (Zhang 2012) were reviewed in Sect. 5.2. In this section, two additional definitions related to the GSES method being proposed in this chapter are introduced. Definition 6.1 (Herrera and Martínez 2000) Let X = {(r1 , α1 ), (r2 , α2 ), . . . , (rn , αn )} be a set of 2-tuples and w =  (w1 , w2 , . . . , wn )T be their associated weights, with wj ∈ [0, 1], j = 1, 2, . . . , n, nj=1 wj = 1. The 2-tuple weighted average (TWA) is defined as: ⎛

⎞ ⎛ ⎞ n n     1 1 TWA(X )⎝ wj −1 rj , αj ⎠ = ⎝ wj βj ⎠. n j=1 n j=1

(6.1)

136

6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

= {[(r1 , α1 ), (t1 , ε1 )], [(r2 , α2 ), (t2 , ε2 )], . . . , [(rn , αn ), (tn , εn )]} Definition 6.2 X               Let and X  = be two r1 , α1 , t1 , ε1 , r2 , α2 , t2 , ε2 , . . . , rn , αn , tn , εn sets of interval 2-tuples, then n              1  −1    

, X  =  D X  rj , αj − −1 rj , αj  + −1 tj , εj − −1 tj , εj  2

(6.2)

j=1

2 .

1 and X is called the distance between X

6.3 The Proposed GSES Method In this section, we present an extended VIKOR method to solve green supplier selection problems in which the criteria weights take the form of 2-tuple linguistic information, and the criteria values take the form of interval 2-tuple linguistic information. Suppose that a GSES problem has H decision makers DMh (h = 1, 2, . . . , H ), P alternatives Ap (p = 1, 2, . . . , P), and Q decision criteria Cq (q = 1, 2, . . . , Q). Each H decision maker DMh is given a weight λh > 0(h = 1, 2, . . . , H ) satisfying his/her h=1 λh = 1 to reflect   relative importance in the group green supplier selech tion process. Let Dh = dpq

P×Q

be the linguistic decision matrix of the hth decision

h dpq

is the linguistic information provided by DMh on the assessment T  of Ap with respect to Cq . Let vh = v1h , v2h , . . . , vQh be the linguistic weight vector

maker, where

given by the hth decision maker, where vqh is the linguistic variable assigned to Cq by DMh . In addition, decision makers may use different linguistic term sets to express their assessments. Based upon these assumptions or notations, the procedure of interval 2-tuple linguistic VIKOR (ITL-VIKOR) method for green supplier selection can be defined as the following steps:   h into an interval 2Step 1 Convert the linguistic decision matrix Dh = dpq     P×Q   h h h = rpq , 0 , tpq ,0 , where tuple linguistic decision matrix

Rh = r˜pq P×Q

P×Q

h h h h , tpq ∈ S, S = {si |i = 0, 1, 2, . . . , g } and rpq ≤ tpq . rpq Suppose that DMh provides his assessments in a set of five linguistic terms S = {s0 = V ery poor, s1 = Poor, s2 = Medium , s3 = Good , s4 = V ery good }. The linguistic information provided in the linguistic decision matrix Dk can be converted into corresponding interval 2-tuple linguistic assessments according to the following ways:

• A certain grade such as Poor, which can be written as [(s1 , 0), (s1 , 0)].

6.3 The Proposed GSES Method

137

• An interval such as Poor-Medium, which means that the assessment of an alternative with respect to the criterion under consideration is between Poor and Medium. This can be written as [(s1 , 0), (s2 , 0)]. • No judgment, which means the decision maker is not willing to or cannot provide an assessment for an alternative with respect to the criterion under consideration. In other words, the assessment by this decision maker could be anywhere between Very poor and Very good and can be expressed as [(s0 , 0), (s4 , 0)]. T  Step 2 Convert the linguistic weight vector vh = v1h , v2h , . . . , vQh into a 2-tuple   T    linguistic weight vector wh = w1h , 0 , w2h , 0 , . . . , wQh , 0 by Eq. (5.5), where wqh ∈ S, S = {si |i = 0, 1, 2, . . . , g }. Step 3 Aggregate decision makers’ opinions by using the ITWA  operator to construct a collective interval 2-tuple linguistic decision matrix

R = r˜pq P×Q , where     rpq , αpq , tpq , εpq             1 1 2 2 H H = ITWA rpq , 0 , tpq , 0 , rpq , 0 , tpq , 0 , . . . , rpq , 0 , tpq ,0  H H       h h λh −1 rpq ,0 , λh −1 tpq , 0 , p = 1, 2, . . . , P, q = 1, 2, . . . , Q. (6.3) =

r˜pq =

h=1

h=1

Step 4 Aggregate criteria weights by using the to determine an aggregated 2-tuple linguistic weight  T  (w1 , α1 ), (w2 , α2 ), . . . , wQ , αQ , where

TWA operator vector w =

  wq , αq = TWA(v1 , v2 , . . . , vH )  H     −1 h = λh  wq , 0 , q = 1, 2, . . . , Q.

(6.4)

k=1

Step 5 Determine the positive ideal solution (PIS) and the negative ideal solution (NIS) as:   r + = r1+ , r2+ , . . . , rQ+ ,

(6.5)

  r − = r1− , r2− , . . . , rQ− ,

(6.6)

where 

rq+ = rq+ , αq+



⎧ ⎫   ⎨ max tpq , εpq , for benefit criteria ⎬ p   = , q = 1, 2, . . . , Q, ⎩ min rpq , αpq , for cost criteria ⎭ p

(6.7)

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6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

⎧ ⎫    ⎨ min rpq , αpq , for benefit criteria ⎬  p   rq− = rq− , αq− = , q = 1, 2, . . . , Q. ⎩ max tpq , εpq , for cost criteria ⎭ p

(6.8)   Step 6 Compute the normalized 2-tuple linguistic distance d pq , αpq by Eq. (6.9). ⎞  ⎛   −1 d rq+ , r˜pq d pq , αpq = ⎝ −1  + −  ⎠, p = 1, 2, . . . , P, q = 1, 2, . . . , Q,  d rq , r˜q

(6.9)

where             1  −1  + +  rq , αq − −1 rpq , αpq  + −1 rq+ , αq+ − −1 tpq , εpq  , d rq+ , r˜pq =   2

        d rq+ , rq− = −1 rq+ , αq+ − −1 rq− , αq−  . 

(6.10) (6.11)

    Step 7 Compute the 2-tuples Sp , αp and Rp , αp , p = 1, 2, …, P, by the relations ⎛

⎞     −1 Q  ⎜ wq , αq ·  d pq , αpq ⎟   ⎜ ⎟ Sp , αp = ⎜ ⎟, Q ⎝ q=1 ⎠   −1   wq , αq −1

(6.12)

q=1

⎞⎞     −1 ⎜ ⎜  wq , αq ·  d pq , αpq ⎟⎟   ⎜ ⎜ ⎟⎟ Rp , αp = ⎜max⎜ ⎟⎟. Q q ⎝ ⎝ ⎠⎠   −1   wq , αq ⎛

⎛

−1

(6.13)

q=1

  Step 8 Compute the 2-tuples Op , αp , p = 1, 2,…, P, by the relation !       −1 Sp , αp − −1 (S ∗ , α ∗ ) −1 Rp , αp − −1 (R∗ , α ∗ ) , Op , αp =  μ −1  − −  + (1 − μ) −1  − −   S , α − −1 (S ∗ , α ∗ )  R , α − −1 (R∗ , α ∗ )

(6.14)         where (S ∗ , α ∗ ) = min Sp , αp , S − , α − = max Sp , αp , (R∗ , α ∗ ) = min Rp , αp , p p  p   − − R , α = max Rp , αp and v is introduced as a weight for the strategy of maximum p

6.3 The Proposed GSES Method

139

group utility, whereas 1-v is the weight of individual regret. The value of v is set to 0.5 in this chapter.       Step 9 Rank the alternatives by sorting the 2-tuples Sp , αp , Rp , αp and Op , αp in increasing order. The results are three ranking lists. (1) Step 10 Propose a compromise  solution, the alternative (A ), which is the best  ranked by the measure Op , αp (minimum) if the following two conditions are satisfied:           C1 Acceptable advantage: −1 O A(2) , α A(2) − −1 O A(1) , α A(1) ≥ (2) 1/(P −1), where A is the alternative with second position in the ranking list by Op , αp . (1) C2 Acceptable in decision   making: The alternative A must also be the  stability best ranked by Sp , αp or/and Rp , αp . This compromise solution is stable within a decision making process, which could be: “voting by majority rule” (when μ > 0.5 is needed), or “by consensus” μ ≈ 0.5, or “with veto” (μ < 0.5). If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: • Alternatives A(1) and A(2) if only the condition C2 is not satisfied or (M) • Alternatives A(1) , A(2) , …, A(M) the condition  if (M  (M )  C1 is−1not   satisfied;   A  is ) (1) (1) −1 ,α A − O A ,α A < determined by the relation  O A 1/(P − 1) for maximum M.

6.4 Illustrative Examples In this section, two real-life examples are provided to demonstrate and validate the application of the proposed method for solving GSES problems.

6.4.1 Example 1 A tertiary care university hospital, which is located in Shanghai, China, has carried out a risk analysis on the general anesthesia process (Liu et al. 2012) because its higher level of risk, and the results showed that the most important failure modes were mainly caused by a key anaesthetic equipment. Hence, this tertiary care hospital needs to determine a most appropriate green supplier for the equipment in order to improve the safety of general anesthesia process. After preliminary screening, five suppliers, named as A1 , A2 , A3 , A4 and A5 , have remained as alternatives for further evaluation. An expert committee of four decision makers, DM1 , DM2 , DM3 and DM4 , has been formed to select the best supplier. The selection decision is made on the basis of the following four criteria: technical capability (C1 ), delivery performance (C2 ), product quality (C3 ), and product price (C4 ).

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6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

The four decision makers employ different linguistic term sets to evaluate the alternatives with respect to the above criteria. Specifically, DM1 provides his assessments in the set of 5 labels, A; DM2 provides his assessments in the set of 7 labels, B; DM3 provides her assessments in the set of 9 labels, C; DM4 provides his assessments in the set of 5 labels, D. Additionally, the relative importance of criteria was rated by the four decision makers with a set of 5 linguistic terms, E. These linguistic term sets are denoted as follows: A = {a0 = V ery poor(V P), a1 = Poor(P), a2 = Medium(M ), a3 = Good (G)} a4 = V ery good (V G)}, B = {b0 = V ery poor(V P), b1 = Poor(P), b2 = Medium poor (MP), b3 = Medium(M ), b4 = Medium good (MG), b5 = Good (G), b6 = V ery good (V G) }. C = {c0 = Extreme poor(EP), c1 = V ery poor(V P), c2 = Poor(P), c3 = Medium poor(MP), c4 = Medium(M ), c5 = Medium good (MG), c6 = Good (G), c7 = V ery good (V G), c8 = Extreme good (EG)}, D = {d0 = V ery poor(V P), d1 = Poor(P), d2 = Medium(M ), d3 = Good (G)} d4 = V ery good (V G)}, E = {e0 = V ery unimportant(V U ), e1 = Unimportant(U ), e2 = Medium(M ), e3 = Important(I ), e4 = V ery important(V I )}. The assessments of the five alternatives on each criterion and the criteria weights provided by the four decision makers are presented in Tables 6.1 and 6.2, where ignorance information is highlighted and shaded. Considering their different domain knowledge and expertise, the four decision makers are assigned the following weights: 0.15, 0.20, 0.30, and 0.35 in the supplier selection process. Next, we utilize the proposed ITL-VIKOR method to derive the most desirable alternative, which includes the following steps: Step 1 Convert the linguistic decision matrix shown   in Table  6.1 into an interval h h

rpq , 0 , tpq , 0 . Taking DM1 as 2-tuple linguistic decision matrix Rh = 5×4

an example, we can get the interval 2-tuple linguistic decision matrix

R1 as shown in Table 6.3. Step 2 Convert the linguistic weight vector shown in Table 6.2 into a 2         T tuple linguistic weight vector wh = w1h , 0 , w2h , 0 , w3h , 0 , w4h , 0 , which is presented in Table 6.4.

6.4 Illustrative Examples

141

Table 6.1 Linguistic assessments of alternatives provided by decision makers Decision makers

Alternatives

DM1

DM2

Criteria C1

C2

C3

C4

A1

M-G

G

G

M-G

A2

G

M

A3

M-G

M-G

G

G

A4

G

VG

M-G

M-G

A5

G-VG

VG

G

G

A1

VG

M

MG

G

M-MG

MG

VG

A3

G

G

MG-G

MG-G

A4

MG

MG

G

G

A5

G

G

G-VG

M

A1

MG-VG

MG

VG

MG

A2

G

M

MG

G

A3

M-G

G

A4

M

G

M

G

A5

G

G-EG

G-VG

M-MG

A1

G

M

G-VG

G

A2

G

M-G

M-G

G

A3

G

VG

G-VG

G

G

G

G

G-VG

VG

VG

M

A2

DM3

DM4

A4 A5

VG

G

Table 6.2 Linguistic assessments of criteria weights Criteria

Decision makers DM1

DM 2

DM 3

DM 4

C1

VI

I

I

VI

C2

I

I

I

I

C3

VI

VI

VI

VI

C4

M

I

M

I

Step 3 The evaluations of the five alternatives obtained from the four decision makers are aggregated by Eq. (6.3) and the collective interval 2-tuple linguistic decision matrix is provided in Table 6.5. Step 4 The criteria weights provided by the four decision makers are aggregated by Eq. (6.4) and the aggregated 2-tuple linguistic weights are listed in the last row of Table 6.5.

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6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

Table 6.3 Interval 2-tuple linguistic decision matrix of DM1 Alternatives

Criteria C1

C2

C3

C4

A1

[(a2 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

[(a2 ,0), (a3 ,0)]

A2

[(a3 ,0), (a3 ,0)]

[(a2 ,0), (a2 ,0)]

[(a0 ,0), (a4 ,0)]

[(a4 ,0), (a4 ,0)]

A3

[(a2 ,0), (a3 ,0)]

[(a2 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

A4

[(a3 ,0), (a3 ,0)]

[(a4 ,0), (a4 ,0)]

[(a2 ,0), (a3 ,0)]

[(a2 ,0), (a3 ,0)]

A5

[(a3 ,0), (a4 ,0)]

[(a4 ,0), (a4 ,0)]

[(a3 ,0), (a3 ,0)]

[(a3 ,0), (a3 ,0)]

Table 6.4 2-Tuple linguistic criteria weights Criteria

Decision makers DM1

DM 2

DM 3

DM 4

C1

(e4 ,0)

(e3 ,0)

(e3 ,0)

(e4 ,0)

C2

(e3 ,0)

(e3 ,0)

(e3 ,0)

(e3 ,0)

C3

(e4 ,0)

(e4 ,0)

(e4 ,0)

(e4 ,0)

C4

(e2 ,0)

(e3 ,0)

(e2 ,0)

(e3 ,0)

Table 6.5 Aggregated interval 2-tuple linguistic decision matrix Alternatives

Criteria C1

C2

C3

C4

A1

[0.725, 0.838]

[0.575, 0.575]

[0.771, 0.858]

[0.692, 0.729]

A2

[0.600, 0.800]

[0.500, 0.621]

[0.496, 0.733]

[0.838, 0.838]

A3

[0.654, 0.767]

[0.817, 0.854]

[0.508, 0.929]

[0.733, 0.767]

A4

[0.396, 0.746]

[0.771, 0.771]

[0.654, 0.692]

[0.729, 0.767]

A5

[0.767, 0.892]

[0.892, 0.967]

[0.854, 0.925]

[0.538, 0.575]

Weights

(0.70)

(0.60)

(0.80)

(0.51)

Step 5 Delivery performance, product quality and technical capability are benefit criteria and price is a cost criterion. Thus, the PIS and the NIS of the collective interval 2-tuple linguistic decision matrix are determined as: r + = ((0.8917), (0.9667), (0.9292), (0.5375)), r − = ((0.3958), (0.5000), (0.4958), (0.8375)).   Step 6 The normalized 2-tuple linguistic distances d pq , αpq are computed by Eq. (6.9) and shown in Table 6.6.

6.4 Illustrative Examples

143

Table 6.6 Normalized 2-tuple linguistic distances Alternatives

Criteria C1

C2

C3

C4

A1

(0.223)

(0.839)

(0.264)

(0.576)

A2

(0.387)

(0.871)

(0.726)

(1.000)

A3

(0.366)

(0.281)

(0.486)

(0.708)

A4

(0.647)

(0.420)

(0.591)

(0.701)

A5

(0.126)

(0.080)

(0.091)

(0.063)

Table 6.7 The 2-tuples (S p , α p ), (Rp , α p ) and (Op , α p ) of the five alternatives (S p , α p ) (Rp , α p ) (Op , α p )

A1

A2

A3

A4

A5

(0.623)

(0.766)

(0.387)

(0.536)

(0.089)

(b4 , −0.044)

(b5 , −0.067)

(b2 , 0.054)

(b3 , 0.036)

(b1 , −0.078)

(0.257)

(0.267)

(0.138)

(0.174)

(0.034)

(b2 , −0.076)

(b2 , −0.066)

(b1 , −0.029)

(b1 , 0.007)

(b0 , 0.034)

(0.873)

(1.000)

(0.445)

(0.63)

(0.000)

(b5 , 0.040)

(b6 , 0.000)

(b3 , −0.055)

(b4 , −0.037)

(b0 , 0.000)

      Steps 7 and 8 The 2-tuples Sp , αp , Rp , αp and Op , αp p = 1, 2, …, 5 are calculated by Eqs. (6.21) - (6.22) and the results are shown in Table   6.7.   Step 9 Rank the alternatives in accordance with the 2-tuples Sp , αp , Rp , αp   and Op , αp , referring to Definition 5.3. The ranking lists of the five alternatives are presented in Table 6.8. Step 10 As we can see from Table 6.8, the ranking order of the  five alternatives is A5  A3  A4  A1  A2 in accordance with the 2-tuples of Op , αp . Thus, the most desirable alternative is A5 . To illustrate the effectiveness of the proposed ITL-VIKOR, we used the above case study to analyze some existing supplier selection approaches, which include the fuzzy VIKOR (Sanayei et al. 2010), the fuzzy TOPSIS (Chen et al. 2006), the intuitionistic fuzzy TOPSIS (IF-TOPSIS) (Boran et al. 2009), and the interval ELECTRE (Vahdani et al. 2010) methods. Table 6.9 exhibits the ranking results of alternative suppliers as derived using these approaches. Table 6.8 Ranking of the alternative suppliers A1

A2

A3

A4

A5

By (S p , α p )

4

5

2

3

1

By (Rp , α p )

4

5

2

3

1

By (Op , α p )

4

5

2

3

1

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6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

Table 6.9 Ranking comparisons for example 1 Alternatives

ITL-VIKOR

Fuzzy VIKOR

Fuzzy TOPSIS

IF-VIKOR

Interval ELECTRE

A1

4

2

2

3

2

A2

5

5

5

5

5

A3

2

3

3

2

2

A4

3

4

4

4

4

A5

1

1

1

1

1

From the results given in Table 6.9, it can be observed that all the five methods suggest suppliers A5 and A2 as the first and last choices respectively. This demonstrates the validity of our suggested model. In addition, the rankings of alternatives by the fuzzy VIKOR are exactly the same as those by the fuzzy TOPSIS: A5  A1  A3  A4  A2 . Both the two methods suggest supplier A1 as the second choice and supplier A4 as the fourth choice, while supplier A3 ranks the second and A1 ranks the fourth by the proposed ITL-VIKOR method. This inconsistency can be understood by the fact that the fuzzy VIKOR and the fuzzy TOPSIS methods are based on the extension principle, which may produce the consequent loss of information and hence the lack of precision in the final results (Herrera and Martínez 2000; Liu et al. 2015). The main advantage of the proposed method is its computational model that offers linguistic results in the initial expression domain in a precise way. Taking the decision maker DM2 as an example, the final results can be expressed by 2-tuples derived from the linguistic term set B with 7 labels, which are listed in Table 6.7. The IF-TOPSIS method uses the concept of intuitionistic fuzzy sets and suggests that supplier A1 is better than supplier A4 . However, a close look at the values of the criteria for suppliers A1 and A4 in Table 6.6 reveals that supplier A4 is comparatively better than supplier A1 in the case of two criteria (i.e., C1 and C3 ). And both the two criteria have higher weights compared with the other criteria. Thus, proposing supplier A4 as the third choice and supplier A1 as the fourth choice which is given by the proposed method seems more logic than that proposed by the IF-TOPSIS method. Furthermore, the proposed method makes a provision to deal with quantitative criteria. But this was missing in the IF-TOPSIS method. In addition, using the interval ELECTRE method leads to supplier A1 as the second choice and supplier A4 as the fourth choice. However, both suppliers A1 and A3 rank the second and cannot be distinguished from each other according to the interval ELECTRE method. Also, the interval ELECTRE utilizes interval numbers to evaluate suppliers with respect to each criterion; but in some situations, decision makers are hard to express their evaluations in this way especially for qualitative criteria.

6.4 Illustrative Examples

145

6.4.2 Example 2 The first example only considers the subjective evaluations of decision makers in green supplier selection process, but in some situations, both quantitative and qualitative criteria are existed in a particular GSES problem. Thus, in what follows, an example of international supplier selection from (Wu 2009) is cited to further demonstrate the proposed ITL-VIKOR method. The same problem was also solved by Deng and Chan (2011) using a fuzzy dempster method. International supplier selection is a very important strategic decision involving decisions balancing a number of conflicting criteria, and these decisions are becoming ever more complex with the increase in outsourcing, offshore sourcing, and various electronic businesses. A group of three experts was identified in the example to aid in the supplier selection (whose weighting vector is λ = (0.203, 0.281, 0.516)T ). The four criteria considered in the global supplier selection are: product late delivery (C1 ), cost (C2 ), risk factor (C3 ), and supplier service performance (C4 ). Product late delivery rate and cost are crisp values as outlined in Table 6.10, but risk factor and supplier service performance are fuzzy data for each alternative supplier. Here, the following linguistic term set is adopted to express the subjective evaluations of decision makers: Table 6.10 Alternative suppliers for example 2 (Wu 2009) Decision makers

Alternatives

C1

C2

C3

C4

DM1

A1

60

40

L

H

A2

60

40

M

M

A3

70

80

L

VH

A4

50

30

M

M

A5

90

130

VH

VL

A6

80

120

VL

VL

A1

60

40

M

H

A2

60

40

H

M

A3

70

80

L

VH

A4

50

30

M

M

A5

90

130

H

L

A6

80

120

L

VL

A1

60

40

M

H

A2

60

40

L

L

A3

70

80

L

H

A4

50

30

M

H

A5

90

130

V

L

A6

80

120

L

VL

DM2

DM3

Criteria

146

6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

Table 6.11 2-Tuple linguistic decision matrix of DM1 for example 2 Alternatives

Criteria C1

C2

C3

C4

A1

(0.667)

(0.308)

(s1 ,0)

(s3 ,0)

A2

(0.667)

(0.308)

(s2 ,0)

(s2 ,0)

A3

(0.778)

(0.615)

(s1 ,0)

(s4 ,0)

A4

(0.556)

(0.231)

(s2 ,0)

(s2 ,0)

A5

(1.000)

(1.000)

(s4 ,0)

(s0 ,0)

A6

(0.889)

(0.923)

(s0 ,0)

(s0 ,0)

S ={s0 = V ery low(V L), s1 = Low(L), s2 = Medium(M ), s3 = High(H ), s4 = V ery high(V H )}. Now, we implement the proposed method to get the most suitable alternative: Step 1 The linguistic evaluations of C3 and C4 for different suppliers are converted into 2-tuple linguistic variables by Eq. (5.5) and the objective data of C1 and C2 for the six suppliers are normalized first using the linear normalization method (Shih et al.    2007) rpq = xpq / maxp xpq and then converted into 2-tuple linguistic variables by Eqs. (5.1)–(5.2). Taking DM1 as an example, we can get the 2-tuple linguistic decision matrix R1 as shown in Table 6.11. It may be mentioned here that the 2-tuple linguistic variables are special cases of interval 2-tuple linguistic variables. Steps 2 and 4 According to the method suggested in (Deng and Chan 2011), the weights of the four criteria are determined as follows: w1 = 0.252, w2 = 0.307, w3 = 0.155, w4 = 0.286. Step 3 The objective information and subjective evaluations of the six alternatives are aggregated by Eq. (6.3) and the collective 2-tuple linguistic decision matrix is obtained as shown in Table 6.12. Table 6.12 Aggregated 2-tuple linguistic decision matrix for example 2 Alternatives

Criteria C1

C2

C3

C4

A1

(s3 , −0.083)

(s1 , 0.058)

(s2 , −0.051)

(s3 , 0)

A2

(s3 , −0.083)

(s1 , 0.058)

(s2 , −0.059)

(s1 , 0.121)

A3

(s3 , 0.028)

(s2 , 0.115)

(s1 , 0)

(s3 , 0.121)

A4

(s2 , 0.056)

(s1 , −0.019)

(s2 , 0)

(s3 , −0.121)

A5

(s4 , 0)

(s4 , 0)

(s4 , −0.07)

(s1 , −0.051)

A6

(s4 , −0.111)

(s4 , −0.077)

(s1 , −0.051)

(s0 , 0)

6.4 Illustrative Examples

147

Table 6.13 Normalized 2-tuple linguistic distances for example 2 Alternatives

Criteria C1

C2

C3

C4

A1

(s1 , 0)

(s0 , 0.1)

(s1 , 0.092)

(s1 , −0.111)

A2

(s1 , 0)

(s0 , 0.1)

(s1 , 0.082)

(s2 , 0.074)

A3

(s2 , 0)

(s2 , 0)

(s0 , 0.07)

(s0 , 0)

A4

(s0 , 0)

(s0 , 0)

(s2 , −0.088)

(s1 , 0.028)

A5

(s4 , 0)

(s4 , 0)

(s4 , 0)

(s3 , 0.021)

A6

(s3 , 0)

(s4 , −0.1)

(s0 , 0)

(s4 , 0)

Step 5 Product late delivery, cost, and risk factor are cost criteria and supplier service performance is a benefit criterion. Thus, the PIS and the NIS of the collective 2-tuple linguistic decision matrix are obtained as: r + = ((s1 , 0.043), (s1 , −0.103), (s1 , −0.051), (s3 , 0.121)), r − = ((s2 , 0.028), (s1 , −0.114), (s4 , −0.07), (s0 , 0)).   Step 6 The normalized 2-tuple linguistic distances d pq , αpq are computed by Eq. (6.9) as shown in Table 6.13.      Steps 7 and 8 The 2-tuples Sp , αp , Rp , αp and Op , αp , p = 1, 2, …, 5 are calculated by Eqs. (6.21) - (6.22) and the results are presented in Table  6.14.  , α , Rp , αp and Step 9 Rank alternatives in accordance with the 2-tuples S p p   Op , αp . The results are shown in Table 6.15 and compared with fuzzy VIKOR (Sanayei et al. 2010) and the methods suggested by (Wu 2009) and (Deng and Chan 2011). For the international supplier selection problem, all of the four methods give the top two ranks to suppliers A1 and A4 . This is because the first ranked alternative has no advantage to be a single solution. According to the results   ofthe proposed model, the first condition (C1) is not satisfied: −1 O A(2) , α A(2) −      1 −1 O A(1) , α A(1) < 6−1 , which indicates that both A1 and A4 are good suppliers and can be considered as the best compromise solutions in this example. The two examples presented above have demonstrated and validated the proposed method for dealing with GSES problems under different situations. From the analysis, Table 6.14 The (S p , α p ), (Rp , α p ) and (Op , α p ) of alternatives for example 2 A1

A2

(S p , α p )

(s1 , −0.064) (s1 , 0.059)

(Rp , α p )

(s0 , 0.063)

(Op , α p ) (s0 , 0.027)

A3

A4

A5

A6

(s1 , 0.04)

(s1 , −0.107) (s4 , −0.065) (s3 , 0.001)

(s1 , −0.086) (s1 , −0.096) (s0 , 0.08)

(s1 , 0.057)

(s1 , 0.036)

(s1 , 0.062)

(s4 , 0)

(s3 , 0.091)

(s1 , 0.028)

(s0, 0.034)

148

6 GSES Using Interval 2-Tuple Linguistic VIKOR Method

Table 6.15 Ranking comparisons for example 2 Alternatives

ITL-VIKOR

Fuzzy VIKOR

Wu (2009)

Deng and Chan (2011)

A1

1

1

2

2

A2

4

4

4

3

A3

3

3

3

4

A4

2

2

1

1

A5

6

6

6

6

A6

5

5

5

5

it can be concluded that the ranking orders of alternative suppliers given by the proposed method are more accurate and reliable. To sum up, the ITL-VIKOR method proposed in this chapter has the following advantages: • The proposed method has exact characteristic in linguistic information processing. It can effectively avoid the loss and distortion of information which occur formerly in the linguistic information processing. • Multiple and conflicting criteria including quantitative as well as qualitative can be considered and evaluated by using the extended VIKOR method during GSES process. The proposed method is a general method and can consider any number of quantitative and qualitative supplier selection criteria. • Performance criteria of suppliers and their relative importance weights are evaluated in a linguistic manner rather than in precise numerical values. This enables decision makers to express their judgments more realistically and makes the assessment easier to be carried out. • The diversity and uncertainty of decision makers’ assessment information can be well reflected and modeled using interval 2-tuple linguistic variables. And it provides an organized method to combine expert knowledge and experience for the use in GSES. • The proposed method is an appropriate and efficient method for GSES problem. By considering three ranking lists and adopting the coefficient v as well as the acceptable advantage, the proposed model is more flexible and convenient for fine adjustments according to a decision maker’s preferences.

6.5 Chapter Summary In this chapter, we studied the green supplier selection problem in supply chain management under incomplete and uncertain information environment. An extended VIKOR method with interval 2-tuple linguistic variables was employed to deal with the GSES problems in green supply chain system. In the proposed method, interval 2-tuple linguistic variables, a new representation of uncertain information, was used to express decision makers’ diversity assessments; the VIKOR method, a recently introduced MCDM method, was utilized to handle multiple conflicting criteria and

6.5 Chapter Summary

149

select the optimum green suppliers. Two empirical examples were given to illustrate the effectiveness of the proposed GSES method. We further tested the validity and demonstrated the advantages of the proposed methodology by comparing with current methods in the literature. From experimental results, it can be concluded that the ITL-VIKOR method is more suitable to address the GSES problem of an organization under uncertain and incomplete information environment. In addition, managers can make full use of the decision information available in green supplier selection to establish an effective supply chain for an organization to reduce operational costs and improve the quality of its end products.

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Hemmati M, Pasandideh SHR (2020) A bi-objective supplier location, supplier selection and order allocation problem with green constraints: Scenario-based approach. J Ambient Intell HumIzed Comput. https://doi.org/10.1007/s12652-020-02555-1 Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752 Hoseini AR, Ghannadpour SF, Ghamari R (2020) Sustainable supplier selection by a new possibilistic hierarchical model in the context of Z-information. J Ambient Intell HumIzed Comput 11(11):4827–4853 Jain N, Singh AR (2020) Sustainable supplier selection under must-be criteria through fuzzy inference system. J Clean Prod 248:119275 Khorram S (2020) A novel approach for ports’ container terminals’ risk management based on formal safety assessment: FAHP-entropy measure - VIKOR model. Nat Hazards 103(2):1671– 1707 Krishankumar R, Gowtham Y, Ahmed I, Ravichandran KS, Kar S (2020) Solving green supplier selection problem using q-rung orthopair fuzzy-based decision framework with unknown weight information. Appl Soft Comput J 94:106431 Lee J, Cho H, Kim YS (2015) Assessing business impacts of agility criterion and order allocation strategy in multi-criteria supplier selection. Expert Syst Appl 42(3):1136–1148 Liu HC, Li P, You JX, Chen YZ (2015) A novel approach for FMEA: combination of interval 2-tuple linguistic variables and gray relational analysis. Qual Reliab Eng Int 31(5):761–772 Liu HC, Liu L, Liu N, Mao LX (2012) Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment. Expert Syst Appl 39(17):12926–12934 Liu HC, Liu L, Wu J (2013) Material selection using an interval 2-tuple linguistic VIKOR method considering subjective and objective weights. Mater Des 52:158–167 Liu HC, You JX, You XY (2014) Evaluating the risk of healthcare failure modes using interval 2-tuple hybrid weighted distance measure. Comput Ind Eng 78:249–258 Opricovic S (1998) Multi-criteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455 Opricovic S, Tzeng GH (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514–529 Pourjavad E, Shahin A (2020) Green supplier development programmes selection: a hybrid fuzzy multi-criteria decision-making approach. Int J Sustain Eng 13(6):463–472 Samanci S, Didem Atalay K, Bahar Isin F (2021) Focusing on the big picture while observing the concerns of both managers and passengers in the post-covid era. J Air Transp Manag 90:101970 Sanayei A, Farid Mousavi S, Yazdankhah A (2010) Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst Appl 37(1):24–30 Shih HS, Shyur HJ, Lee ES (2007) An extension of TOPSIS for group decision making. Math Comput Model 45(7–8):801–813 Vahdani B, Jabbari AHK, Roshanaei V, Zandieh M (2010) Extension of the ELECTRE method for decision-making problems with interval weights and data. Int J Adv Manuf Technol 50(5– 8):793–800 Wu DD (2009) Supplier selection in a fuzzy group setting: a method using grey related analysis and Dempster-Shafer theory. Expert Syst Appl 36(5):8892–8899 Xu Y, Li Y, Zheng L, Cui L, Li S, Li W, Cai Y (2020) Site selection of wind farms using GIS and multi-criteria decision making method in Wafangdian. China Energy 207:118222 You SY, Zhang LJ, Xu XG, Liu HC (2020) A new integrated multi-criteria decision making and multi-objective programming model for sustainable supplier selection and order allocation. Symmetry 12(2):302 Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353 Zhang H (2012) The multiattribute group decision making method based on aggregation operators with interval-valued 2-tuple linguistic information. Math Comput Model 56(1–2):27–35

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Chapter 7

GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

Selecting the best green supplier is essential for companies to promote green supply chain management, which is a complex multi-criteria decision making (MCDM) problem. Besides, decision makers tend to utilize linguistic terms for expressing their evaluations owing to their fuzzy knowledge. This chapter reports a new MCDM model for green supplier selection by integrating best-worst method (BWM) and alternative queuing method (AQM) within interval-valued intuitionistic uncertain linguistic setting. This approach allows to capture the uncertainty and vagueness of decision makers’ judgements with the aid of interval-valued intuitionistic uncertain linguistic sets. Furthermore, the BWM method can obtain the optimal weights of criteria via a nonlinear programing model. The AQM is reliable and intuitive to generate the ranking of candidate suppliers. Finally, a watch manufacturer is used as an example for illustrating the practicability and effectiveness of the proposed GSES model.

7.1 Introduction The public concerns regarding environmental problems have raised worldwide in recent years. Government attach high importance to environmental pollution problems and sustainable development, leading to the promulgation of a range of environmental rules and regulations (Wang et al. 2017). In this context, companies cannot elide their environmental performance if they aim to gain competitive advantages in the international market. In consequence, green supply chain management (GSCM) plays an increasingly significant part and receives growing attention from practitioners and scholars (Fallahpour et al. 2017; Ijadi Maghsoodi et al. 2018; Liao et al. 2018; Daultani et al. 2019). The GSCM is a new management paradigm to chase both commercial profit and environmental performance of organizations (Shi et al. 2018). There are a lot of programs for firms to implement GSCM, such as utilizing

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_7

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environmental ingredients, designing environmental products and monitoring pollution in manufacturing processes (Tavana et al. 2017; Wang et al. 2017). However, an organization’s environmental performance relies on not only its own sustainable behaviors but also its suppliers’ environmental practices. Consequently, selecting an optimal green supplier in the supply chain is an essential priority of carrying out GSCM for companies (Ecer 2020; Krishankumar et al. 2020; Mousavi et al. 2020; Stevi´c et al. 2020; Zhang et al. 2020). During the process of supplier assessment, exact and specific data are not enough to reflect real-world cases owing to the complexity of GSES problems as well as the ambiguity of human thinking (Chen and Han 2018; Li et al. 2018; Liu and Chen 2018; Wu et al. 2019). Thus, many researchers have employed fuzzy sets and intuitionistic fuzzy sets (IFSs) to deal with uncertain and fuzzy judgements of decision makers (Ecer and Pamucar 2020; Kumari and Mishra 2020; Pourjavad and Shahin 2020; Rouyendegh et al. 2020). However, the fuzzy and the intuitionistic fuzzy methods may lead to loss and distortion of assessment information since the fuzzy set only includes membership function, and as for the IFS, the membership and the nonmembership degrees are crisp numbers. As a result, interval-valued intuitionistic uncertain linguistic sets (IVIULSs), combining uncertain linguistic variables with interval-valued intuitionistic fuzzy sets (IVIFSs), were documented by Liu (2013) to reflect the vagueness and uncertainty of subjective expressions given by decision makers. The linguistic variables, membership and non-membership degrees in IVIULSs are represented as interval numbers rather than specific values (Quan et al. 2018; Shi et al. 2018). Because of its features and competences, the IVIULS theory has been employed in numerous domains under uncertain conditions, such as logistics supplier selection (Pang et al. 2020), plant location selection (Liu et al. 2020), enterprises knowledge management (Kan et al. 2016), enterprise financial performance evaluation (Wang and Li 2019), and investment decision making (Meng and Chen 2017). Accordingly, IVIULSs are of great value in managing the diversity and uncertainty of decision makers’ evaluation information in GSES. On the other side, green supplier selection is usually regarded as a multi-criteria decision making (MCDM) problem. A great deal of MCDM methods were used for selecting the optimal supplier in previous studies (Hendiani et al. 2020; Hoseini et al. 2020; Ma et al. 2020; You et al. 2020). The alternative queuing method (AQM) initially proposed by Gou et al. (2016) is thought of as a new and useful technique to address MCDM problems. The core merits of the AQM are that (Duan et al. 2019; Liu et al. 2019b): (1) It can make the ranking result more intuitive by using a directed graph; (2) It can flexibly manage intricate MCDM problems with substantial numbers of criteria and alternatives; (3) Its calculation process is simple and the results can be derived in a short time. Owing to these advantages, the AQM has been applied to many practical decision-making fields. For example, Liu et al. (2019a) proposed a failure mode and effects analysis (FMEA) method by combing two-dimensional uncertain linguistic variables with AQM. Gou et al. (2017) and Farhadinia and Xu (2018) handled the tertiary hospital management problem by using a hesitant fuzzy linguistic AQM approach. Mirnezami et al. (2020) utilized interval type-2 fuzzy AQM and dependency structure matrix for multi-scenario project cash flow assessment.

7.1 Introduction

155

Thereby, it is expected to adopt the AQM to derive a more reasonable and credible ranking result of alternatives in solving GSES problems. Based on the motivations mentioned above, the aim of this chapter is to develop a new GSES model by integrating IVIULSs and AQM, named as IVIUL-AQM, to evaluate and rank alternative green suppliers in GSCM. In addition, a modified best-worst method (BWM), called IVIUL-BWM, is utilized for computing evaluation criteria weights based on a nonlinear optimization model. The fuzziness and uncertainty of assessment information can be well captured in the developed model. The structure of this chapter is given as follows: In Sect. 7.2, we introduce some elementary definitions and operational rules of the IVIULSs. Section 7.3 elaborates upon a GSES method based on the IVIUL-BWM and the IVIUL-AQM methods. In Sect. 7.4, a watch manufacturer is used as an example to demonstrate the developed model. Finally, we conclude the chapter in Sect. 7.5.

7.2 Preliminaries 7.2.1 Interval-Valued Intuitionistic Uncertain Linguistic Sets Let S = {s1 , s2 , . . . , st } be a totally ordered discrete linguistic term set, where t is an odd value. The discrete linguistic term set S can be extended to a continuous linguistic term set S¯ = {sα |s1 ≤ sα ≤ st } to preserve all the given information.   Definition 7.1 (Liu 2013) Suppose that X is a given domain, s˜x = sθ(x) , sτ (x)   ˜ where S˜ is a set of all sθ(x) , sτ (x) ∈ S¯ is an uncertain linguistic variable, and s˜x ∈ S, uncertain linguistic variables. Then, an IVIULS can be represented by     A˜ = < x s˜x , u˜ A˜ (x), v˜ A˜ (x) > |x ∈ X ,

(7.1)

where the interval numbers u˜ A˜ : X → D[0, 1] and v˜ A˜ : X → D[0, 1] represent the membership values of an element x to s˜x , respectively, and  and non-membership   0 ≤ sup u˜ A˜ (x) + sup v˜ A˜ (x) ≤ 1, for any x ∈ X . Note that D[0,1] is the set of all closed subintervals of the interval [0, 1]. For each x ∈ X , u˜ A˜ (x)(˜vA˜ (x)) is a closed interval value and its lower and upper points are denoted as uAL˜ (x) and uAU˜ (x) (vAL˜ (x) and vAU˜ (x)), respectively. Then A˜ can be expressed by A˜ =

       |x ∈ X , x sθ(x) , sτ (x) , uAL˜ (x), uAU˜ (x) , vAL˜ (x), vAU˜ (x)

¯ 0 ≤ uU (x) + vU (x) ≤ 1, uL (x) ≥ 0 and vL (x) ≥ 0. where sθ(x) , sτ (x) ∈ S, A A A˜ A˜

(7.2)

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7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

The hesitation  interval of x to theuncertain linguistic variable s˜x can be represented as π˜ A˜ (x) = πA˜L (x), πA˜U (x) = 1 − uAU˜ (x) − vAU˜ (x), 1 − uAL˜ (x) − vAL˜ (x) . For an       IVIULS, the a˜ = sθ(a) , sτ (a) , uL (a), uU (a) , vL (a), vU (a) is called an intervalvalued intuitionistic uncertain linguistic number (IVIULN). Definition 7.2 (Meng and Chen 2017; Quan  et al. 2018)  Suppose that  L U and a˜ 2 = [sθ (a2 ), sτ (a2 ) ], a˜ 1 = [sθ(a1 ) , sτ (a1 ) ], [uL (a1 ), uU (a1 )],  [v (a1 ), v (a1 )] L U L U [u (a2 ), u (a2 )], [v (a2 ), v (a2 )] are two IVIULNs and λ ∈ [0, 1]. The operational rules of a˜ 1 and a˜ 2 are defined below:       (1) a˜ 1 ⊕ a˜ 2 = sθ(a1 )+θ(a2 ) , sτ (a1 )+τ (a2 ) , 1 − 1 − uL (a1 ) 1 − uL (a2 ) ,      1 − 1 − uU (a1 ) 1 − uU (a2 ) , vL (a1 )vL (a2 ), vU (a1 )vU (a2 ) ;     (2) a˜ 1 ⊗ a˜ 2 = sθ(a1 )×θ(a2 ) , sτ (a1 )×τ (a2 ) , uL (a1 )uL (a2 ), uU (a1 )uU (a2 ) ,        1 − 1 − vL (a1 ) 1 − vL (a2 ) , 1 − 1 − vU (a1 ) 1 − vU (a2 ) ; (3) λ˜a1 =

(4) a˜ 1λ =

(5)

     λ λ sλ×θ(a1 ) , sλ×τ (a1 ) , 1 − 1 − uL (a1 ) , 1 − 1 − uU (a1 ) ,  λ  λ  vL (a1 ) , vU (a1 ) ;







λ

λ  

λ

λ  , 1 − 1 − v L (a1 ) , 1 − 1 − v U (a1 ) ; s(θ (a1 ))λ , s(τ (a1 ))λ , uL (a1 ) , uU (a1 )

       a˜ 1 = sθ(a1 )/τ (a2 ) , sτ (a1 )/θ(a2 ) , min uL (a1 ), uL (a2 ) , min uU (a1 ), uU (a2 ) , a˜ 2      max vL (a1 ), vL (a2 ) , max vU (a1 ), vU (a2 ) .

Definition 7.3 (Liu 2013) Suppose that a˜ =[sθ(a) , sτ (a) ], [uL (a), uU (a)], [vL (a), vU (a)] is an IVIULN. The expected function of a˜ is expressed as:   L  v (a) + vU (a) 1 uL (a) + uU (a) +1− × s(θ(a)+τ (a))/2 E(˜a) = 2 2 2 = s(θ(a)+τ (a))×(uL (a))+uU (a)+2−vL (a)−vU (a))/8 . (7.3) Besides, the accuracy function of a˜ is computed by: 

uL (a) + uU (a) vL (a) + vU (a) + 2 2 = s(uL (a)+uU (a)+vL (a)+vU (a))×(θ(a)+τ (a))/4 .



T (˜a) = s(θ(a)+τ (a))/2 ×

(7.4)

7.2 Preliminaries

157

Definition 7.4 (Liu and Jin 2012) Suppose that a˜ 1 =[sθ(a1 ) , sτ (a1 ) ], [uL (a1 ), uU (a1 )], [vL (a1 ), vU (a1 )] and a˜ 2 =[sθ(a2 ) , sτ (a2 ) ], [uL (a2 ), uU (a2 )], [vL (a2 ), vU (a2 )] are IVIULNs. Their comparison operations can be described below: (1) (2)

If E(˜a1 ) > E(˜a2 ), then a˜ 1 > a˜ 2 ; If E(˜a2 ) = E(˜a2 ), then (a) (b)

if T (˜a1 ) > T (˜a2 ), then a˜ 1 > a˜ 2 ; if T (˜a1 )=T (˜a2 ), then a˜ 1 = a˜ 2 .

Definition 7.5 (Shi et al. 2018) For any two IVIULNs U a˜ 1 = [sθ(a1 ) , sτ (a1 ) ], [uL (a1 ), uU (a1 )], [vL (a ), v (a )] and 1 1  a˜ 2 = [sθ(a2 ) , sτ (a2 ) ], [uL (a2 ), uU (a2 )], [vL (a2 ), vU (a2 )] , the Hamming distance between a˜ 1 and a˜ 2 is expressed as:    (|θ (a1 ) − θ (a2 )|+|τ (a1 ) − τ (a2 )|)/9 + uL (a1 ) − uL (a2 ) 1       . d (˜a1 , a˜ 2 ) = 6 +uU (a1 ) − uU (a2 ) + vL (a1 ) − vL (a2 ) + vU (a1 ) − vU (a2 ) (7.5) To aggregate the interval-valued intuitionistic uncertain linguistic information, Meng et al. (2014) defined the interval-valued intuitionistic uncertain linguistic Choquet averaging (IVIULCA) operator and the interval-valued intuitionistic uncertain linguistic Choquet geometric mean (IVIULCGM) operator.       Definition 7.6 Let a˜ i = sθ(ai ) , sτ (ai ) , uL (ai ), uU (ai ) , vL (ai ), vU (ai ) be a collection of IVIULNs and μ be a fuzzy measure on A = {˜a1 , a˜ 2 , . . . , a˜ n }. Then the IVIULCA operator is defined by:    n   IVIULCAμ (˜a1 , a˜ 2 , . . . , a˜ n ) = ⊕ μ A(i) − μ A(i+1) a˜ (i) i=1 ⎛⎡ ⎤ # n

(μ(A(i) )−μ(A(i+1) )) $ ⎦, 1 − 1 − uL (ai ) =⎝⎣s n ,s n , μ A −μ A θ μ A −μ A τ (a (a ) ) ( ( (i) ) ( (i+1) )) i ( ( (i) ) ( (i+1) )) i i=1 i=1 i=1 % % # n n

n

(μ(A(i) )−μ(A(i+1) )) $ $ $ 1 − uU (ai ) v L (ai )(μ(A(i) )−μ(A(i+1) )) , v U (ai )(μ(A(i) )−μ(A(i+1) )) , 1− , i=1

i=1

i=1

(7.6) where (·) denotes a permutation on A for a˜ (1) ≤ a˜ (2) ≤  . . .  ≤ a˜(n) , and   A(i) = a˜ (i) , a˜ (i+1) , . . . , a˜ (n) with A(i+1) = ∅. It is clear that μ A(i) − μ A(i+1) is a weight vector with the condition that μ A(i) − μ A(i+1) ≥ 0 and n      μ A(i) − μ A(i+1) = 1. i=1

      Definition 7.7 Let a˜ i = sθ(ai ) , sτ (ai ) , uL (ai ), uU (ai ) , vL (ai ), vU (ai ) be a set of IVIULNs and μ be the fuzzy measure of A = {˜a1 , a˜ 2 , . . . , a˜ n }. The IVIULCGM operator is defined by

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7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM n





μ A(i) −μ A(i+1)

IVIULCGMμ (˜a1 , a˜ 2 , . . . , a˜ n ) = ⊗ a˜ (i) i=1 ⎛⎡

⎤

⎜⎢ ⎥



,s



⎥, ⎢ =⎜ ⎝ ⎣s ( ⎦ n  μ A n  μ A ( (i) −μ A(i+1) (i) −μ A(i+1) ⎡ ⎣

i=1

θ ai

i=1

τ ai





n





⎤ $ μ A(i) −μ A(i+1) μ A(i) −μ A(i+1) L U ⎦ u (ai ) , u (ai ) i=1 i=1 ⎡











⎤ n

n

μ A −μ A

μ A −μ A $ $ (i) (i+1) (i) (i+1) ⎦ L U ⎣1 − ,1 − 1 − v (ai ) 1 − v (ai ) , i=1 i=1 n $

(7.7)

on A for a˜ (1) ≤ a˜ (2) ≤ . . . ≤ a˜ (n) , and A(i) =  where (·) is a permutation a˜ (i) , a˜ (i+1) , . . . , a˜ (n) with A(i+1) = ∅.

7.2.2 Precedence Relationship Between Alternatives Directed graph and 0–1 precedence relationship matrix are two intuitive tools to describe precedence relationship between alternatives, which are introduced as follows. The symbols   ,  ≺ and  ≈ respectively represent “prior”, “not prior” and “indifference”. A small circle is utilized to denote an alternative in a directed graph. The arrow draws from the good alternative to the poor one. For instance, if Ai Aj , then the arrow draws from Ai and points to Aj . If Ai ≈ Aj , then there are two arrows: one draws from Ai and points to Aj , and the other draws from Aj and points to Ai . If Ai and Aj cannot be compared, then there is no arrow between the two alternatives. An example of a directed graph is shown in Fig. 7.1: A1 is superior to A2 and A5 ; A2 Fig. 7.1 A directed graph of alternatives

7.2 Preliminaries

159

is superior to A3 , A4 and A5 ; there is no difference between A1 and A3 ; A1 and A4 cannot be compared. The precedence relationship between alternatives can be presented by using a 0-1 precedence relationship matrix. If Ai Aj , then pij = 1 and pji = 0; if Ai ≈ Aj , then pij = pji = 1; if Ai and Aj cannot be compared, then pij = pji = 0. Based on these rules, the directed graph in Fig. 7.1 can be converted into a 0–1 precedence relationship matrix M as:

A1 A M = 2 A3 A4 A5

A⎡ A5 1 A2 A3 A4 ⎤ 11101 ⎢0 1 1 1 1⎥ ⎢ ⎥ . ⎢ ⎥ ⎢1 0 1 0 0⎥ ⎢ ⎥ ⎣0 0 1 1 0⎦ 00001

7.3 The Proposed GSES Model In this section, we propose a new model that integrates IVIUL-BWM and IVIULAQM for selecting the most favorable green supplier. To be specific, the IVIUL-BWM technique is adopted to calculate criteria weights and the IVIUL-AQM is utilized for generating the ranking order of alternative green suppliers. The proposed GSES model including two stages is shown in Fig. 7.2. For a GSES problem, assume that there are m alternatives Ai (i = 1, 2, . . . , m), n selection criteria Cj (j = 1, 2, . . . , n), and l decision makers DMk (k = 1, 2, . . . , l). is the performance evaluation matrix of DMk , where Suppose that P˜ k = p˜ ijk   m×n    L U L U p˜ ijk = sθ(ijk) , sτ (ijk) , uijk , vijk is the IVIULN given by DMk for alter, uijk , vijk L L native supplier Ai regarding criterion Cj , with the condition 0 ≤ uijk ≤ 1,0 ≤ vijk ≤ U U L U L U L U 1, uijk + vijk ≤ 1, uijk ≤ uijk , vijk ≤ vijk , saijk , saijk ∈ S. According to these symbolizations and assumptions, the developed approach for green supplier selection is expressed specifically in the following subsections.

7.3.1 The IVIUL-BWM for Computing Criteria Weights The BWM is a weighting approach proposed by Rezaei (2015), which includes two comparison vectors: the most important criterion versus the other criteria and the other criteria versus the least important criterion (Hafezalkotob et al. 2018; Salimi and Rezaei 2018). In this part, we extend the BWM to interval-valued intuitionistic

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7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

Fig. 7.2 Flowchart of the proposed GSES model

uncertain linguistic circumstance for calculating the weights of evaluation criteria. Next, we outline the steps of the IVIUL-BWM method. Step 1.1 Determine the best and the worst criteria Based on the selection criteria Cj (j = 1, 2, . . . , n), each decision maker DMk should determine the best (most important) criterion CBk and the wort (least important) k from his or her own perspective. criterion CW Step 1.2 Define the IVIUL preference of the best criterion to other criteria The preference of the best criterion over all other criteria can be assessed by each decision maker using a linguistic term set S  = {s1 = Equally important,s2 = Weakly important,s3 = Fairly important,s4 = Very important and s5 = Absolutely important}. The best-to-others vector determined by DMk is obtained as:   k k k , , v˜ B2 , . . . , v˜ Bn V˜ Bk = v˜ B1

(7.8)

7.3 The Proposed GSES Model k where v˜ Bj =

161

     L U L U , vBjk indicates the kth decision sθ(Bjk) , sτ (Bjk) , uBjk , uBjk , vBjk

maker’s IVIUL assessment of the best criterion CBk over the other criteria. Step 1.3 Compute the IVIUL preference of other criteria over the worst criterion By using the same linguistic terms above, the IVIUL preference of all the other criteria over the worst criterion can be determined. The others-to-worst vector of DMk is derived as:   k k k , ˜W ˜ Wn V˜ Wk = v˜ W 1, v 2, . . . , v k where v˜ Wj =

(7.9)

     L U L U , vWjk represents the kth decision sθ(Wjk) , sτ (Wjk) , uWjk , uWjk , vWjk

k maker’s IVIUL preference of the criterion Cjk over the worst criterion CW . Step 1.4 Compute the optimal criteria weights for each decision maker   L , uU ], [v L , v U ] , w L , uU ], [v L , v U ] , ˜ jk = [sθ (jk) , sτ (jk) ], [ujk Assume w˜ Bk = [sθ (Bk) , sτ (Bk) ], [uBk Bk Bk Bk jk jk jk     L  k  L U U w˜ W , vWk , vWk . For the decision maker DMk , the = sθ(Wk) , sτ (Wk) , uWk , uWk

w˜ k

k w˜ k k and d w˜ kj , v˜ Wj for j = 1, 2, . . . , n should be minimized to distances d w˜ Bk , v˜ Bj j W obtain criteria weights. Thus, the following nonlinearly constrained optimization model can be established to derive the weights of criteria:

minξ    ⎧         ⎪ ≤ ξ, /s − s /s − s s s  ⎪ θ(Bk) τ (jk) θ(Bk) θ(jk) τ (Bjk)  ≤ ξ θ(Bjk) ⎪ ⎪ ⎪    



⎪ ⎪   L L L  U U U  ⎪ min u min u ≤ ξ, − u − u , u , u ⎪    ≤ξ Bk jk Bjk Bk jk Bjk ⎪ ⎪ ⎪    



⎪ ⎪   L L L  U U U  ⎪ ⎪ v v ≤ ξ, − v − v , v , v max max  ⎪ Bk jk Bjk Bk jk Bjk  ≤ ξ ⎪ ⎪     ⎪ ⎪    ⎨   /s   − sτ (Wjk)  ≤ ξ sθ(jk) τ (Wk) − sθ(Wjk)  ≤ ξ, sτ (jk) /sθ(Wk) s.t.    



⎪ ⎪ ⎪ min uL , uL − uL  ≤ ξ, min uU , uU − uU  ≤ ξ ⎪ Wk jk Wjk Wk jk Wjk ⎪ ⎪ ⎪    



⎪ ⎪    L L U U  ⎪ ⎪ max vWk ≤ ξ, max vWk , vjkL − vWjk , vjkU − vWjk   ≤ξ ⎪ ⎪ ⎪ ⎪ ⎪ n

⎪ . ⎪ ⎪ k ⎪ = 1, S w˜ jk ≥ 0 , j = 1, 2, . . . , n. S w ˜ ⎪ j ⎩

(7.10)

j=1

(7.12), the optimal IVIUL weight vector of criteria w˜ k =   kBy ksolving kmodel w˜ 1 , w˜ 2 , . . . , w˜ n determined by DMk can be obtained. Step 1.5 Compute the collective IVIUL weights of criteria Based on the weight vector of criteria w˜ k (k = 1, 2, . . . , l), the collective IVIUL weights of criteria w˜ = w˜ 1 , w˜ 2 , . . . , w˜ n can be acquired by utilizing the IVIULCA operator. That is,

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7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM





l

  − μ W(k+1) w˜ j(k) , w˜ j = IVIULCAμ w˜ j1 , w˜ j2 , . . . , w˜ jl = ⊕ μ W(k) k=1

j = 1, 2, . . . , n,

(7.11)

 where (·) indicates a permutation on W  with w˜ j(1) ≤ w˜ j(2) ≤ . . . ≤ w˜ j(l) , and W(k) =   (k) (k+1) (l)  , . . . , w˜ j with W(l+1) = ∅. w˜ j , w˜ j

7.3.2 The IVIUL-AQM for Ranking Alternative Suppliers The AQM is effective and intuitive to find the priority ranking of alternatives according to their directed graph or 0–1 precedence relationship matrix. In this stage, we apply the AQM under IVIUL environment for ranking the alternative suppliers Ai (i = 1, 2, . . . , m). The IVIUL-AQM approach is explained as follows: Step 2.1 Establish the collective IVIUL evaluation matrix Applying the IVIULCGM operator, all the individual evaluation matrices P˜ k (k = 1,  2, . . . , l) can be combined to build a collective IVIUL evaluation matrix P˜ = p˜ ij m×n , where

l μP −μP(k+1) p˜ ij = IVIULCGMμ p˜ ij1 , p˜ ij2 , . . . , p˜ ijl = ⊗ p˜ ij(k)(k) k=1 ⎤ # % l l $ $ L μP(k) −μP(k+1) U μP(k) −μP(k+1) ⎦ uij(k) , uij(k) , μP(k) −μP(k+1)

⎛⎡ = ⎝⎣s (l k=1

μP

−μP(k+1)

(k) aθ (ij(k))

# 1−

, s (l k=1

aτ (ij(k))

l

$

1−

k=1

k=1 L vij(k)

μP(k) −μP(k+1)

k=1

,1 −

l

$

1−

U vij(k)

μP(k) −μP(k+1)

% .

k=1

(7.12)   Note that (·) indicates a permutation on P = p˜ ij1 , p˜ ij2 , . . . , p˜ ijl such that p˜ ij(1) ≤   p˜ ij(2) ≤ . . . ≤ p˜ ij(l) and P(k) = p˜ ij(k) , p˜ ij(k+1) , . . . , p˜ ij(l) with P(l+1) = ∅. Step 2.2 Make pairwise comparisons of suppliers on each criterion The pairwise comparisons of suppliers to each criterion can  pertaining   be acquired by computing the expected function E p˜ ij and accuracy function T p˜ ij of p˜ ij , i = 1, 2, . . . , m, j = 1, 2, . . . , n. For the supplier pair (Ai , At ), (Ai At )j denotes that Ai is better than At on the criterion Cj ; (Ai ≺ At )j denotes that Ai is worse than At on the criterion Cj ; (Ai ≈ At )j represents that there is no difference between Ai and At on the criterion Cj . Step 2.3 Compute three kinds of overall IVIUL weights In this step, we need to calculate the overall pros weight w(A ˜ i At ), the overall ˜ i ≈ At ) of supplier cons weight w(A ˜ i ≺ At ) and the overall indifference weight w(A

7.3 The Proposed GSES Model

163

pairs (Ai , At )(i, t = 1, 2, . . . , m) with respect to the criteria Cj (j = 1, 2, . . . , n). For example, w(A ˜ i At ) can be calculated by w(A ˜ i At ) =

.

w˜ j

(7.13)

j∈(Ai At )j

Similarly, w(A ˜ i ≺ At ) and w(A ˜ i ≈ At ) can be calculated in the same way. Step 2.4 Derive the overall pros and cons indicated value of each supplier pair To acquire the overall pros and cons indicated value for the supplier pair (Ai , At ), we can use the following formula: ˜ i At )+σ w(A ˜ i ≈At ) ˜ σ (Ai , At ) = w(A , O ˜ i ≈At ) w(A ˜ i ≺At )+σ w(A i, t = 1, 2, . . . , m,

(7.14)

where σ denotes the important degree of (Ai ≈ At ), satisfying 0 ≤ σ ≤ 1. Step 2.5 Find the precedence relationships among

alternative suppliers ˜ Suppose that there is a threshold value λ with E λ˜ > 1. The relationships among the m suppliers can be obtained by ⎧



⎪ ˜ σ (Ai , At ) ≥ E θ˜ ; A , E O A ⎪ i t ⎪ ⎨





˜ σ (Ai , At ) < E θ˜ ; Ai ≈ At , 1/E θ˜ < E O ⎪



⎪ ⎪ ⎩ Ai ≺ A t , 0 < E O ˜ σ (Ai , At ) ≤ 1/E θ˜ .

(7.15)

As a result, a directed graph and a 0–1 precedence relationship matrix can be established. Step 2.6 Compute the ranking value of each alternative supplier Finally, the ranking value δi (i = 1, 2, . . . , m) of each supplier is determined using the following formula: δi = ri − qi ,

(7.16)

where ri is the quantity of the arrows that start from Ai in the obtained directed graph or the quantity of elements whose value is 1 in the ith row of the 0–1 precedence relationship matrix. Parameter qi is the quantity of the arrows that point to Ai in the obtained directed graph or the quantity of elements whose value is 0 in the ith row of the 0–1 precedence relationship matrix. The larger δi , the more suitable the supplier Ai . Finally, we can rank the m suppliers in line with their δi (i = 1, 2, . . . , m) values in descendent order.

164

7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

7.4 Case Study In this section, a watch manufacturing company (Liao et al. 2016) is adopted to show the applicability and usefulness the presented GSES model. Manufacturing sector is one of the highly consuming and polluting industries that contribute to environmental pollution and global warming. Faced with enormous environmental pressure from government and customers, manufactures have to decrease the negative environment impact of their production operation activities. The target of this case study is to help a case firm to seek the optimal green supplier for implementing GSCM. In the case, five suppliers (Ai , i = 1, 2, . . . , 5) are selected for further evaluation after preliminary screening. Based on a literature review and expert interviews, five evaluation criteria are determined, i.e. purchase cost (C1 ), product quality (C2 ), technology capability (C3 ), environmental skill (C4 ) and delivery performance (C5 ). Besides, an expert group of five decision makers, DMk , k = 1, 2, . . . , 5, is built; it includes a chief executive officer, a chief marketing manager, a chief purchase officer of the company and two environmental experts. To address interactions between decision makers, the fuzzy measures of decision makers and decision maker sets are offered in Table 7.1. Table 7.1 Fuzzy measures of decision maker sets Decision maker sets

Fuzzy measures

One decision maker

μ(DM1 ) = 0.3, μ(DM2 ) = μ(DM3 ) = 0.2, μ(DM4 ) = μ(DM5 ) = 0.15 μ(DM1 , DM2 ) = μ(DM1 , DM3 ) = 0.6 μ(DM1 , DM4 ) = μ(DM1 , DM5 ) = 0.55

Two decision maker sets

. μ(DM2 , DM3 ) = 0.3, μ(DM4 , DM5 ) = 0.25 μ(DM2 , DM4 ) = μ(DM2 , DM5 ) = μ(DM3 , DM4 ) = μ(DM3 , DM5 ) = 0.45

Three decision maker sets

μ(DM1 , DM2 , DM3 ) = 0.8, μ(DM1 , DM4 , DM5 ) = 0.7 μ(DM2 , DM3 , DM4 ) = μ(DM2 , DM3 , DM5 ) = 0.65 μ(DM2 , DM4 , DM5 ) = μ(DM3 , DM4 , DM5 ) = 0.6 μ(DM1 , DM2 , DM4 ) = μ(DM1 , DM2 , DM5 ) = μ(DM1 , DM3 , DM4 ) = μ(DM1 , DM3 , DM5 ) = 0.75

Four decision maker sets

μ(DM2 , DM3 , DM4 , DM5 ) = 0.8 μ(DM1 , DM2 , DM3 , DM4 ) = μ(DM1 , DM2 , DM3 , DM5 ) = 0.9 μ(DM1 , DM2 , DM4 , DM5 ) = μ(DM1 , DM3 , DM4 , DM5 ) = 0.85

Five decision maker set

μ(DM1 , DM2 , DM3 , DM4 , DM5 ) = 1

7.4 Case Study Table 7.2 The best and the worst criteria identified

165 Decision makers

The best criteria

The worst criteria

DM1

Technology capability (C3 )

Product quality (C2 )

DM2

Technology capability (C3 )

Purchase cost (C1 )

DM3

Delivery Product quality (C2 ) performance (C5 )

DM4

Purchase cost (C1 )

Environmental skill (C4 )

DM5

Purchase cost (C1 )

Product quality (C2 )

7.4.1 Calculating the Criteria Weights In this stage, we utilize the IVIUL-BWM to compute the weights of evaluation criteria, and the implementation steps are described as below. Step 1.1 The five decision makers first identify the best and the worst criteria from their own perspectives, and the results are listed in Table 7.2. Step 1.2 By using the linguistic term set S  , the preferences of the best criterion versus all the other criteria given by the decision makers are presented in Table 7.3.  S  = s1 = Equally important, s2 = Weakly important, s3 = Fairly important,  s4 = Very important, s5 = Absolutely important . Step 1.3 Based on the same linguistic term set S  , the preferences of the other criteria versus the worst criterion are obtained as in Table 7.4. Step 1.4 According to all the decision makers’ preference evaluations, we establish five nonlinear programming models to acquire the optimal weights of the five evaluation criteria. For example, the nonlinearly constrained optimization model concerning DM1 is obtained as follows:

Decision Best Other criteria makers criteria C 1      DM1 C3 s2 , s3 , [0.5, 0.6], [0.3, 0.4]      DM2 C3 s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s5 , s6 , [0.7, 0.8], [0.1, 0.2] DM3 C5      s1 , s1 , [1.0, 1.0], [0.0, 0.0] DM4 C1      DM5 C1 s1 , s1 , [1.0, 1.0], [0.0, 0.0] C2      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s5 , s6 , [0.7, 0.8], [0.1, 0.2]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.2, 0.3]

Table 7.3 Preference of the best criterion over other criteria C3      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]

C4      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s3 , s4 , [0.6, 0.7], [0.2, 0.2]      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]

C5      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s2 , s3 , [0.5, 0.6], [0.3, 0.3]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]

166 7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

Decision Worst Other criteria makers criteria C 1      DM1 C2 s2 , s3 , [0.5, 0.6], [0.3, 0.4]      DM2 C1 s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s1 , s1 , [1.0, 1.0], [0.0, 0.0] DM3 C2      s3 , s4 , [0.6, 0.7], [0.2, 0.3] DM4 C4      DM5 C2 s2 , s3 , [0.5, 0.6], [0.3, 0.4] C2      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]

Table 7.4 Preference of the other criteria over the worst criterion C3      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]

C4      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]

C5      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s3 , s4 , [0.6, 0.7], [0.2, 0.3]      s2 , s3 , [0.5, 0.6], [0.3, 0.4]      s1 , s1 , [1.0, 1.0], [0.0, 0.0]

7.4 Case Study 167

168

7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

minξ     ⎧      ⎪  sθ (31) − 2 ≤ ξ,  sτ (31) − 3 ≤ ξ, ⎪ ⎪  sτ (i1)  sθ(i1)   ⎪ ⎪ ⎪ ⎪ minuL , uL  − 0.5 ≤ ξ, minuU , uU  − 0.6 ≤ ξ, ⎪ ⎪ 31 31 i1 i1 ⎪ ⎪ ⎪ maxv L , v L  − 0.3 ≤ ξ, maxv U , v U  − 0.4 ≤ ξ, i = 1, 4, 5. ⎪ ⎪ 31  i1 31 i1    ⎪ ⎪   ⎪ ⎪  sθ (31) − 3 ≤ ξ,  sτ (31) − 4 ≤ ξ, ⎪   ⎪     s s ⎪ τ (21) θ(21) ⎪ ⎪         ⎪ ⎪ min uL , uL − 0.6 ≤ ξ, min uU , uU − 0.7 ≤ ξ, ⎪ 31 21 21  ⎪      31   ⎪ ⎪ L L U U ⎪ max v31 , v21 − 0.2 ≤ ξ, max v31 , v21 − 0.3 ≤ ξ, ⎪     ⎪  ⎪  sτ (i1)   ⎨  sθ (i1)     − 3 ≤ ξ, s.t.  sτ (21) − 2 ≤ ξ,  sθ(21) ⎪         ⎪ ⎪ min uL , uL − 0.5 ≤ ξ, min uU , uU − 0.6 ≤ ξ, ⎪ ⎪ i1 21  i1 21  ⎪       ⎪ L L ⎪  ξ, max v U , v U − 0.4 ≤ ξ, i = 1, 4, 5. ⎪ max i1 21 ⎪

vi1 , v21 − 0.3

≤

 ⎪  

 ⎪ L + u U − v L − v U + s L + uU − v L − v U ⎪ + sτ (21) ∗ 2 + u21 ⎪ 18 sθ (11) + sτ (11) ∗ 2 + u11 ⎪ 11 11 11 21 21 21 θ (21) ⎪







⎪   ⎪ L + u U − v L − v U + s  L U L U ⎪ + sθ (31) + sτ (31) ∗ 2 + u31 ⎪ ⎪ 31 31 31 θ (41) + sτ (41) ∗ 2 + u41 + u41 − v41 − v41 ⎪

⎪   ⎪ L + uU − v L − v U = 1, ⎪ sθ (51) + sτ (51) ∗ 2 + u51 ⎪ ⎪ 51 51 51 ⎪ ⎪ ⎪ L ≤ uU , v L ≤ v U , uU + v U ≤ 1, ⎪ ⎪ uj1 j1 j1 j1 j1 j1 ⎪ ⎩ j = 1, 2, . . . , 5

By solving the above model, the optimal criteria weights w˜ 1 provided by DM1 are determined as:      , [0.04, 0.14], [0.00, 0.06] , s0.21 , s0.25      = s0.16 , s0.18 , [0.45, 0.47], [0.00, 0.00] ,      , [0.19, 0.24], [0.02, 0.06] , = s0.61 , s0.69      , [0.07, 0.14], [0.00, 0.02] , = s0.27 , s0.39      = s0.27 , s0.39 , [0.04, 0.14], [0.00, 0.01] .

w˜ 11 = w˜ 21 w˜ 31 w˜ 41 w˜ 51

Analogously, the optimal criteria weights derived from other decision makers’ assessments can be calculated in the same way. Step 1.5 By Eq. (7.11), the individual criteria weights w˜ k (k = 1, 2, . . . , 5) are aggregated to determine the collective criteria weights w, ˜ in which      , [0.027, 0.098], [0.006, 0.127] , s0.249 , s0.285      , [0.288, 0.522], [0.001, 0.003] , = s0.174 , s0.218      , [0.313, 0.375], [0.005, 0.022] , = s0.399 , s0.481      , [0.229, 0.262], [0.002, 0.007] , = s0.209 , s0.296      , [0.206, 0.345], [0.005, 0.028] . = s0.319 , s0.454

w˜ 1 = w˜ 2 w˜ 3 w˜ 4 w˜ 5

7.4 Case Study

169

7.4.2 Determining the Ranking of Green Suppliers In the second phase, the IVIUL-AQM is applied to rank the five alternative suppliers. The linguistic term set S is utilized by the decision makers to assess suppliers’ performance on each criterion, and the assessment results are shown in Table 7.5. S = {s1 = Very low, s2 = Low, s3 = Medium, s5 = High, s5 = Very high }. Step 2.1 With Eq. (7.12)  and based on the data in Table 7.5, the collective evaluation matrix P˜ = p˜ ij 5×5 is obtained as presented in Table 7.6. Step 2.2 Via the pairwise comparison of suppliers on each criterion, the following 0–1 precedence relationship matrices are constructed: A⎡ A⎡ 1 A2 A3 A4⎤A5 1 A2 A3 A4⎤A5 10011 11000 A1 A1 1 1 1 1 1⎥ 0 1 0 0 0⎥ A2 ⎢ A2 ⎢ ⎢ ⎥ ⎢ ⎥ M1 = ⎢ ⎥ M2 = ⎢ ⎥ A3 ⎢ 1 0 1 1 1 ⎥, A3 ⎢ 1 1 1 0 1 ⎥, ⎢ ⎥ ⎢ ⎥ A4 ⎣ 1 0 0 1 1 ⎦ A4 ⎣ 1 1 1 1 1 ⎦ A5 A5 00001 11001 A A A A A⎡ A 1 2 3 4⎤ 5 1 A2 A3 A4⎤A5 ⎡ 11111 11101 A1 A1 0 1 1 0 1⎥ 0 1 1 0 1⎥ A2 ⎢ A2 ⎢ ⎢ ⎥ ⎢ ⎥ M3 = ⎢ ⎥ M4 = ⎢ ⎥ A3 ⎢ 0 0 1 0 1 ⎥, A3 ⎢ 0 0 1 0 0 ⎥, ⎢ ⎢ ⎥ ⎥ A4 ⎣ 0 1 1 1 1 ⎦ A4 ⎣ 1 1 1 1 1 ⎦ A5 A5 00001 00101

A1 A2 M5 = A3 A4 A5

A⎡ 1 A2 A3 A4⎤A5 11111 ⎢0 1 0 0 0⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0 1 1 1 0 ⎥. ⎢ ⎥ ⎣0 1 0 1 0⎦ 01111

Step 2.3 Based on Eq. (7.13), the overall pros weights of all supplier pairs (Ai , At )(i, t = 1, 2, . . . , 5) are computed as shown in Table 7.7. Similarly, the overall cons weights and the overall indifference weights can be determined and the results are displayed in Table 7.7. Step 2.4 Taking σ = 0.5 and using Eq. (7.14), the overall pros and cons indicated values O0.5 (Ai , At )(i, t = 1, 2, . . . , 5) are calculated as provided in Table 7.8. Step 2.5 Let θ˜ = [s2 , s2 ], [0.5, 0.6], [0.5, 0.5] . Then according to Eq. (7.15), we can obtain a directed graph of the five suppliers as shown in Fig. 7.3. Step 2.6 By utilizing Eq. (7.16), the ranking values δi (i = 1, 2, . . . , 5) of the five suppliers are computed as follows:

C4

C3

C2

C1

([s3 , s4 ], [0.6, 0.7], [0.2, 0.2]) ([s4 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s4 , s5 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5])

([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s2 , s3 ], [0.3, 0.5], [0.4, 0.4]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s4 , s5 ], [0.6, 0.7], [0.1, 0.3]) ([s5 , s5 ], [0.6, 0.7], [0.1, 0.3])

([s3 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.2]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4])

DM4

DM5

(continued)

([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s2 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.2])

DM3

([s4 , s5 ], [0.7, 0.8], [0.1, 0.2]) ([s5 , s5 ], [0.6, 0.7], [0.1, 0.3]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s4 , s4 ], [0.6, 0.7], [0.1, 0.3])

([s3 , s4 ], [0.6, 0.7], [0.1, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s2 , s3 ], [0.3, 0.5], [0.4, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4])

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s5 , s5 ], [0.7, 0.8], [0.1, 0.2]) ([s1 , s2 ], [0.1, 0.2], [0.7, 0.8])

DM5

DM2

([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s2 , s3 ], [0.3, 0.5], [0.4, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s4 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s4 , s5 ], [0.7, 0.8], [0.1, 0.2])

DM4

DM1

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.2]) ([s4 , s5 ], [0.7, 0.7], [0.1, 0.2]) ([s5 , s5 ], [0.6, 0.7], [0.1, 0.3]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.3])

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5])

DM3

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s2 , s2 ], [0.1, 0.2], [0.7, 0.8]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s4 , s5 ], [0.7, 0.8], [0.0, 0.2]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3])

DM5

([s4 , s5 ], [0.7, 0.8], [0.1, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s2 , s3 ], [0.3, 0.6], [0.3, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5])

([s4 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s4 , s5 ], [0.7, 0.8], [0.0, 0.2]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3])

DM4

DM2

([s1 , s2 ], [0.1, 0.2], [0.7, 0.8]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s4 , s5 ], [0.7, 0.8], [0.0, 0.2]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5])

DM3

DM1

([s3 , s3 ], [0.3, 0.4], [0.5, 0.5]) ([s2 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s4 , s5 ], [0.7, 0.8], [0.0, 0.2]) ([s5 , s5 ], [0.7, 0.9], [0.0, 0.1]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3])

([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s3 ], [0.3, 0.4], [0.5, 0.5]) ([s4 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s4 , s5 ], [0.7, 0.9], [0.0, 0.1])

DM2

([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3])

DM5

DM1

([s3 , s3 ], [0.3, 0.4], [0.4, 0.5]) ([s2 , s3 ], [0.3, 0.4], [0.3, 0.5]) ([s3 , s4 ], [0.4, 0.5], [0.3, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5]) ([s3 , s4 ], [0.4, 0.5], [0.3, 0.4])

DM4

A5

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.4, 0.5])

A4

DM3

A3

DM2

A2

([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s3 ], [0.3, 0.5], [0.5, 0.5])

DM1

Criteria Decision Suppliers makers A1

Table 7.5 Performance assessments of green suppliers by decision makers

170 7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

C5

([s4 , s5 ], [0.7, 0.9], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s5 , s5 ], [0.7, 0.9], [0.1, 0.1])

([s3 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.3]) ([s4 , s5 ], [0.7, 0.9], [0.0, 0.1]) ([s3 , s4 ], [0.6, 0.7], [0.2, 0.3]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.2])

([s4 , s5 ], [0.7, 0.8], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s4 ], [0.6, 0.8], [0.1, 0.2]) ([s5 , s5 ], [0.8, 0.9], [0.0, 0.1])

DM4

DM5

A5

([s4 , s5 ], [0.7, 0.9], [0.0, 0.1]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s1 , s2 ], [0.3, 0.5], [0.4, 0.5]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.3]) ([s3 , s4 ], [0.6, 0.8], [0.1, 0.2])

A4

DM3

A3

DM2

A2

([s3 , s4 ], [0.6, 0.7], [0.1, 0.2]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s4 , s5 ], [0.8, 0.9], [0.0, 0.1]) ([s3 , s3 ], [0.3, 0.5], [0.3, 0.4]) ([s3 , s4 ], [0.6, 0.7], [0.1, 0.2])

DM1

Criteria Decision Suppliers makers A1

Table 7.5 (continued)

7.4 Case Study 171

[s3.125 , s3.311 ], [0.372, 0.564], [0.358, 0.373] [s3.499 , s4.175 ], [0.591, 0.738], [0.171, 0.186] [s3.000 , s3.400 ], [0.409, 0.581], [0.331, 0.397]

[s3.000 , s3.352 ], [0.395, 0.572], [0.346, 0.407] [s3.823 , s4.831 ], [0.766, 0.866], [0.111, 0.117] [s3.213 , s4.033 ], [0.581, 0.708], [0.192, 0.246]

[s3.082 , s3.232 ], [0.354, 0.548], [0.388, 0.404] [s3.000 , s3.499 ], [0.439, 0.602], [0.302, 0.377] [s2.802 , s3.163 ], [0.347, 0.456], [0.355, 0.433]

A3

A4

A5

[s3.000 , s3.499 ], [0.439, 0.602], [0.302, 0.377] [s3.400 , s4.414 ], [0.682, 0.783], [0.146, 0.183]

[s3.000 , s3.225 ], [0.332, 0.536], [0.235, 0.363] [s3.000 , s3.213 ], [0.356, 0.543], [0.397, 0.400]

[s3.000 , s3.213 ], [0.356, 0.543], [0.397, 0.440] [s3.006 , s3.663 ], [0.463, 0.517], [0.207, 0.254]

[s3.168 , s4.051 ], [0.592, 0.711], [0.191, 0.253] [s3.000 , s3.351 ], [0.395, 0.572], [0.346, 0.408]

[s3.082 , s3.277 ], [0.361, 0.557], [0.371, 0.394] [s3.213 , s4.223 ], [0.644, 0.745], [0.168, 0.277]

A1

A2

A3

A4

A5

C5

[s3.168 , s3.441 ], [0.405, 0.591], [0.315, 0.335] [s2.624 , s3.125 ], [0.239, 0.399], [0.460, 0.533] [s3.182 , s3.377 ], [0.467, 0.657], [0.371, 0.394]

Suppliers C4

[s3.000 , s3.352 ], [0.395, 0.572], [0.346, 0.407] [s2.741 , s3.352 ], [0.317, 0.476], [0.359, 0.447] [s3.269 , s4.130 ], [0.653, 0.688], [0.209, 0.266]

C3

A2

C2

A1

C1

Suppliers Criteria

Table 7.6 Collective evaluation matrix

172 7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

7.4 Case Study

173

Table 7.7 Overall weights of each supplier pair Overall pros weights w(A ˜ 1 A2 ) = w(A ˜ 3 A4 ) =           , [0.700, 0.855], [0.000, 0.000] , [0.227, 0.409], [0.000, 0.003] s1.099 , s1.477 s0.568 , s0.739 w(A ˜ 1 A3 ) = w(A ˜ 3 A5 ) =           s0.926 , s1.229 , [0.579, 0.697], [0.000, 0.000] s0.821 , s0.938 , [0.523, 0.731], [0.000, 0.000] w(A ˜ 1 A4 ) = w(A ˜ 4 A1 ) =           , [0.454, 0.590], [0.000, 0.001] , [0.451, 0.647], [0.000, 0.000] s0.715 , s0.934 s0.382 , s0.513 w(A ˜ 1 A5 ) = w(A ˜ 4 A2 ) =           s1.175 , s1.515 , [0.591, 0.727], [0.000, 0.000] s1.099 , s1.447 , [0.700, 0.855], [0.000, 0.000] w(A ˜ 2 A1 ) = w(A ˜ 4 A3 ) =           s0.249 , s0.285 s0.785 , s0.994 , [0.027, 0.098], [0.006, 0.127] , [0.622, 0.779], [0.000, 0.000] w(A ˜ 2 A3 ) = w(A ˜ 4 A5 ) =           s0.865 , s1.061 , [0.485, 0.583], [0.000, 0.000] s1.029 , s1.279 , [0.633, 0.801], [0.000, 0.000] w(A ˜ 2 A4 ) = w(A ˜ 5 A1 ) =           s0.249 , s0.285 s0.174 , s0.218 , [0.027, 0.098], [0.006, 0.127] , [0.288, 0.522], [0.001, 0.003] w(A ˜ 2 A5 ) = w(A ˜ 5 A2 ) =           s0.865 , s1.061 , [0.485, 0.583], [0.000, 0.000] s0.493 , s0.671 , [0.434, 0.687], [0.000, 0.000] w(A ˜ 3 A1 ) = w(A ˜ 5 A3 ) =           , [0.307, 0.569], [0.000, 0.000] , [0.388, 0.516], [0.000, 0.000] s0.423 , s0.503 s0.528 , s0.749 w˜  (A3 A2 ) = w(A ˜ 5 A4 ) =           s0.493 , s0.671 s0.319 , s0.454 , [0.434, 0.687], [0.000, 0.000] , [0.206, 0.345], [0.004, 0.028] Overall cons weights w(A ˜ 1 ≺ A2 ) = w(A ˜ 3 ≺ A4 ) =           s0.249 , s0.285 s0.785 , s0.994 , [0.027, 0.098], [0.006, 0.127] , [0.622, 0.779], [0.000, 0.000] w(A ˜ 1 ≺ A3 ) = w(A ˜ 3 ≺ A5 ) =           s0.423 , s0.503 s0.528 , s0.749 , [0.307, 0.569], [0.000, 0.000] , [0.388, 0.516], [0.000, 0.000] w(A ˜ 1 ≺ A4 ) = w(A ˜ 4 ≺ A1 ) =           s0.382 , s0.513 s0.715 , s0.934 , [0.451, 0.647], [0.000, 0.000] , [0.454, 0.590], [0.000, 0.001] w(A ˜ 1 ≺ A5 ) = w(A ˜ 4 ≺ A2 ) =           s0.174 , s0.218 s0.249 , s0.285 , [0.288, 0.522], [0.001, 0.003] , [0.027, 0.098], [0.006, 0.127] w(A ˜ 2 ≺ A1 ) = w(A ˜ 4 ≺ A3 ) =           s1.099 , s1.477 s0.568 , s0.739 , [0.700, 0.855], [0.000, 0.000] , [0.227, 0.409], [0.000, 0.003] w(A ˜ 2 ≺ A3 ) = w(A ˜ 4 ≺ A5 ) =           s0.493 , s0.671 s0.319 , s0.454 , [0.434, 0.687], [0.000, 0.000] , [0.206, 0.345], [0.004, 0.028] w(A ˜ 2 ≺ A4 ) = w(A ˜ 5 ≺ A1 ) =           s1.099 , s1.447 s1.175 , s1.515 , [0.700, 0.855], [0.000, 0.000] , [0.591, 0.727], [0.000, 0.000] w(A ˜ 2 ≺ A5 ) = w(A ˜ 5 ≺ A2 ) =           s0.493 , s0.671 s0.865 , s1.061 , [0.434, 0.687], [0.000, 0.000] , [0.485, 0.583], [0.000, 0.000] (continued)

174

7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

Table 7.7 (continued) w(A ˜ 3 ≺ A1 ) = w(A ˜ 5 ≺ A3 ) =           s0.926 , s1.229 s0.821 , s0.938 , [0.579, 0.697], [0.000, 0.000] , [0.523, 0.731], [0.000, 0.000] w(A ˜ 3 ≺ A2 ) = w(A ˜ 5 ≺ A4 ) =           s0.865 , s1.061 s1.029 , s1.279 , [0.485, 0.583], [0.000, 0.000] , [0.633, 0.801], [0.000, 0.000] Overall indifference weights w(A ˜ 1 ≈ A2 ) = w(A ˜ 2 ≈ A4 ) =           , [0.000, 0.000], [0.000, 0.000] , [0.000, 0.000], [0.000, 0.000] s0.000 , s0.000 s0.000 , s0.000 w(A ˜ 1 ≈ A3 ) = w(A ˜ 2 ≈ A5 ) =           s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] w(A ˜ 1 ≈ A4 ) = w(A ˜ 3 ≈ A4 ) =          s0.249 , s0.285 s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] , [0.027, 0.098], [0.006, 0.127] w(A ˜ 1 ≈ A5 ) = w(A ˜ 3 ≈ A5 ) =           s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] w(A ˜ 2 ≈ A3 ) = w(A ˜ 4 ≈ A5 ) =           s0.000 , s0.000 s0.000 , s0.000 , [0.000, 0.000], [0.000, 0.000] , [0.000, 0.000], [0.000, 0.000]

δ1 = 4 − 0 = 4, δ2 = 2 − 2 = 0, δ3 = 1 − 3 = −2, δ4 = 3 − 1 = 2, δ5 = 0 − 4 = −4.

Then the ranking result of the five suppliers is derived as A1 A4 A2 A3 A5 . Thus, A1 is the optimal green supplier among the five alternatives.

7.4.3 Comparisons Analysis To illustrate the accuracy of the developed GSES model, we make a comparative analysis with the fuzzy AHP-ARAS (Liao et al. 2016), the fuzzy TOPSIS (Kannan et al. 2014) and the IF-GRA (Bali et al. 2013). Using the proposed model and the three comparative methods, the orders of the five suppliers derived for the above case study are depicted in Fig. 7.4. As visualized in Fig. 7.4, A1 is the optimal green supplier based on the presented model and the three comparative methods. Therefore, it verifies the effectiveness of the new GSES model. Additionally, there are some differences of the orders determined by the listed methods. For instance, A4 ranks before A2 using the proposed model while A2 ranks before A4 using the fuzzy AHP-ARAS. Besides, A4 is ranked before A2 by the fuzzy TOPSIS and the IF-GRA methods. Therefore, A4 is more appropriate than A2 . It can also be seen that the last alternative is A5 by the proposed model while the last alternative is A2 by the fuzzy TOPSIS. In practice, A2 is better than A5 since A2 has higher evaluation values than A5 on C1 , C3 , and C4 , and the weights of C1 and C3 are bigger than C2 and C5 , respectively. According to the IFGRA method, A3 is ranked before A2 ; but when using the proposed model, A2 is

Table 7.8 Comprehensive pros and cons indicated value of each supplier pair     ˜ 0.5 (A1 , A2 )= s O 3.858 , s5.811 , [0.027, 0.098], [0.006, 0.127]     ˜ 0.5 (A1 , A3 )= s O 1.843 , s2.910 , [0.307, 0.568], [0.000, 0.000]     ˜ 0.5 (A1 , A4 )= s O 1.285 , s2.125 , [0.469, 0.611], [0.000, 0.009]      ˜ 0.5 (A1 , A5 )= s O 5.402 , s8.729 , [0.288, 0.522], [0.001, 0.003]      ˜ 0.5 (A2 , A3 )= s O 1.275 , s2.154 , [0.434, 0.584], [0.000, 0.000]

    ˜ 0.5 (A2 , A4 )= s O 0.172 , s0.259 , [0.027, 0.098], [0.006, 0.127]     ˜ 0.5 (A2 , A5 )= s O 1.275 , s2.154 , [0.434, 0.584], [0.000, 0.000]     ˜ 0.5 (A3 , A4 )= s O 0.571 , s0.946 , [0.227, 0.409], [0.000, 0.003]      ˜ 0.5 (A3 , A5 )= s O 1.096 , s1.864 , [0.388, 0.516], [0.000, 0.000]      ˜ 0.5 (A4 , A5 )= s O 2.270 , s4.008 , [0.206, 0.345], [0.005, 0.028]

7.4 Case Study 175

176

7 GSES with Interval-Valued Intuitionistic Uncertain Linguistic AQM

Fig. 7.3 The final directed graph

Fig. 7.4 Ranking comparison

ranked before A3 . Actually, A2 is more suitable than A3 , and the reason is similar to the comparison between A2 and A5 . Therefore, the ranking of the five suppliers acquired according to the developed GSES model is more credible and reasonable. The explanations for the ranking inconsistences largely depend on the features of the presented model and the three comparative methods. First, the fuzzy AHPARAS and the fuzzy TOPSIS use triangular fuzzy numbers and the IF-GRA uses intuitionistic fuzzy numbers for assessing the performance of suppliers. However, the proposed model adopts the IVIULSs to assess green suppliers, which are able to

7.4 Case Study

177

capture the vagueness and uncertainty of evaluations provided by decision makers. Second, the fuzzy AHP-ARAS method utilizes AHP to compute criteria weights. In contrast, the IVIUL-BWM used in the developed model can derive a more accurate result since it can reduce the inconsistency from pairwise comparisons. Third, comparing with the weighted averaging, the geometric mean and the ordered weighted averaging operators used in fuzzy AHP-ARAS, fuzzy TOPSIS and IFGRA, respectively, the IVIULCGM operator is employed in the developed model, which considers the interactions among decision makers and thus makes the ranking result of alternatives more practical. Furthermore, based on the IVIUL-AQM, a more actual and accurate ranking of candidate suppliers can be derived under vague and uncertain information environment.

7.5 Chapter Summary This chapter reports a new GSES model by combining the IVIUL-BWM with the IVIUL-AQM to choose the most appropriate green supplier. In the developed model, IVIULSs are utilized to manage decision makers’ assessments on green suppliers’ performance; the IVIUL-BWM is used for computing the optimal evaluation criteria weights; and the IVIUL-AQM is applied to generate the ranking orders of candidate green suppliers. Finally, a practical example of a watch manufacturer is adopted to demonstrate the feasibility of the developed GSES model. The results show that the proposed model is more capable to capture ambiguity and uncertainty of decision makers’ evaluations and is more efficient and effective to derive the ranking orders of candidate green suppliers.

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Chapter 8

GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

With strengthening global consciousness of environmental protection, green supply chain management plays an increasingly important role in modern enterprise production operation management. A critical means to implement the green supply chain management is incorporating environmental requirements into supplier selection practices. In this chapter, we put forward a new integrated approach by using intervalvalued intuitionistic uncertain linguistic sets (IVIULSs) and grey relational analysis (GRA)-technique for order preference by similarity to ideal solution (TOPSIS) method for the evaluation and selection of green suppliers. First, various qualitative assessments of alternatives provided by decision makers are described by the IVIULSs. Then, the GRA-TOPSIS method is extended and employed to prioritize the alternative suppliers. Finally, an illustrative example in the agri-food industry is presented to verify the proposed GSES method and demonstrate its practicality and effectiveness.

8.1 Introduction In recent years, public concerns on environmental issues and sustainable development have increased greatly throughout the world (Agyabeng-Mensah et al. 2020; Micheli et al. 2020). As a result, many business organizations have modified their supply chain activities to reduce negative environmental impacts and enhance sustainability levels (Fallahpour et al. 2017; Liu et al. 2017; Centobelli et al. 2018). Nowadays, green supply chain management (GSCM) has become more prominent than ever before, because the competitiveness of a company is strongly dependent on the performance of its supply chain (Pourhejazy and Kwon 2016; Luthra et al. 2017). GSCM, as a new management mode to pursue both economic benefits and environment sustainable development, is the management of the flows of funds, information, and products between and among all stages of a supply chain by taking into account the goals from the economic, environmental and social dimensions of sustainable development © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_8

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

derived from customer and stakeholder requirements (Hamdan and Cheaitou 2017; Qin et al. 2017). The GSCM literature has focused on aiding existing organizations enhance their environmental performance through acquiring certifications or introducing green practices (Centobelli et al. 2017; Zhao et al. 2017). GSCM comprises all the activities related to the transformation and flow of goods and services, such as green product design, green supplier evaluation, green production, green packaging and transportation, green marketing and resource recycling. Among them, green supplier selection is the essential core, which directly impacts the compatibility of a supply chain and the environmental performance of a manufacturer (Wang et al. 2017). Therefore, selection of the optimal green supplier is a key strategic decision in the management of green supply chain, which needs to be explored methodically to implement green initiatives in supply chains (Bektur 2020; Çalık 2020; Ecer 2020; Hendiani et al. 2020). Generally, there are two issues in green supplier selection, which are the evaluation of suppliers and the prioritization of suppliers. In many real situations, due to the complexity of GSES problems, decision makers feel more confident to express their judgements using linguistic descriptors rather than in the form of numerical values (Uygun and Dede 2016; Wang et al. 2017). Moreover, due to information insufficiency or professional restriction, experts may have difficulties in giving their assessments by simple linguistic terms. Instead, they often doubt among different linguistic terms or require complex linguistic expressions to represent their opinions accurately (Rodríguez and Martínez 2013; Rodríguez et al. 2016). The definition of interval-valued intuitionistic uncertain linguistic sets (IVIULSs), a combination of uncertain linguistic variables (Xu 2004, 2006) and interval-valued intuitionistic fuzzy sets (Li 2010; Meng et al. 2013), was proposed by Liu (2013) for handling the ambiguity and uncertainty of decision makers’ subjective assessments. The basic feature of the IVIULSs is that the linguistic variable, membership degree and non-membership degree of each element in a given set are presented by interval ranges rather than crisp numbers. Owing to its characteristics and capacities, the IVIULSs have been widely utilized by researchers in various areas, including disaster risk management response capabilities assessment (Otay and Jaller 2020), knowledge representation and reasoning (Yue et al. 2020), renewable energy project selection (Davoudabadi et al. 2021), failure mode and effect analysis (Liu et al. 2019c), and technology portfolios assessment of clean energy-driven desalination-irrigation systems (Hu et al. 2020). On the other hand, many economic and environmental criteria should be considered during the GSES process. The economic factors include price, quality, delivery, flexibility, and so on (Lima Junior and Carpinetti 2016; Büyüközkan and Göçer 2017; Zhao et al. 2017); the environmental factors comprise green image, green competencies, reverse logistics, green packaging, and so on (Büyüközkan and Göçer 2017; Hamdan and Cheaitou 2017; Wang et al. 2017). Thus, green supplier selection is a complicated multi-criteria decision making (MCDM) problem and MCDM methods have been recognized as a meritorious tool for evaluating the performance of green suppliers under conflicting criteria. Grey relational analysis (GRA), as one of wellknown MCDM methods, is a multi-factor analysis tool to indicate and measure the

8.1 Introduction

183

similarity in order to analyze uncertain relations between alternative series and a reference series (Deng 1989). The advantage of the GRA method is that it can deal with complex real-world problems marked by vague, incomplete and inaccurate information (Banaeian et al. 2018; Tseng et al. 2018; Liu et al. 2019b). Besides, technique for order preference by similarity to ideal solution (TOPSIS) is a typical MCDM method proposed by Hwang and Yoon (1981), which has been extensively applied in a variety of fields. The basic principle of the TOPSIS method is that the most satisfactory alternative should have the nearest distance to the positive ideal solution (PIS) and the farthest distance to the negative ideal solution (NIS) (Lu et al. 2016; Wang and Chen 2017; Ameri et al. 2018). In order to combine the desired properties of the two methods, the GRA has been integrated with TOPSIS, called as GRA-TOPSIS, for solving MCDM problems recently (Gan et al. 2019; Hu et al. 2019; Liu et al. 2019a; Nie et al. 2019; Prabhu and Ilangkumaran 2019). Based on the analyses discussed above, this chapter proposes a new integrated approach combining IVIULSs and the GRA-TOPSIS method for addressing GSES problems with uncertain linguistic information. First, the IVIULSs are utilized to deal with various uncertainties in the performance assessments of decision makers on alternative suppliers. Second, the GRA-TOPSIS method is extended to prioritize and compare green suppliers by simultaneously computing the grey relational degrees to PIS and NIS. Third, an illustrate example from the agri-food industry is presented to elaborate the application and effectiveness of the proposed GSES approach. The new model has a good reflection of subjective assessments and objective information under uncertain information environment. It is more realistic and practical to select and evaluate the most efficient green supplier from a set of alternatives in a supply chain. The remaining part of this chapter is structured as follows. Section 8.2 provides a review of the existing literature relevant to food supply chain management. Section 8.3 introduces the basic concepts and definitions of IVIULSs. In Sect. 8.4, we develop the integrated GSES framework based on IVIULSs and GRA-TOPSIS method. In Sect. 8.5, a practical example of agri-food industry is given to confirm the practicability and effectiveness of the proposed approach. Finally, we summarize concluding remarks in Sect. 8.6.

8.2 Literature Review Due to the increasing demand for high-quality and nutritious food, stakeholders are more than ever encouraging food processing companies to improve the sustainability performance of their supply chains. Therefore, many researches have been conducted for green supply management in the agri-food industry. For instance, Banaeian et al. (2018) applied three fuzzy group decision making methods, including fuzzy TOPSIS, fuzzy VIKOR and fuzzy GRA, to complete the supplier evaluation and selection for a manufacturer of edible vegetable oils and detergents. Govindan

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

et al. (2017) applied a preference ranking organization method for enrichment evaluation (PROMETHEE)-based approach to deal with green supplier selection for an India food processing industry. Yazdani et al. (2017) presented an integrated approach consisting of decision-making trial and evaluation laboratory (DEMATEL), quality function deployment (QFD), and COPRAS (COmplex PRoportional ASsessment of alternatives) methods, and applied it for an Iranian dairy company. Tavana et al. (2017) developed an integrated sustainable supplier selection model to analyze the case study of a dairy company, in which analytic network process (ANP) is integrated with QFD to weight customer requirements and evaluation criteria, and multiobjective optimization based on ratio analysis (MOORA) and weighted aggregated sum product assessment (WASPAS) are used to rank suppliers. Shashi et al. (2017) investigated the value addition relationships between different parties involved in the food supply chain to improve overall as well as individual benefits of the supply chain players. In (Baraki and Kianfar 2017), a multi-objective mathematical model was proposed to select suppliers and allocate optimal orders to them in a two-echelon supply chain, including supply and distribution echelons. The efficiency and effectiveness of the proposed model were validated through implementing in a food distribution chain in Iran. In (Ravi and Shankar 2014), the authors explored the relationships among critical issues of reverse logistics and the dissimilarities among different industrial sectors in implementing common reverse logistics practices. A nationwide survey showed that companies in electronics sector significantly differ from those of other sectors (i.e., auto, paper, and food and beverage processing) in adoption of reverse logistics practices. Shashi et al. (2018) provided a literature review focused on the topic of food cold chain management over the last sixteen years to identify state of the art in the literature and define appropriate research questions for future research. Recently, Mehdiyeva et al. (2020) investigated the barriers and drivers of the implementation and management of green agricultural supply chains in Azerbaijan. Liu et al. (2020) adopted big data and blockchain for investment decision and coordination in a green agri-food supply chain considering information service. Giallanza and Puma (2020) considered a three-echelon fuzzy green vehicle routing problem for designing a regional agri-food supply chain on a time horizon. Chauhan et al. (2020) established a hybrid model using structural modeling (ISM), DEMATEL, and ANP to evaluate and select a sustainable supply chain for agri-produce in India.

8.3 Preliminary The basic knowledge about IVIULSs are introduced in Sect. 7.2, including their definitions, operations, and distance measure. Here, the interval-valued intuitionistic uncertain linguistic weighted geometric average (IVIULWGA) operator is given to facilitate understanding of the GSES method proposed in this chapter.

8.3 Preliminary

185

      Definition 8.1 (Liu 2013) Let a˜ i = sθ(a˜ i ) , sτ (a˜ i ) , u L (a˜ i ), u U (a˜ i ) , v L (a˜ i ), vU (a˜ i ) (i = 1, 2, . . . , n) be a collection of IVIULNs. Then, the IVIULWGA operator is defined as: n

IVIULWGAw (a˜ 1 , a˜ 2 , . . . , a˜ n ) = ⊗ (a˜ i )wi i=1   n n

  U wi

wi L u (a˜ i ) , u (a˜ i ) = s n , s n , , wi wi  1−

(θ(a˜ i ))

(θ(a˜ i ))

i=1

n



i=1

i=1

i=1

n

 wi wi L 1 − v (a˜ i ) , 1 − 1 − vU (a˜ i )

i=1

,

(8.1)

i=1

where w = (w1 , w2 , . . . , wn )T is the weight vector of a˜ i (i = 1, 2, . . . , n) with the n  wi = 1. condition wi ∈ [0, 1] and i=1

8.4 The Proposed GSES Approach In this section, we put forward an integrated approach based on IVIULSs and GRATOPSIS method to evaluate and select the optimal green supplier. In the proposed GSES model, the IVIULSs are used to assess the green performance of suppliers under economic and environmental criteria, and the GRA-TOPSIS method is utilized for ranking alternative green suppliers. The flowchart of the proposed approach for the selection of green suppliers is shown in Fig. 8.1. Suppose that a GSES problem has m alternatives Ai (i = 1, 2, . . . , m), n evaluation criteria C j ( j = 1, 2, . . . , n) and l decision makers DMk (k = 1, 2, . . . , l). The l  weight of DMk is given as λk which satisfies λk > 0 and λk = 1; it reflect the k=1

relative significance  of the decision maker in the process of green supplier selection. k ˜ is the evaluation matrix by the kth decision maker for alterSuppose P = p˜ ikj m×n       native Ai with regard to criterion C j , and p˜ ikj = saiLjk , saiUjk , u iLjk , u Uijk , viLjk , viUjk   is the IVIULN given by DM k based on the linguistic term set S = s0 , s1 , . . . , sg .  = w˜ 1k , w˜ 2k , .. . , w˜ nk be Let w˜ k   the weight  vector of criteria provided by DMk , where k U U    L w˜ j = sa L , saU , u jk , u jk , v jk , v jk is the IVIULN assigned to the weight of jk jk   C j by using the linguistic term set Sw = s0 , s1 , . . . , sh . Based on these notations and assumptions, the procedure of the proposed GSES model is expressed as the following steps. ˜ Step 1 Construct the collective evaluation matrix P. First, we use the IVIULWGA operator to aggregate the individual evaluation matrices P˜ k (k = 1, 2, . . . , l) to establish the collective evaluation matrix P˜ =

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

Fig. 8.1 Flowchart of the proposed green supplier selection approach



p˜ i j

 m×n

, where λk  l  p˜ i j = IVIULWGA p˜ i1j , p˜ i2j , . . . , p˜ il j = ⊗ p˜ ikj ,

(8.2)

k=1

where p˜ i j =

      saiLj , saiUj , u iLj , u Uij , viLj , viUj is the collective assessment of alter-

native Ai with respect to criterion C j , and saiLj = s l  k=1

aiLjk

λk ,sa U ij

= s l  k=1

aiUjk

λk ,u iLj

=

8.4 The Proposed GSES Approach

λk l   u iLjk , u Uij

k=1 l   k=1

1 − viUjk

 λk

187

 λk λk l  l    u Uijk , viLj = 1 − 1 − viLjk , viUj

=

k=1

= 1 −

k=1

.

Step 2 Acquire the collective criteria weight vector w. ˜ Each decision maker has his/her own experience, which may result in different assessments on the criteria weights. The collective weight vector of criteria,w˜ = (w˜ 1 , w˜ 2 , . . . , w˜ n ), can also be computed by the IVIULWGA operator, i.e., λk  l  w˜ j = IVIULWGA w˜ 1j , w˜ 2j , . . . , w˜ lj = ⊗ w˜ kj ,

(8.3)

k=1

where w˜ j =  sa L = s l j

1−

l  k=1



k=1



     , vL is the aggregated weight of C j , and sa L , sa U , u L , u U , vU j j j j j j λk l l    L λk U  U   L  λk , s U = s   λk ,u j = u u , u = ,vL j jk jk j = a l U

 a Ljk

1 − vL jk

j

 λk

k=1

,vUj = 1 −

a jk

l  k=1

k=1

k=1

  λk 1 − vU . jk

Step 3 Determine the PIS and the NIS. The PIS and the NIS represent the most desirable alternative and the least desirable alternative, respectively. The sets of beneficial criteria and cost criteria are denoted as J1 and J2 . Then, the PIS and the NIS can be defined by the following equations:

Suppose p˜ +j = Then, we have

 p˜ + = p˜ 1+ , p˜ 2+ , . . . , p˜ n+ ,

(8.4)

 p˜ − = p˜ 1− , p˜ 2− , . . . , p˜ n− .

(8.5)

      L+ U+ L+ U + U+ , u , v for j = 1, 2, . . . , n. sa L+ , s , u , v a j j j j j j     max saiLj | j ∈ J1 , min saiLj | j ∈ J2 ,

(8.6)

s

=

   U max s | j ∈ J1 , min sai j | j ∈ J2 ,

(8.7)

u L+ j

    L L = max u i j | j ∈ J1 , min u i j | j ∈ J2 ,

(8.8)

    max u Uij | j ∈ J1 , min u Uij | j ∈ J2 ,

(8.9)

    L L = min vi j | j ∈ J1 , max vi j | j ∈ J2 ,

(8.10)

sa L+ = j

i

 a Uj +

i

u Uj + = v L+ j

i

i

i

i

aiUj

i

i

i

i

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

vUj + Suppose p˜ −j = Then, we have

    U U = min vi j | j ∈ J1 , max vi j | j ∈ J2 . i

i

(8.11)

      L− U− L− U − U− , u , v for j = 1, 2, . . . , n. sa L− , s , u , v aj j j j j j     = min saiLj | j ∈ J1 , max saiLj | j ∈ J2 ,

(8.12)

saUj − =

   min saiUj | j ∈ J1 , max saiUj | j ∈ J2 ,

(8.13)

u L− j =

    min u iLj | j ∈ J1 , max u iLj | j ∈ J2 ,

(8.14)

    U U = min u i j | j ∈ J1 , max u i j | j ∈ J2 ,

(8.15)

v L− = j

    max viLj | j ∈ J1 , min viLj | j ∈ J2 ,

(8.16)

vUj − =

    max viUj | j ∈ J1 , min viUj | j ∈ J2 .

(8.17)

sa L− j

i



u Uj −

i

i

i

i

i

i

i

i

i

i

i

Step 4 Calculate the grey relation coefficients to the PIS and the NIS. The PIS and the NIS can be taken as reference sequences and all the alternative green suppliers can be considered as comparative sequences. The grey relation coefficients are used to determine how close p˜ i j to p˜ +j and p˜ −j . The grey relation coefficients of each criterion of the m green suppliers to the PIS and the NIS can be calculated by

ri+j

    min min d p˜ i j , p˜ +j + ς max max d p˜ i j , p˜ +j i j i j     , = + d p˜ i j , p˜ j + ς max max d p˜ i j , p˜ +j i

ri−j

j

    min min d p˜ i j , p˜ −j + ς max max d p˜ i j , p˜ −j i j i j     = , − d p˜ i j , p˜ j + ς max max d p˜ i j , p˜ −j i

i = 1, 2, . . . , m, j = 1, 2, . . . , n,

(8.18) i = 1, 2, . . . , m, j = 1, 2, . . . , n,

j

(8.19)     where d p˜ i j , p˜ +j and d p˜ i j , p˜ −j represent the distances from p˜ i j to p˜ +j and p˜ −j , respectively. ς is the distinguishing coefficient, ς ∈ [0, 1]; generally, ς = 0.5 is applied in the real decision making problems.

8.4 The Proposed GSES Approach

189

As a result, the grey relation coefficient matrices of alternatives to the PIS R + and the NIS R − can be represented as: ⎡

+ r11 ⎢ r+ ⎢ 21 + R =⎢ . ⎣ ..

+ r12 + r22 .. .

··· ··· .. .

+ r1n + r2n .. .

− r12 − r22 .. .

··· ··· .. .

− r1n − r2n .. .

⎤ ⎥ ⎥ ⎥, ⎦

(8.20)

+ + + rm2 · · · rmn rm1

⎡

− r11 ⎢ r− ⎢ 21 R− = ⎢ . ⎣ ..

⎤ ⎥ ⎥ ⎥. ⎦

(8.21)

− − − rm2 · · · rmn rm1

Step 5 Compute the grey relation grades to the PIS and the NIS. This step is to calculate the grey relation grades of the alternative suppliers to the PIS r˜i+ and the NIS r˜i− by n   w˜ j ri+j , r˜i+ = r˜ p˜ i , p˜ + =

i = 1, 2, . . . , m,

(8.22)

w˜ j ri−j , i = 1, 2, . . . , m.

(8.23)

j=1

r˜i−



= r˜ p˜ i , p˜

−



=

n  j=1

Here, w˜ j ri+j =



   ri+j ri+j   L ri+j  L ri+j   , vj . sr + a L , sr + aU , 1 − 1 − u L , 1 − 1 − u U , vj j j ij

j

ij

j

(8.24) Then,˜ri+ can be represented by ⎡

⎤ ⎡

r˜i+ = ⎣s  n ⎡ ⎣

j=1

ri+j a Lj

, s  n j=1

⎤ n n



+ +   r r ij ij ⎦ ⎦ , ⎣1 − 1 − u L 1 − u U ,1 − , j j U

ri+j a j

⎤

j=1

n n

 L ri+j

 U ri+j ⎦ , i = 1, 2, . . . , m. vj vj , j=1

j=1

In addition,˜ri− can be calculated as

j=1

(8.25)

190

8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

⎤ ⎡

⎡ r˜i− = ⎣s  n ⎡ ⎣

j=1

ri−j a Lj

, s  n j=1

⎤ n n



− −   r r ij ij ⎦ ⎦ , ⎣1 − 1 − u L 1 − u U , ,1 − j j U

ri−j a j

⎤

j=1

n n

 L ri−j

 U ri−j ⎦ , i = 1, 2, . . . , m. , vj vj j=1

j=1

(8.26)

j=1

Step 6 Calculate the relative closeness degrees of alternatives. The relative closeness degree c˜i of every alternative supplier is calculated by using the following formula: c˜i =

r˜i+ , i = 1, 2, . . . , m. r˜i+ + r˜i−

(8.27)

For ranking the alternative green suppliers and selecting the most appropriate one, we need to calculate the expected values E(c˜i )(i = 1, 2, . . . , m) and the accuracy degrees T (c˜i )(1, 2, . . . , m), respectively. Finally, we can sort the m alternatives in descending order to obtain the optimum green supplier.

8.5 Case Illustration 8.5.1 Implementation In this section, a case study from (Banaeian et al. 2018) is used for demonstrating the proposed GSES approach. Food processing industry is one of the heavily polluting industries which makes contributes to climate change and global warming. Under great environmental pressure from society, the agri-food sector in a food processing company needs to take actions to control and reduce the environmental impacts of food production (You et al. 2015; Govindan et al. 2017). The case company is one of the leading Iranian manufactures of edible vegetable oils which contributes to the economy of the country; it is International Organization for Standardization (IOS) 14,000 certified and undertakes its related environmental responsibilities including improving its suppliers’ environmental performance (Banaeian et al. 2018). The main raw materials of the company contain olive oil, palm oil, sunflower oil and soybean oil. The objective of this case study is to assist the company to choose the best green supplier from some alternatives. After initial screening, there are ten alternative suppliers remained for further assessment, including four olive oil suppliers (O1 , O2 , O3 , and O4 ), three palm oil suppliers (P1 , P2 , and P3 ) and three sunflower-soybean oil suppliers (SS1 , SS2 , and SS3 ). Based on a review of the supplier selection literature, service level, product quality and price are identified as the conventional criteria, and environmental management

8.5 Case Illustration

191

system is identified as the environmental criterion. These four criteria are represented as C j ( j = 1, 2, 3, 4). A committee of five decision makers,(DMk , k = 1, 2, . . . , 5), is built to give the evaluation of suppliers’ performance on each criterion and the relative importance of criteria. In consideration of their different experience and knowledge, the weight vector of the five decision makers is determined as λ = (0.25, 0.2, 0.3, 0.15, 0.1). The following linguistic term sets are used to evaluate the suppliers’ performance and the criteria importance: S = {s0 = extremly poor, s1 = very poor, s2 = poor, s3 = medium poor, s4 = fair, s5 = medium good, s6 = good, s7 = very good, s8 = extremely good},  Sw = s0 = extr emly low, s1 = ver y low, s2 = low, s3 = medium low,

 s4 = f air, s5 = medium high, s6 = high, s7 = ver y high, s8 = extr emely high .

The performance assessments of the alternative suppliers with regard to each criterion are in the form of IVIULNs. For example, the assessment results of the ten suppliers offered by the first decision maker DM1 are tabulated in Table 8.1. In addition, the weights of criteria evaluated by the five decision makers are shown in Table 8.2. Next, the calculation procedure of the proposed model for the selection of green suppliers is described. We choose the olive oil suppliers as an example and similar steps can be applied to other types of vendors. Step 1 By Eq. (8.2), the five individual evaluation matrices P˜ k(k = 1, 2, . . . , 5) are aggregated to obtain the collective evaluation matrix P˜ = pi j 10×4 , as shown in Table 8.3. Step 2 Opinions of the five decision makers on criteria importance are aggregated based on Eq. (8.3) and the collective weights of the four criteria are derived as:      , [0.725, 0.824], [0.071, 0.146] , , s7.223 w˜ 1 = s6.513      w˜ 2 = s5.590 , [0.667, 0.818], [0.086, 0.158] , , s6.789      w˜ 3 = s4.849 , [0.648, 0.767], [0.100, 0.184] , , s5.527      w˜ 4 = s3.936 , [0.626, 0.749], [0.112, 0.192] . , s4.648 Step 3 Since service level, product quality and environmental management system are benefit criteria,J1 = {C1 , C2 , C4 } and price is a cost criterion,J2 = {C3 }, the PIS and the NIS of the olive oil suppliers are determined as: P˜ + = ([s5.598 , s6.614 ], [0.673, 0.738], [0.071, 0.171] , [s4.512 , s5.554 ], [0.696, 0.800], [0.122, 0.171], [s3.224 , s4.084 ], [0.600, 0.714], [0.171, 0.246], [s6.283 , s6.957 ], [0.706, 0.789], [0.071, 0.146]),

[s5 , s6 ], [0.6, 0.7], [0.1, 0.2] [s5 , s5 ], [0.6, 0.7], [0.2, 0.2] [s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s5 , s6 ], [0.6, 0.7], [0.1, 0.2]

[s2 , s3 ], [0.6, 0.7], [0.2, 0.2] [s7 , s8 ], [0.6, 0.7], [0.1, 0.2] [s4 , s5 ], [0.7, 0.7], [0.1, 0.2] [s4 , s5 ], [0.7, 0.8], [0.1, 0.1]

SS3

[s7 , s8 ], [0.7, 0.8], [0.1, 0.2] [s4 , s5 ], [0.6, 0.7], [0.1, 0.2] [s7 , s7 ], [0.7, 0.7], [0.1, 0.2] [s4 , s4 ], [0.7, 0.7], [0.1, 0.2]

[s5 , s6 ], [0.7, 0.8], [0.1, 0.1] [s4 , s4 ], [0.7, 0.8], [0.1, 0.1] [s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s4 , s5 ], [0.6, 0.7], [0.1, 0.3]

[s2 , s3 ], [0.6, 0.7], [0.2, 0.2] [s3 , s3 ], [0.7, 0.7], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.1, 0.2] [s1 , s2 ], [0.7, 0.7], [0.1, 0.2]

P3

[s6 , s7 ], [0.6, 0.6], [0.2, 0.3] [s5 , s6 ], [0.7, 0.8], [0.1, 0.2] [s5 , s5 ], [0.7, 0.8], [0.1, 0.1] [s5 , s6 ], [0.7, 0.8], [0.1, 0.1]

[s1 , s2 ], [0.6, 0.7], [0.1, 0.2] [s0 , s1 ], [0.7, 0.7], [0.1, 0.2] [s2 , s2 ], [0.8, 0.8], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.1, 0.1]

O4

P2

[s3 , s4 ], [0.7, 0.7], [0.1, 0.2] [s7 , s8 ], [0.7, 0.8], [0.1, 0.2] [s5 , s6 ], [0.6, 0.7], [0.1, 0.2] [s6 , s7 ], [0.7, 0.7], [0.1, 0.2]

P1

[s6 , s7 ], [0.6, 0.7], [0.2, 0.3] [s4 , s5 ], [0.6, 0.6], [0.2, 0.2] [s4 , s4 ], [0.8, 0.9], [0.1, 0.1] [s5 , s6 ], [0.7, 0.7], [0.1, 0.2]

O3

C4

[s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.1, 0.2] [s3 , s3 ], [0.6, 0.7], [0.2, 0.3] [s6 , s7 ], [0.7, 0.8], [0.1, 0.1]

C3

O1

C2

O2

C1

Suppliers Criteria

Sunflower-soybean SS1 oil SS2

Palm oil

Olive oil

Kind of suppliers

Table 8.1 Performance assessments of alternatives by the first decision maker

192 8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

DM5

DM4

DM3

DM2

DM1

Decision makers

C1      s6 , s7 , [0.8, 0.9], [0.1, 0.1]      s7 , s8 , [0.7, 0.8], [0.1, 0.2]      s7 , s7 , [0.8, 0.8], [0.0, 0.1]      s7 , s8 , [0.6, 0.8], [0.1, 0.2]      s5 , s6 , [0.6, 0.8], [0.1, 0.2]

Criteria C2      s6 , s7 , [0.7, 0.8], [0.1, 0.1]      s5 , s6 , [0.7, 0.8], [0.1, 0.2]      s7 , s8 , [0.7, 0.9], [0.1, 0.1]      s7 , s8 , [0.7, 0.8], [0.0, 0.2]      s5 , s6 , [0.5, 0.7], [0.1, 0.3]

Table 8.2 Criteria weight ratings by the five decision makers C3      s5 , s6 , [0.6, 0.7], [0.1, 0.3]      s6 , s6 , [0.7, 0.7], [0.1, 0.2]      s4 , s5 , [0.7, 0.8], [0.1, 0.1]      s5 , s5 , [0.6, 0.9], [0.1, 0.1]      s5 , s6 , [0.6, 0.8], [0.1, 0.2]

C4      s3 , s4 , [0.7, 0.8], [0.2, 0.2]      s4 , s4 , [0.7, 0.9], [0.1, 0.1]      s4 , s5 , [0.6, 0.7], [0.1, 0.2]      s5 , s6 , [0.5, 0.7], [0.0, 0.2]      s5 , s5 , [0.6, 0.6], [0.1, 0.3]

8.5 Case Illustration 193

Sunflower-soybean oil

Palm oil

O1

Olive oil

SS3

SS2

SS1

P3

P2

P1

O4

O3

O2

Suppliers

SS3

SS2

SS1

P3

P2

P1

O4

O3

Kind of suppliers

Sunflower-soybean oil

Palm oil

O1

Olive oil

O2

Suppliers

Kind of suppliers

Table 8.3 The collective evaluation matrix Criteria

C3    s3.224 , s4.084 , [0.678, 0.751], [0.171, 0.246]    s4.830 , s5.275 , [0.743, 0.823], [0.115, 0.176]    s5.821 , s6.430 , [0.724, 0.762], [0.126, 0.236]    s3.512 , s4.143 , [0.659, 0.743], [0.126, 0.185]    s5 , s5.378 , [0.700, 0.800], [0.075, 0.131]    s2.499 , s3.112 , [0.648, 0.709], [0.100, 0.171]    s4.657 , s5.578 , [0.718, 0.784], [0.056, 0.146]    s5.669 , s6.118 , [0.678, 0.698], [0.056, 0.146]    s2.297 , s2.692 , [0.612, 0.680], [0.166, 0.251]    s3.365 , s4.128 , [0.683, 0.783], [0.111, 0.156]

Criteria

C1    s1.866 , s2.958 , [0.673, 0.738], [0.071, 0.171]    s5.598 , s6.614 , [0.553, 0.648], [0.171, 0.271]    s3.458 , s4.839 , [0.676, 0.718], [0.071, 0.171]    s1.722 , s2.805 , [0.640, 0.711], [0.071, 0.187]    s6.382 , s7.384 , [0.629, 0.711], [0.146, 0.196]    s2.822 , s3.657 , [0.653, 0.743], [0.105, 0.148]    s4.394 , s5.405 , [0.707, 0.800], [0.071, 0.126]    s6.123 , s6.804 , [0.723, 0.792], [0.056, 0.126]    s4.148 , s5.169 , [0.578, 0.701], [0.081, 0.176]    s3.047 , s3.901 , [0.590, 0.753], [0.136, 0.200] C4    s4.704 , s5.720 , [0.673, 0.789], [0.100, 0.146]    s4.884 , s5.638 , [0.655, 0.718], [0.071, 0.146]    s6.283 , s6.957 , [0.706, 0.753], [0.131, 0.185]    s4.255 , s5.275 , [0.653, 0.709], [0.090, 0.179]    s5.378 , s6.058 , [0.678, 0.809], [0.046, 0.120]    s1.899 , s2.564 , [0.668, 0.780], [0.085, 0.146]    s3.565 , s4.573 , [0.609, 0.709], [0.046, 0.198]    s4.128 , s4.522 , [0.629, 0.753], [0.076, 0.156]    s2.326 , s2.849 , [0.568, 0.700], [0.056, 0.148]    s4.276 , s4.884 , [0.706, 0.828], [0.081, 0.126]

C2    s3.866 , s4.891 , [0.696, 0.753], [0.122, 0.190]    s2.681 , s3.852 , [0.600, 0.643], [0.185, 0.251]    s4.512 , s5.554 , [0.676, 0.800], [0.126, 0.171]    s0.000 , s2.806 , [0.610, 0.687], [0.148, 0.176]    s5.632 , s6.382 , [0.700, 0.738], [0.110, 0.231]    s2.470 , s3.318 , [0.643, 0.700], [0.156, 0.246]    s3.886 , s4.276 , [0.684, 0.762], [0.090, 0.192]    s3.867 , s4.884 , [0.643, 0.773], [0.120, 0.200]    s3.337 , s4.194 , [0.547, 0.687], [0.126, 0.200]    s3.152 , s4.239 , [0.587, 0.687], [0.068, 0.171]

194 8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

8.5 Case Illustration

195

P˜ − = ([s1.722 , s2.805 ], [0.553, 0.648], [0.171, 0.271] , [s0.000 , s2.806 ], [0.600, 0.643], [0.185, 0.251], [s5.821 , s6.430 ], [0.743, 0.823], [0.115, 0.176], [s4.255 , s5.275 ], [0.653, 0.709], [0.131, 0.185]). Step 4 Based on Eqs. (8.24), (8.25), the grey relation coefficient matrices of the four olive oil suppliers to the PIS and the NIS are computed as shown below: ⎡

  R + = ri+j

4×4

  R − = ri−j

4×4

⎤ 0.404 0.738 0.995 0.608 ⎢ 0.584 0.418 0.484 0.581 ⎥ ⎥ =⎢ ⎣ 0.556 1.000 0.448 0.826 ⎦, 0.378 0.349 0.750 0.484 ⎡ ⎤ 0.651 0.426 0.481 0.812 ⎢ 0.467 0.671 0.812 0.855 ⎥ ⎥ =⎢ ⎣ 0.481 0.381 0.911 0.586 ⎦. 0.723 0.889 0.533 1.000

Step 5 The grey relation grades of each supplier to the PIS and the NIS are calculated by using Eqs. (8.28), (8.29), and the results are listed as follows:      , [0.948, 0.986], [0.002, 0.008] , , s16.255 r˜1+ = s14.235      r˜2+ = s10.907 , [0.898, 0.960], [0.007, 0.026] , , s12.415      r˜3+ = s14.995 , s17.129 , [0.955, 0.988], [0.001, 0.006] ,      r˜4+ = s10.074 , [0.881, 0.951], [0.010, 0.032] ; , s11.490      r˜1− = s12.303 , [0.926, 0.957], [0.004, 0.015] , , s14.031      r˜2− = s14.337 , s16.397 , [0.952, 0.987], [0.001, 0.007] ,      r˜3− = s12.124 , [0.923, 0.973], [0.004, 0.016] , , s13.823      r˜4− = s16.591 , [0.968, 0.993], [0.001, 0.004] . , s18.860 Step 6 By utilizing Eq. (8.27), the relative closeness degrees c˜i (i = 1, 2, 3, 4) of the four olive oil suppliers are calculated as:      , s0.537 , [0.948, 0.986], [0.002, 0.008] , c˜1 = s0.536      c˜2 = s0.431 , [0.898, 0.960], [0.007, 0.008] , , s0.431      c˜3 = s0.552 , [0.955, 0.988], [0.001, 0.006] , , s0.553      c˜4 = s0.378 , [0.881, 0.951], [0.010, 0.032] . , s0.393

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

By computing the expect values and the accuracy degrees of the relative closeness degrees c˜i (i = 1, 2, 3, 4), the ranking of the four olive oil suppliers is obtained as O3  O1  O2  O4 . Therefore, O3 is the most appropriate green supplier among the alternative olive oil suppliers. The palm oil suppliers and the sunflower-soybean oil suppliers can be evaluated and ranked in the same way. The ranking orders obtained are P1  P2  P3 and SS1  SS2  SS3 , respectively. Thus, the company can select P1 and SS1 as the palm oil supplier and the sunflower-soybean oil supplier for procurement.

8.5.2 Comparison and Discussion To further validate the proposed GSES approach, we make a comparison to analyze some existing green supplier selection methods by using the above example, which include the fuzzy TOPSIS, the fuzzy VIKOR and the fuzzy GRA methods (Banaeian et al. 2018). The ranking results of the ten suppliers by utilizing the three approaches are displayed in Table 8.4. From Table 8.4, it can be seen that the optimal suppliers obtained by the proposed approach and the three comparative methods are the same: O3 , P1 and SS1 are respectively the most suitable green suppliers of olive oil, palm oil and sunflower-soybean oil. This reveals the effectiveness of the GSES model proposed in this chapter. In addition, there are still some differences between the ranking results acquired by the proposed approach and the three comparative methods. The least optimal green suppliers are O4 , P3 and SS3 of olive oil, palm oil and sunflower-soybean oil by the proposed approach. According to the three comparative methods, the least optimal green suppliers are O4 , P2 and SS2 , correspondingly. The reasons that bring the inconsistence mainly lie in the characteristics of the three comparative methods. First, Table 8.4 Ranking comparison Kind of suppliers

Suppliers

Fuzzy TOPSIS

Fuzzy VIKOR

Fuzzy GRA

The proposed approach

Olive oil

O1

3

3

3

2

O2

2

2

2

3

O3

1

1

1

1

O4

4

4

4

4

P1

1

1

1

1

P2

3

3

3

2

P3

2

2

2

3

Sunflower-soybean oil SS1

1

1

1

1

SS2

3

3

3

2

SS3

2

2

2

3

Palm oil

8.5 Case Illustration

197

triangular fuzzy numbers are applied in the three comparative methods. In contrast, the IVIULSs used in the proposed approach can better reflect the uncertainty and vagueness of decision makers’ assessments. Second, GRA, TOPSIS, VIKOR are utilized to rank alternatives in the three comparative methods, respectively. But the GRA-TOPSIS can reflect the similarity between case data curves and the relationships of these curves simultaneously as compared with the GRA and TOPSIS; the GRA-TOPSIS is more convenient and rapid in determining the best supplier by comparing with the VIKOR method. Therefore, the ranking result of the alternative suppliers produced by the proposed approach is more accurate and reasonable. In comparison with the existing approaches for the selection of green suppliers, the proposed GSES model has the following strength points: • The approach can well reflect the uncertainty and fuzziness of decision makers’ subjective data by utilizing IVIULSs. This enables decision makers to express their judgments more realistically and makes the assessment easier to be carried out. • Both quantitative and qualitative criteria can be considered in the green supplier selection which makes the developed model more reasonable. The proposed approach is a general method and not limited to the four criteria used in the case study, but applicable to any number of criteria. • By utilizing the GRA-TOPSIS method, a more precise and reasonable ranking of alternative suppliers can be obtained based on the basic principles of GRA and TOPSIS methods, which facilitates a company to choose the most appropriate green supplier.

8.6 Chapter Summary In this chapter, we presented an integrated approach by integrating IVIULSs and the GRA-TOPSIS method to assess and select the best green supplier under uncertain information context. In the proposed approach, IVIULSs were used to represent decision makers’ diversity evaluations of alternatives; the GRA-TOPSIS method was utilized to derive the optimum supplier with respect to economic criteria and environmental criteria. We made use of an empirical example of the agri-food industry to illustrate the effectiveness and practicability of the proposed GSES model. By using IVIULSs, managers can more effectively handle decision makers’ diversity assessments on the green performance of alternatives. The released model also aids managers to obtain a more reasonable and credible ranking of the evaluation suppliers by combining GRA and TOPSIS methods. The GSES procedure introduced in this chapter can be used to help a company to construct a consensus ranking of green suppliers while taking into account viewpoints of different stakeholders.

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8 GSES with Interval-Valued Intuitionistic Uncertain Linguistic GRA-TOPSIS

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Chapter 9

GSES with Large Group Uncertain Linguistic MULTIMOORA Method

To derive the best result, large group of decision makers are often involved in the green supplier selection nowadays. Besides, decision makers tend to express their evaluations utilizing uncertain linguistic terms due to the vagueness of human thinking. Hence, this chapter aims to propose a hybrid approach for green supplier selection within the large group setting. More concretely, interval-valued intuitionistic uncertain linguistic sets (IVIULSs) are applied for assessing the performance of green suppliers concerning each criterion. Ant colony algorithm is utilized to cluster decision makers into several subgroups. The linear programming technique for multidimensional analysis of preference (LINMAP) is adopted for the determination of criteria weights objectively. Finally, an extended MULTIMOORA approach is utilized to generate the ranking of alternative suppliers. The practicality and usefulness of the developed large group GSES framework is illustrated using an empirical example of a real estate company.

9.1 Introduction Because of growing public concerns over the environmental issues and government regulations toward sustainable development, green supply chain management (GSCM) has become popular in production operation management of modern enterprises (Qin et al. 2017a). By integrating environmental concerns into supply chain practices, GSCM is considered as a promising approach to improve the commercial benefit and environmental performance of organizations simultaneously. The major aim of GSCM is to decrease environmental pollution and eliminate waste during the process of purchasing, manufacturing, distributing and selling products (Kuo et al. 2010). As a result, there are a lot of programs for companies to implement GSCM, including green design, green production, green transportation and green marketing (Fallahpour et al. 2016). But an organization’s environmental performance depends on not only its own green efforts but also its providers’ green practices. Thus, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_9

201

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9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

selecting the optimal green supplier is a vital part of the GSCM for firms to develop sustainability (Hendiani et al. 2020a; Mi et al. 2020; Mohammed 2020; Zhang et al. 2020). In previous studies, many scholars have applied fuzzy set theory (Zadeh 1965) and intuitionistic fuzzy sets (IFSs) (Atanassov 1986) to cope with the vague evaluations of decision makers and improve the effectiveness of green supplier selection. However, when transforming linguistic assessments of alternatives into fuzzy numbers, the information of decision makers’ subjective judgements may be lost and distorted (Wang et al. 2016). As for IFSs, the membership and non-membership degrees are signified by exact values, which cannot well handle the uncertainty and fuzziness of assessment information. The concept of interval-valued intuitionistic uncertain linguistic sets (IVIULSs) was proposed by Liu (2013) by combing uncertain linguistic variables and interval-valued intuitionistic fuzzy sets (IVIFSs). The linguistic variable, membership degree and nonmembership degree of each element in an IVIULS are denoted by interval values rather than crisp values, which can better capture the ambiguity and uncertainty of evaluation information (Davoudabadi et al. 2021; Zou et al. 2021). Owing to its characteristics and merits, the IVIULS theory has been utilized in different fields (Liu et al. 2019c; Davoudabadi et al. 2020; Hu et al. 2020; Nguyen 2020; Yue et al. 2020). Therefore, it is natural to use the IVIULSs to evaluate the green performance of alternative suppliers on each criterion. On the other hand, selecting the best-fit green supplier is often viewed as a multicriteria decision making (MCDM) problem and a variety of MCDM approaches have been used for green supplier selection in recent years (Ecer 2020; Hendiani et al. 2020b; Kumari and Mishra 2020; Liu et al. 2020; Mohammed 2020). The multi-objective optimization by a ratio analysis plus full multiplicative form (MULTIMOORA) method is a distinctive MCDM technique proposed by Brauers and Zavadskas (2010). It includes three parts: the ratio system, the reference point and the full mutiplicative form (Stanujkic et al. 2017). The final ranking of alternatives is made in accordance with the dominance theory (Brauers and Zavadskas 2011). Comparing with other MCDM methods, the merits of the MULTIMOORA approach are that (Zhao et al. 2017; Liu et al. 2019a, b): (1) It can make the ranking result more accurate by aggregating the three basic parts; (2) It can effectively solve complicated MCDM problems with numerous alternatives and criteria; (3) Its calculation process is easily comprehensible and the result can be obtained rapidly. Also, researchers have made considerable extensions of the MULTIMOORA method to handle various MCDM problems (Asante et al. 2020; Hafezalkotob et al. 2020; Wu et al. 2020; Yazdi 2020; Yörüko˘glu and Aydın 2020; Sarabi and Darestani 2021). Hence, it is desirable to apply the MULTIMOORA method to address GSES problems. Against the above discussions, we propose a hybrid model based on IVIULSs and MULTIMOORA method in this chapter for evaluating and ranking green suppliers under large group environment. We utilize ant colony algorithm to cluster decision makers, an extended LINMAP approach to calculate the objective weights of criteria, and an improved MULTIMOORA technique to rank alternative green suppliers. The presented large group GSES approach is able to reflect the vagueness and ambiguity

9.1 Introduction

203

of decision makers’ judgements and acquire an accurate ranking result of green suppliers. The remaining sections of this chapter are arranged as follows: The basic concepts and definitions regarding IVIULSs are introduced in Sect. 9.2. In Sect. 9.3, we put forward a hybrid MCDM model using IVIULSs and MULTIMOORA method for large group green supplier selection. In Sect. 9.4, a case of a real estate company in China is given to demonstrate the proposed approach. The last section presents concluding remarks.

9.2 Preliminaries Some basic concepts and operational rules on IVIULSs (Liu 2013) are recalled in this section. ˜ then an IVIULS is denoted by. Definition 9.1 Let X be a given domain and s˜x ∈ S,     A˜ = < x s˜x , u˜ A˜ (x), v˜ A˜ (x) > ,

(9.1)

  where s˜x = sθ(x) , sτ (x) is regarded as an uncertain linguistic variable; θ (x) and τ (x) are the subscripts of the lower limit and upper limit to s˜x , respectively. The intervals u˜ A˜ : X → D[0, 1] and v˜ A˜ : X → D[0, 1] respectively represent the membership degree and non-membership degreeof theelement  x to the uncertain linguistic variable s˜x with the constraint 0 ≤ sup u˜ A˜ (x) + sup v˜ A˜ (x) ≤ 1, x ∈ X . For any element x ∈ X , u˜ A˜ (x) and v˜ A˜ (x) are closed intervals and their lower points and upper points are presented as uAL˜ (x), uAU˜ (x), vAL˜ (x) and vAU˜ (x). Then A˜ can be denoted by A˜ =

       |x ∈ X , x sθ(x) , sτ (x) , uAL˜ (x), uAU˜ (x) , vAL˜ (x), vAU˜ (x)

(9.2)

where sθ(x) , sτ (x) ∈ S, 0 ≤ uAU˜ (x) + vAU˜ (x) ≤ 1, uAL (x) ≥ 0 and vAL (x) ≥ 0. For any element x ∈ X , the hesitation interval of the element x to the uncertain  linguistic variable s˜x = sθ(x) , sτ (x) is computed as:  π˜ A˜ (x) = πA˜L (x), πA˜U (x)  = 1 − uAU˜ (x) − vAU˜ (x), 1 − uAL˜ (x) − vAL˜ (x) .

(9.3)

       be x sθ(x) , sτ (x) , uAL˜ (x), uAU˜ (x) , vAL˜ (x), vAU˜ (x) |x ∈ X      L an IVIULS, then the 6-tuple sθ(x) , sτ (x) , uA˜ (x), uAU˜ (x) , vAL˜ (x), vAU˜ (x) is called an interval-valued intuitionistic uncertain linguistic number Let A˜

=

204

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

˜ (IVIULN). A˜ can be regarded of   as a collection   IVIULNs, thus, A  L  U L U sθ(x) , sτ (x) , uA˜ (x), uA˜ (x) , vA˜ (x), vA˜ (x) |x ∈ X .

=

Definition 9.2 and Li 2009) Suppose  (Xu and Yager 2008;  Wang  L U =  sθ(˜a1 ) , sτ (˜a1 ) , uL (˜ = a u a , v a vU (˜a1 ) and a˜ 2 ˜1 a ), (˜ ) (˜ ), 1 1 1  L  L U U sθ(˜a2 ) , sτ (˜a2 ) , u (˜a2 ), u (˜a2 ) , v (˜a2 ), v (˜a2 ) are two IVIULNs and λ ≥ 0, the operational rules of a˜ 1 and a˜ 2 are given below:       (1) a˜ 1 ⊕ a˜ 2 = sθ(˜a1 )+θ(˜a2 ) , sτ (˜a1 )+τ (˜a2 ) , 1 − 1 − uL (˜a1 ) 1 − uL (˜a2 ) ,      1 − 1 − uU (˜a1 ) 1 − uU (˜a2 ) , vL (˜a1 )vL (˜a2 ), vU (˜a1 )vU (˜a2 ) ; (2)

    a˜ 1 ⊗ a˜ 2 = sθ(˜a1 )×θ(˜a2 ) , sτ (˜a1 )×τ (˜a2 ) , uL (˜a1 )uL (˜a2 ), uU (˜a1 )uU (˜a2 )        1 − 1 − vL (˜a1 ) 1 − vL (˜a2 ) , 1 − 1 − vU (˜a1 ) 1 − vU (˜a2 ) ;

(3)

λ˜a1 =

     λ λ sλ×θ(˜a1 ) , sλ×τ (˜a1 ) , 1 − 1 − uL (˜a1 ) , 1 − 1 − uU (˜a1 ) ,  λ  λ  ; vL (˜a1 ) , vU (˜a1 )

(4)

a˜ 1λ =



  λ  λ s(θ(˜a1 ))λ , s(τ (˜a1 ))λ , uL (˜a1 ) , uU (˜a1 ) ,    λ λ  . 1 − 1 − vL (˜a1 ) , 1 − 1 − vU (˜a1 )

     Definition 9.3 (Liu 2013) Suppose a˜ 1 = sθ(˜a1 ) , sτ (˜a1 ) , uL (˜a1 ), uU (˜a1 ) ,   L  v (˜a1 ), vU (˜a1 ) is an IVIULN, its expected value E(˜a1 ) is computed by:   L  v (˜a1 ) + vU (˜a1 ) 1 uL (˜a1 ) + uU (˜a1 ) +1− E(˜a1 ) = 2 2 2 × s(θ(˜a1 )+τ (˜a1 ))/2 = s(θ(˜a1 )+τ (˜a1 ))×(uL (˜a1 ))+uU (˜a1 )+2−vL (˜a1 )−vU (˜a1 ))/8 ,

(9.4)

and the accuracy function T (˜a1 ) of a˜ 1 is defined by: 

uL (˜a1 ) + uU (˜a1 ) vL (˜a1 ) + vU (˜a1 ) + 2 2 =s(uL (˜a1 )+uU (˜a1 )+vL (˜a1 )+vU (˜a1 ))×(θ(˜a1 )+τ (˜a1 ))/4 .



T (˜a1 ) =s(θ(˜a1 )+τ (˜a1 ))/2 ×

(9.5)

9.2 Preliminaries

205

     Definition 9.4 (Liu and Jin 2012) Let a˜ 1 = sθ(˜a1 ) , sτ (˜a1 ) , uL (˜a1 ), uU (˜a1 ) ,   L        U v (˜a1 ), v (˜a1 ) , a˜ 2 = sθ(˜a2 ) , sτ (˜a2 ) , uL (˜a2 ), uU (˜a2 ) , vL (˜a2 ), vU (˜a2 ) are two IVIULNs. The comparison rules of IVIULNs are defined as follows: (1) (2) (a) (b)

If E(˜a1 ) > E(˜a2 ), then a˜ 1 > a˜ 2 ; If E(˜a2 ) = E(˜a2 ), then if T (˜a1 ) > T (˜a2 ), then a˜ 1 > a˜ 2 ; if T (˜a1 ) = T (˜a2 ), then a˜ 1 = a˜ 2 .

To aggregate uncertain linguistic information, the interval-valued intuitionistic uncertain linguistic weighted average (IVIULWA) operator is proposed by Liu (2013).       = sθ(˜ai ) , sτ (˜ai ) , uL (˜ai ), uU (˜ai ) , vL (˜ai ), vU (˜ai ) Definition 9.5 Let a˜ i (i = 1, 2, . . . , n) be a collection of IVIULNs, then the IVIULWA operator is defined as: IVIULWA(˜a1 , a˜ 2 , . . . , a˜ n ) =

n 

wj a˜ j ,

(9.6)

j=1

=

(w1 , w2 , . . . , wn )T

is the associated weight vector of n  wj = 1. a˜ j (j = 1, 2, . . . , n), which satisfies wj ∈ [0, 1] and where w

j=1

  L     Definition. uU (˜a1 ) , vL (˜a1 ), vU (˜a1 ) ,   La˜ 1 = U sθ(˜a1 ), sτ (˜La1 ) , u U(˜a1 ),   9.6 Suppose a˜ 2 = sθ(˜a2 ) , sτ (˜a2 ) , u (˜a2 ), u (˜a2 ) , v (˜a2 ), v (˜a2 ) are two IVIULNs. The distance between a˜ 1 and a˜ 2 is defined as:    L  L 1 (|θ (˜a1 ) − θ (˜a2 )|+|τ (˜a1 ) − τ (˜a2 )|)/9 + u (˜a1 ) − u (˜a2 )       . d (˜a1 , a˜ 2 ) = 6 +uU (˜a1 ) − uU (˜a2 ) + vL (˜a1 ) − vL (˜a2 ) + vU (˜a1 ) − vU (˜a2 ) (9.7)

9.3 The Proposed GSES Model This section develops a new GSES approach for selecting the most appropriate green suppliers under the large group environment. In the proposed model, decision makers are clustered by employing an ant colony algorithm; assessment values of clusters are aggregated by the IVIULWA operator; criteria weights are computed by the LINMAP method; the alternative suppliers are ranked finally based on a modified MULTIMOORA approach. The flowchart of the GSES method being proposed is shown in Fig. 9.1.

206

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

Fig. 9.1 Schematic diagram of the proposed GSES model

For a GSES problem with m alternatives Ai (i = 1, 2, . . . , m), n criteria Cj (j = 1, 2, . . . , n), and L decision makers DMk (k = 1, 2, . . . , L; L> 20), the evalk k ˜ , where uation matrix by the kth decision maker is denoted as P = p˜ ij m×n     L U L U p˜ ijk = saijkL , saijkU , uijk , vijk is the IVIULN given by DMk for the alter, uijk , vijk L L native supplier Ai on the criterion Cj , with the condition 0 ≤ uijk ≤ 1,0 ≤ vijk ≤ U U L U L U 1,uijk + vijk ≤ 1,uijk ≤ uijk ,vijk ≤ vijk ,saijkL , saijkU ∈ S. Next, the procedure of the proposed green supplier selection approach is explained in the following subsections.

9.3 The Proposed GSES Model

207

9.3.1 Cluster Decision Makers Ant colony algorithm is an effective clustering method inspired by the foraging behavior of ant colony. It is a promising method for data classification, which intend to discover a list of classification rules (Liang et al. 2016). In the first stage, we cluster decision makers by using the ant colony algorithm. For each supplier Ai (i = 1, 2, . . . , m), the L decision makers DMk (k = 1, 2, . . . , L) can be clustered into m clustering results based on their evaluations. The algorithm under the IVIUL environment is expressed as follows: (1) (2) (3) (4)

(5) (6)

(7)

Transform all the IVIULNs into expected values as input data. Set parameters: the number of clusters g, the number of ants f , the maximum number of iterations tmax , pheromone threshold q, and evaporation rate ε. Initialize the pheromone matrix L×g . The initial value of each element in L×g is 0.01. Determine ants’ path according to the value in pheromone matrix L×g . If all the pheromone values of a sample are less than the pheromone threshold q, then the cluster corresponding to the largest pheromone is selected. If the pheromone values are greater than the pheromone threshold q, the cluster is determined based on the proportion of pheromone in each path of total pheromones. Identify the cluster centers on all criteria of each cluster. The cluster center is the average of all samples in the cluster with respect to each criterion. Compute the sum of the Euclidean distances (deviation error) of each ant from each sample to its corresponding cluster center, and select the path corresponding to the smallest deviation error as the best path for this iteration. The smaller the deviation error, the better the clustering effect. Update pheromone matrix L×g .The updated value is the original pheromone value multiply (1 − ε) and plus the reciprocal of the minimum deviation error. Choose the best path according to the new pheromone matrix and perform iteration operations until reach the maximum number of iterations tmax .

9.3.2 Aggregate Clusters Suppose Gz (z = 1, 2, . . . , g) is the zth cluster and lz is the number of decision makers g  in Gz , with the condition lz = L. The evaluation for supplier Ai with respect to z=1

criterion Cj of the cluster Gz is the average of the assessments given by decision makers, i.e.,     L , uU , v L , v U s L , s U , uijz ijz ijz ijz aijz aijz ⎡ ⎤ ⎡

 p˜ ijz = 

⎢ = ⎣s 1

lz

 k∈Gz

aL ijk

,s 1 lz

⎤ ⎡ ⎤ 1  L 1  U⎦ ⎣1  L 1  U⎦ ⎥ ⎣  U ⎦, uijk , uijk , vijk , vijk , a lz lz lz lz ijk

k∈Gz

k∈Gz

k∈Gz

k∈Gz

k∈Gz

208

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

(9.8)

i = 1, 2, . . . , m, j = 1, 2, . . . , n, z = 1, 2, . . . , g.

To eliminate the effects of different dimensions and ensure the compatibility of IVIULNs  with respect to all criteria, we normalize the cluster decision matrix ˜P z = p˜ ijz by using the following formulas: m×n

r˜ijz = r˜ijz =



   L U L U , vijz , (j ∈ J1 ), saijzL /ajUmax , saijzU /ajUmax , uijz , uijz , vijz

(9.9)

'  &   L U L U , uijz , (j ∈ J2 ), s 1−aU /aU , s 1−aL /aU , vijz , vijz , uijz ijz

j max

ijz

j max

i = 1, 2, . . . , m, j = 1, 2, . . . , n, z = 1, 2, . . . g,

(9.10)

where J1 and J 2 denote the sets of benefit criteria and

cost criteria, respectively, U , i = 1, 2, . . . , m, z = 1, 2, . . . , g . and ajUmax = max aijz Generally, the cluster with more decision makers should be given a bigger weight. Thus, the weight of each cluster Gz (z = 1, 2, . . . , g) can be calculated by λz =

lz , z = 1, 2, . . . , g. L

(9.11)

Then, weadopt  the IVIULWA operator to obtain the group normalized decision matrix R˜ = r˜ij m×n , where r˜ij is determined by g

r˜ij = IVIULWA(˜rij1 , r˜ij2 , . . . , r˜ij ) = ⎡ = ⎣s l z=1

 g (

z=1

g 

λz r˜ijz

z=1

λz aijL z

, s l z=1

L λz aijz

⎤   g

l

λz

λz ( ( L U ⎦, 1 − 1 − uijz 1 − uijz ,1 − ,

g

λz (

λz L U vijz vijz ,



z=1

k=1

,

z=1

i = 1, 2, . . . , m, j = 1, 2, . . . , n,

(9.12)

is the associated weight of r˜ijz = where λ  z    L U L U saijzL , saijzU , uijz , uijz , vijz , vijz (z = 1, 2, . . . , g), with the condition λz ∈ [0, 1] g  and λz = 1. z=1

9.3 The Proposed GSES Model

209

9.3.3 Calculate the Weights of Criteria The LINMAP is a classical and effective MCDM method proposed by Srinivasan and Shocker (1973). It is can be used for computing the objective criteria weights by establishing a mathematical programming (Wan and Li 2013). Therefore, in this chapter, we extend the LINMAP method to the IVIUL context for deriving the weights of evaluation criteria. The specific steps are given below: Step 1 The decision makers give the united preference relations between the candidate suppliers  = {(Ah , Ai )|Ah ≥ Ai , (h, i = 1, 2, . . . , m)}. The decision makers provide the corresponding pairwise comparisons of the candidate suppliers as a whole. The priority relations between alternatives are determined by overall judgement rather than on each criterion. Step 2 Define the consistency index and inconsistency index between objective ranking order and subjective preference relation. The IVIULN ideal solution (reference point) on each criterion  are represented as    ∗ ∗ ∗ L U L U ∗ ∗ r = r1 , r2 , . . . , rn , where rj = sajL , sajU , uj , uj , vj , vj (j = 1, 2, . . . , n) is the best rating on the criterion Cj . Then the distance between each alternative of (Ah , Ai ) ∈  and ideal solution r ∗ is calculated by Dh =

n 



wj d r˜hj , r˜j∗ ,

(9.13)



wj d r˜ij , r˜j∗ ,

(9.14)

j=1

Di =

n  j=1

where w = (w1 , w2 , . . . , wn ) is the criteria weight vector. For each pair of alternative suppliers (Ah , Ai ) ∈ , the decision makers prefer supplier Ah to Ai or make no difference between Ah and Ai . Thus, if Di ≥ Dh , the ranking order determined by Di and Dh is consistent with the preference relation by decision makers. Otherwise, if Di < Dh , then the ranking order determined by Di and Dh is inconsistent with the preference relation by decision makers. Accordingly, the indexes (Di − Dh )+ and (Di − Dh )− are respectively used to measure consistency and inconsistency between the objective ranking orders determined by Di , Dh and subjective preference relation (Chen 2013; Qin et al. 2017b). (Di − Dh )+ = max{0, (Di − Dh )},

(9.15)

(Di − Dh )− = max{0, (Dh − Di )}.

(9.16)

Hence, the total consistency index and inconsistency index of all pairs of suppliers can be calculated by

210

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

H=



(Di − Dh )+ =

(h,i)∈

B=





max{0, Di − Dh },

(9.17)

max{0, Dh − Di }.

(9.18)

(h,i)∈

(Di − Dh )− =

(h,i)∈



(h,i)∈

Step 3 Construct a mathematical programming to derive criteria weight vector. Let Zhi = max{0, Dh − Di } for each pair (Ah , Ai ) ∈ , with the condition Zhi ≥ 0. Then Zhi ≥ Dh − Di is obtained. Since the total inconsistency index B reflects the group inconsistency between the objective ranking order and subjective preference relations, then B should be minimized. Therefore, we can construct a mathematical programming as follows:

min

⎧ ⎨ 

⎫ ⎬

Zhi ⎩ ⎭ (h,i)∈ ⎧   (Di − Dh )+ − (Di − Dh )− ≥ μ, ⎪ ⎪ ⎪ (h,i)∈ (h,i)∈ ⎪ ⎪ ⎪ ⎪ ⎪ Zhi + Dh − Di ≥ 0, ⎨ s.t. Zhi ≥ 0, n ⎪  ⎪ ⎪ ⎪ wj = 1, ⎪ ⎪ ⎪ j=1 ⎪ ⎩ wj ≥ δ, (j = 1, 2, . . . , n)

(9.19)

where μ > 0 is used to ensure the total consistency indexH bigger or equal to the inconsistency index B, and δ > 0 can ensure the weight of each crterion greater than 0.

9.3.4 Rank the Alternative Suppliers After obtaining the group normalized evaluations of suppliers in the second stage, we utilize a modified MULTIMOORA method to rank the alternative suppliers in this subsection. The ranking process is presented as below. Step 1 Rank alternative suppliers based on the ratio system approach. The evaluation values of ratio system is obtained by adding the normalized ratings on the criteria of each supplier, i.e., γ˜i =

n  j=1

wj r˜ij , i = 1, 2, . . . , m,

(9.20)

9.3 The Proposed GSES Model

211

where γ˜i represents the overall evaluation value of Ai with regard to all the criteria. The ranking of alternative suppliers are determined by the values γ˜i (i = 1, 2, . . . , m) in descending order. Step 2 Rank alternative suppliers by the reference point approach. In the third stage, we have determined the ieal solution as the best rating. Then the weighted distance of each supplier to the ieal solution is computed by di =

n 



wj d r˜ij , r˜j∗ , i = 1, 2, . . . , m.

(9.21)

j=1

The alternative suppliers are ranked based on distances di (i = 1, 2, . . . , m) in increasing order. Step 3 Rank alternative suppliers based on the full multiplicative form approach. The overall utility of each supplier can be represented as an IVIULN by U˜ i =

n (

wj r˜ij , i = 1, 2, . . . , m.

(9.22)

j=1

The green suppliers are ranked according to the values U˜ i (i = 1, 2, . . . , m) in descending order. Step 4 Determine the final ranking of alternative suppliers. By utilizing the theory of dominance, we can integrate the three ranking lists acquired by the ratio system, the reference point and the full multiplicative form to determine the final ranking of the m green suppliers.

9.4 Case Study 9.4.1 Implementation This section applies the proposed GSES model to select the optimal timber green supplier for a real estate company in Shanghai, China. The related research data show that the carbon produced by the real estate industry in China accounted for about eight percent of global carbon emissions. As facing the great opportunity of green tranformation, Alashan SEE ecological association, China urban real estate developers strategic alliance, all real estate association, Vanke enterprise and Landsea green real estate co-sponsored the action of green supply chain in the real estate industry on June 5, 2016. The white lists of qualtified suppliers are determined by real estate companies participating in the green supply chain action according to green standards, which include steel suppliers, cement suppliers, timber suppliers, and aluminum suppliers. This case study aims to assisst the real estate company to find out the most appropriate timber supplier.

212

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

After initial screening, four suppliers (Ai , i = 1, 2, . . . , 4) are remained for further assessment and  selection. Based on expert interviews, five evaluation criteria  Cj , j = 1, 2, . . . , 5 , product quality, purchase cost, technology capability, green degree and delivery level, are identified for the green supplier selection. Besides, an expert group consisting of 22 decision makers,(DMk , k = 1, 2, . . . , 22), is invited to evaluation the performance of the four alternative suppliers with respect to each criterion. The linguistic terms set S is used in the performance evaluation of suppliers. S ={s0 = very poor, s1 = poor, s2 = medium poor, s3 = fair, s4 = medium good , s5 = good , s6 = very good }. The assessments of the four alternative suppliers provided by the decision makers are shown in Tables 9.1, 9.2, 9.3, 9.4. First, we transform the IVIULNs into their expected values as input data. Then the parameters of the ant colony algorithm are set as: the number of clusters g = 5, the number of ants f = 1000, the maximum number of iterations tmax = 1000, pheromone threshold q = 0.9, and evaporation rate ε = 0.1. By using the ant colony algorithm, the clustering results of decision makers are shown in Table 9.5. Based on Eq. (9.8), the evaluation values for the four suppliers of the five clusters are calculated as shown in Table 9.6. Next the evaluation values of the five clusters are normalize by Eqs. (9.9), (9.10), and the results are shown in Table 9.7. By Eq. (9.12), the normalized evaluations of the five are aggregated to obtain the collective   clusters normalized evaluation matrix R˜ = r˜ij 4×5 as shown in Table 9.8. The united preference relations of the candidate suppliers given by the 22 decision makers are:  = {(1, 3), (2, 1), (2, 4), (1, 4)}. The ideal solution is set as [s1 , s1 ], [1, 1], [0, 0] for each criterion. Then the following linear programming is eatablished to calculate the weights of criteria: min Z13 + Z21 + Z24 + Z14 ⎧ 0.839w1 − 0.768w2 + 2.792w3 + 1.117w4 + 0.924w5 ≥ 1, ⎪ ⎪ ⎪ ⎪ ⎪ 0.019w1 + 0.229w2 + 0.574w3 + 0.057w4 + 0.130w5 + Z13 ⎪ ⎪ ⎪ ⎪ 0.252w ⎨ 1 − 0.664w2 + 0.537w3 + 0.231w4 + 0.133w5 + Z21 s.t. 0.273w1 − 0.282w2 + 0.553w3 + 0.386w4 + 0.265w5 + Z24 ⎪ ⎪ ⎪ 0.294w1 − 0.052w2 + 1.127w3 + 0.443w4 + 0.395w5 + Z14 ⎪ ⎪ ⎪ ⎪ wj ≥ 0.01, (j = 1, 2, . . . , 5), ⎪ ⎪ ⎩ w1 + w2 + w3 + w4 + w5 = 1.

≥ 0, ≥ 0, ≥ 0, ≥ 0,

By solving the above model, the weights of the five criteria is derived as w = (0.28, 0.10, 0.10, 0.42, 0.10). In the fourth stage, the modified MULTIMOORA method is used to rank the four timber green suppliers. First, based on the ratio system approach, the ranking order of the alternative suplliers are determined by Eq. (9.20), and the result is:

…

…

[s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s5 , s6 ], [0.7, 0.8], [0.0, 0.1] [s5 , s6 ], [0.6, 0.7], [0.1, 0.2] [s4 , s4 ], [0.7, 0.7], [0.1, 0.2] [s2 , s3 ], [0.7, 0.9], [0.1, 0.1]

…

DM22

…

…

[s6 , s6 ], [0.7, 0.9], [0.1, 0.1] [s4 , s5 ], [0.7, 0.9], [0.1, 0.1] [s5 , s6 ], [0.7, 0.8], [0.1, 0.1] [s4 , s5 ], [0.6, 0.7], [0.1, 0.2] [s5 , s6 ], [0.6, 0.7], [0.1, 0.3]

DM21

[s4 , s5 ], [0.6, 0.6], [0.1, 0.3] [s5 , s6 ], [0.7, 0.8], [0.1, 0.2] [s5 , s5 ], [0.7, 0.9], [0.0, 0.1] [s3 , s4 ], [0.6, 0.7], [0.0, 0.2] [s4 , s5 ], [0.5, 0.6], [0.1, 0.2]

…

[s3 , s4 ], [0.4, 0.5], [0.2, 0.3] [s4 , s5 ], [0.6, 0.8], [0.1, 0.2] [s3 , s4 ], [0.5, 0.7], [0.1, 0.2] [s4 , s5 ], [0.6, 0.8], [0.0, 0.2] [s5 , s6 ], [0.7, 0.7], [0.1, 0.2]

C5

DM3

C4

[s5 , s6 ], [0.7, 0.8], [0.1, 0.2] [s4 , s5 ], [0.6, 0.7], [0.1, 0.2] [s5 , s6 ], [0.8, 0.9], [0.1, 0.1] [s4 , s4 ], [0.5, 0.6], [0.1, 0.3] [s5 , s6 ], [0.8, 0.8], [0.1, 0.2]

C3

DM2

C2

DM1

Decision Criteria makers C1

Table 9.1 Performance values of the first supplier A1 by decision makers

9.4 Case Study 213

…

…

[s4 , s5 ], [0.7, 0.8], [0.1, 0.1] [s5 , s6 ], [0.8, 0.9], [0.0, 0.1] [s6 , s6 ], [0.6, 0.8], [0.1, 0.2] [s3 , s4 ], [0.5, 0.7], [0.1, 0.3] [s5 , s6 ], [0.6, 0.8], [0.0, 0.2]

…

DM22

…

…

[s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s4 , s4 ], [0.6, 0.9], [0.0, 0.1] [s4 , s5 ], [0.6, 0.7], [0.1, 0.1] [s3 , s4 ], [0.8, 0.8], [0.1, 0.2] [s4 , s4 ], [0.7, 0.7], [0.1, 0.3]

DM21

[s5 , s6 ], [0.6, 0.8], [0.1, 0.2] [s4 , s5 ], [0.6, 0.7], [0.2, 0.3] [s3 , s4 ], [0.8, 0.9], [0.0, 0.1] [s4 , s4 ], [0.5, 0.7], [0.1, 0.2] [s4 , s5 ], [0.8, 0.9], [0.1, 0.1]

…

[s5 , s6 ], [0.7, 0.8], [0.2, 0.2] [s5 , s5 ], [0.6, 0.7], [0.1, 0.2] [s5 , s6 ], [0.7, 0.7], [0.1, 0.2] [s3 , s4 ], [0.5, 0.7], [0.0, 0.2] [s4 , s5 ], [0.5, 0.6], [0.2, 0.3]

C5

DM3

C4

[s6 , s6 ], [0.6, 0.8], [0.1, 0.2] [s4 , s5 ], [0.5, 0.7], [0.1, 0.3] [s4 , s5 ], [0.8, 0.8], [0.1, 0.2] [s3 , s4 ], [0.5, 0.6], [0.1, 0.2] [s4 , s5 ], [0.6, 0.8], [0.1, 0.2]

C3

DM2

C2

DM1

Decision Criteria makers C1

Table 9.2 Performance values of the second supplier A2 by decision makers

214 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

…

…

[s4 , s5 ], [0.8, 0.9], [0.1, 0.1] [s5 , s5 ], [0.8, 0.9], [0.0, 0.1] [s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s5 , s6 ], [0.5, 0.7], [0.1, 0.2] [s3 , s4 ], [0.6, 0.8], [0.1, 0.2]

…

DM22

…

…

[s4 , s4 ], [0.5, 0.6], [0.1, 0.2] [s4 , s5 ], [0.6, 0.8], [0.0, 0.1] [s3 , s4 ], [0.6, 0.7], [0.2, 0.2] [s3 , s4 ], [0.7, 0.8], [0.1, 0.2] [s2 , s3 ], [0.6, 0.7], [0.1, 0.3]

DM21

[s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s4 , s4 ], [0.6, 0.7], [0.2, 0.2] [s3 , s3 ], [0.7, 0.8], [0.0, 0.1] [s3 , s4 ], [0.6, 0.8], [0.1, 0.2] [s2 , s3 ], [0.8, 0.9], [0.0, 0.1]

…

[s5 , s6 ], [0.7, 0.8], [0.1, 0.2] [s4 , s4 ], [0.8, 0.9], [0.1, 0.1] [s5 , s6 ], [0.6, 0.7], [0.1, 0.2] [s5 , s6 ], [0.5, 0.7], [0.1, 0.2] [s3 , s4 ], [0.5, 0.6], [0.3, 0.4]

C5

DM3

C4

[s4 , s5 ], [0.6, 0.7], [0.1, 0.3] [s5 , s5 ], [0.5, 0.6], [0.2, 0.3] [s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s4 , s5 ], [0.7, 0.8], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.1, 0.2]

C3

DM2

C2

DM1

Decision Criteria makers C1

Table 9.3 Performance values of the third supplier A3 by decision makers

9.4 Case Study 215

…

…

[s4 , s5 ], [0.6, 0.8], [0.0, 0.1] [s5 , s5 ], [0.6, 0.8], [0.0, 0.2] [s4 , s5 ], [0.7, 0.7], [0.1, 0.2] [s3 , s4 ], [0.5, 0.7], [0.2, 0.3] [s4 , s4 ], [0.5, 0.7], [0.2, 0.3]

…

DM22

…

…

[s3 , s4 ], [0.5, 0.6], [0.3, 0.3] [s2 , s3 ], [0.6, 0.8], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.2, 0.3] [s3 , s3 ], [0.7, 0.7], [0.1, 0.2] [s3 , s4 ], [0.6, 0.9], [0.1, 0.1]

DM21

[s3 , s4 ], [0.7, 0.9], [0.1, 0.1] [s4 , s5 ], [0.6, 0.8], [0.1, 0.2] [s3 , s4 ], [0.7, 0.8], [0.0, 0.2] [s4 , s5 ], [0.5, 0.6], [0.1, 0.3] [s2 , s3 ], [0.7, 0.7], [0.0, 0.1]

…

[s4 , s5 ], [0.8, 0.8], [0.1, 0.2] [s4 , s4 ], [0.6, 0.7], [0.0, 0.1] [s3 , s4 ], [0.5, 0.7], [0.2, 0.2] [s4 , s5 ], [0.5, 0.6], [0.1, 0.3] [s3 , s4 ], [0.6, 0.7], [0.3, 0.3]

C5

DM3

C4

[s5 , s6 ], [0.6, 0.6], [0.1, 0.3] [s4 , s5 ], [0.5, 0.6], [0.2, 0.4] [s3 , s4 ], [0.7, 0.7], [0.1, 0.2] [s5 , s5 ], [0.6, 0.8], [0.1, 0.2] [s3 , s4 ], [0.6, 0.7], [0.1, 0.3]

C3

DM2

C2

DM1

Decision Criteria makers C1

Table 9.4 Performance values of the fourth supplier A4 by decision makers

216 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

9.4 Case Study

217

Table 9.5 Clustering results of the four suppliers Suppliers

Clusters G1

G2

G3

G4

G5

A1

DM1 , DM6 , DM7 , DM9 , DM11 , DM19 , DM21

DM2 , DM10 , DM14 , DM15 , DM16 , DM18

DM5 , DM8 , DM13 , DM20 ,

DM4 , DM12 , DM17

DM3 , DM22

A2

DM1 , DM2 , DM3 , DM5 , DM6 , DM15 , DM16 , DM21

DM4 , DM7 , DM8 , DM9 , DM22

DM10 , DM11 , DM14 , DM17 , DM18

DM12 , DM13 , DM20

DM19

A3

DM1 , DM2 , DM6 , DM12 , DM15 , DM17

DM4 , DM5 , DM9 , DM10 , DM11 , DM16

DM7 , DM8 , DM13 , DM19 , DM22

DM3 , DM14 , DM20 , DM21

DM18

A4

DM1 , DM2 , DM5 , DM6 , DM13 , DM17

DM4 , DM7 , DM9 , DM10 , DM12 , DM16

DM3 , DM11 , DM14 , DM19

DM18 , DM20 , DM21

DM8 , DM15 , DM22

γ˜1 = [s0.687 , s0.803 ], [0.608, 0.742], [0.099, 0.206] , γ˜2 = [s0.698 , s0.810 ], [0.910, 0.953], [0.000, 0.000] , γ˜3 = [s0.597 , s0.736 ], [0.599, 0.734], [0.122, 0.229] , γ˜4 = [s0.588 , s0.725 ], [0.576, 0.717], [0.146, 0.241] . Based on the comparison rules of IVIULNs, the ranking of the four suppliers is derived as A2 > A1 > A3 > A4 . Second, in accordance with the reference point approach, the weighted distance of each supplier to the ideal solution is computed by Eq. (9.21), and the result is: d1 = 1.581, d2 = 1.458, d3 = 1.750, d4 = 1.874. Thus, the four timber supplilers are ranked as: A2 > A1 > A3 > A4 . Third, according to the the full multiplicative form approach, the overall utility value of each supplier is determined by Eq. (9.22).     U˜ 1 = [s6.966∗10−6 , s2.049∗10−5 ], 8.472 ∗ 10−6 , 6.566 ∗ 10−5 , [0.999, 0.999] ,     U˜ 2 = [s1.168∗10−5 , s2.947∗10−5 ], 9.033 ∗ 10−5 , 4.075 ∗ 10−4 , [0.997, 0.999] ,     U˜ 3 = [s4.783∗10−6 , s1.487∗10−5 ], 1.834 ∗ 10−5 , 9.952 ∗ 10−5 , [0.999, 0.999] ,     U˜ 4 = [s5.213∗10−6 , s1.716∗10−5 ], 5.696 ∗ 10−6 , 5.342 ∗ 10−5 , [0.999, 0.999] . As a reslult, the ranking of the four suppliers is derived as A2 > A1 > A3 > A4 . To summarize, the final ranking of the four timber suppliers is A2 > A1 > A3 > A4 based on the dominance theory. Therefore, A2 is the optimum green supplier among the four alternatives for the considered application.

[s3.857 , s4.714 ], [0.586, 0.729], [0.114, 0.186]

[s3.833 , s4.333 ], [0.633, 0.767], [0.083, 0.183]

[s4.750 , s5.500 ], [0.650, 0.800], [0.075, 0.175]

[s4.000 , s4.667 ], [0.600, 0.733], [0.100, 0.200]

[s5.000 , s6.000 ], [0.700, 0.800], [0.050, 0.150]

[s3.875 , s4.500 ], [0.575, 0.713], [0.100, 0.213]

[s5.200 , s6.000 ], [0.700, 0.840], [0.080, 0.140]

[s3.400 , s3.800 ], [0.620, 0.760], [0.120, 0.200]

[s2.667 , s3.667 ], [0.667, 0.800], [0.067, 0.167]

[s3.000 , s4.000 ], [0.600, 0.900], [0.100, 0.100]

[s3.667 , s4.167 ], [0.633, 0.717], [0.117, 0.200]

[s3.667 , s4.667 ], [0.550, 0.717], [0.117, 0.267]

[s3.750 , s4.500 ], [0.625, 0.800], [0.075, 0.150]

[s5.400 , s5.800 ], [0.700, 0.800], [0.060, 0.140]

[s3.000 , s3.000 ], [0.700, 0.900], [0.000, 0.100]

[s4.167 , s4.500 ], [0.533, 0.633], [0.100, 0.267]

[s2.833 , s3.833 ], [0.583, 0.717], [0.150, 0.217]

[s4.000 , s5.000 ], [0.600, 0.825], [0.125, 0.175]

[s2.333 , s3.333 ], [0.633, 0.833], [0.033, 0.133]

[s4.667 , s5.333 ], [0.600, 0.733], [0.033, 0.200]

[s3.500 , s4.333 ], [0.550, 0.700], [0.150, 0.233]

[s5.000 , s5.750 ], [0.650, 0.800], [0.100, 0.150]

[s4.000 , s4.333 ], [0.567, 0.767], [0.100, 0.233]

[s4.000 , s5.000 ], [0.650, 0.700], [0.100, 0.250]

[s4.750 , s5.500 ], [0.663, 0.788], [0.125, 0.175]

[s5.000 , s5.800 ], [0.580, 0.780], [0.120, 0.200]

[s3.800 , s4.800 ], [0.600, 0.760], [0.120, 0.220]

[s4.667 , s5.333 ], [0.733, 0.800], [0.067, 0.200]

[s3.000 , s4.000 ], [0.500, 0.700], [0.100, 0.100]

[s4.167 , s5.000 ], [0.617, 0.700], [0.150, 0.267]

[s4.000 , s4.667 ], [0.667, 0.783], [0.083, 0.150]

[s3.750 , s4.250 ], [0.675, 0.750], [0.100, 0.175]

[s4.200 , s5.200 ], [0.660, 0.760], [0.120, 0.220]

[s2.000 , s3.000 ], [0.500, 0.600], [0.200, 0.300]

[s4.333 , s5.333 ], [0.567, 0.700], [0.133, 0.267]

[s4.333 , s5.000 ], [0.650, 0.800], [0.133, 0.183]

[s3.250 , s4.250 ], [0.600, 0.825], [0.100, 0.150]

[s2.667 , s3.667 ], [0.500, 0.633], [0.233, 0.333]

[s4.333 , s5.333 ], [0.633, 0.767], [0.100, 0.167]

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

A4

A3

A2

C2

[s5.142 , s5.571 ], [0.671, 0.829], [0.086, 0.157]

G1

A1

Criteria

C1

Clusters

Suppliers

Table 9.6 Evaluation values by the five clusters

(continued)

218 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

[s4.000 , s4.714 ], [0.600, 0.757], [0.071, 0.200]

[s3.500 , s4.167 ], [0.583, 0.733], [0.050, 0.200]

[s3.750 , s4.500 ], [0.675, 0.775], [0.100, 0.150]

[s5.333 , s6.000 ], [0.667, 0.767], [0.067, 0.167]

[s3.500 , s4.000 ], [0.650, 0.700], [0.050, 0.200]

[s3.500 , s4.125 ], [0.575, 0.725], [0.088, 0.200]

[s4.800 , s5.800 ], [0.600, 0.780], [0.080, 0.200]

[s2.200 , s2.800 ], [0.660, 0.760], [0.080, 0.180]

[s4.000 , s4.667 ], [0.667, 0.833], [0.100, 0.100]

[s5.000 , s5.000 ], [0.800, 0.900], [0.100, 0.100]

[s4.167 , s5.000 ], [0.633, 0.800], [0.083, 0.183]

[s3.333 , s4.000 ], [0.600, 0.733], [0.167, 0.267]

[s2.750 , s3.750 ], [0.650, 0.775], [0.100, 0.200]

[s4.400 , s5.400 ], [0.600, 0.760], [0.100, 0.180]

[s2.000 , s3.000 ], [0.500, 0.800], [0.100, 0.200]

[s4.167 , s4.833 ], [0.617, 0.767], [0.083, 0.200]

[s3.500 , s4.500 ], [0.667, 0.767], [0.117, 0.217]

[s3.833 , s4.833 ], [0.567, 0.783], [0.133, 0.183]

[s3.750 , s4.750 ], [0.600, 0.800], [0.075, 0.175]

[s4.667 , s5.333 ], [0.767, 0.867], [0.067, 0.133]

[s5.000 , s5.500 ], [0.650, 0.800], [0.050, 0.150]

[s4.125 , s5.000 ], [0.688, 0.800], [0.088, 0.150]

[s5.000 , s5.400 ], [0.640, 0.780], [0.100, 0.180]

[s3.200 , s4.000 ], [0.680, 0.780], [0.140, 0.180]

[s3.000 , s4.000 ], [0.600, 0.733], [0.100, 0.200]

[s4.000 , s5.000 ], [0.800, 0.900], [0.000, 0.100]

[s4.333 , s5.333 ], [0.650, 0.767], [0.083, 0.183]

[s3.333 , s3.833 ], [0.600, 0.750], [0.100, 0.200]

[s2.750 , s3.250 ], [0.625, 0.750], [0.100, 0.200]

[s4.200 , s5.200 ], [0.640, 0.760], [0.100, 0.220]

[s2.000 , s2.000 ], [0.600, 0.700], [0.100, 0.300]

[s3.167 , s4.167 ], [0.583, 0.700], [0.133, 0.217]

[s4.500 , s5.333 ], [0.650, 0.767], [0.150, 0.200]

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

A4

A3

A2

C4

[s4.857 , s5.571 ], [0.714, 0.842], [0.071, 0.129]

G1

A1

Criteria

C3

Clusters

Suppliers

Table 9.6 (continued)

(continued)

[s4.333 , s5.000 ], [0.583, 0.733], [0.100, 0.217]

[s2.833 , s3.833 ], [0.633, 0.700], [0.150, 0.267]

[s1.000 , s2.000 ], [0.700, 0.700], [0.100, 0.300]

[s4.000 , s4.800 ], [0.600, 0.760], [0.120, 0.240]

[s2.250 , s3.250 ], [0.625, 0.775], [0.075, 0.200]

[s4.333 , s5.333 ], [0.650, 0.800], [0.067, 0.167]

[s3.167 , s4.167 ], [0.600, 0.667], [0.133, 0.283]

[s5.000 , s6.000 ], [0.800, 0.800], [0.100, 0.200]

[s3.000 , s3.667 ], [0.600, 0.733], [0.100, 0.267]

[s2.800 , s3.800 ], [0.660, 0.780], [0.100, 0.200]

[s4.000 , s5.000 ], [0.650, 0.700], [0.100, 0.250]

[s4.000 , s4.875 ], [0.663, 0.750], [0.125, 0.225]

[s3.000 , s4.000 ], [0.600, 0.750], [0.100, 0.150]

[s4.000 , s4.000 ], [0.567, 0.700], [0.100, 0.200]

[s3.750 , s4.500 ], [0.575, 0.725], [0.125, 0.225]

[s4.167 , s5.167 ], [0.650, 0.783], [0.100, 0.167]

[s4.000 , s4.714 ], [0.629, 0.757], [0.114, 0.200]

C5

9.4 Case Study 219

Suppliers C4 [s3.250 , s3.750 ], [0.600, 0.725], [0.125, 0.225]

[s3.000 , s3.333 ], [0.600, 0.667], [0.167, 0.200]

[s3.000 , s4.000 ], [0.533, 0.667], [0.200, 0.300]

[s2.750 , s3.750 ], [0.725, 0.800], [0.050, 0.175]

[s3.000 , s3.667 ], [0.567, 0.667], [0.167, 0.267]

[s3.667 , s4.667 ], [0.633, 0.800], [0.133, 0.167]

G3

G4

G5

Criteria

C3

Clusters

Table 9.6 (continued)

[s4.000 , s4.333 ], [0.567, 0.767], [0.167, 0.233]

[s2.333 , s3.333 ], [0.533, 0.800], [0.133, 0.200]

[s2.000 , s3.000 ], [0.625, 0.800], [0.050, 0.125]

C5

220 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

[s0.214 , s0.357 ], [0.114, 0.186], [0.586, 0.729]

[s0.278 , s0.361 ], [0.083, 0.183], [0.633, 0.767]

[s0.083 , s0.208 ], [0.075, 0.175], [0.650, 0.800]

[s0.222 , s0.333 ], [0.100, 0.200], [0.600, 0.733]

[s0.000 , s0.167 ], [0.050, 0.150], [0.700, 0.800]

[s0.250 , s0.354 ], [0.100, 0.212], [0.575, 0.713]

[s0.000 , s0.1333 ], [0.080, 0.140], [0.700, 0.840]

[s0.367 , s0.433 ], [0.120, 0.200], [0.620, 0.760]

[s0.389 , s0.556 ], [0.067, 0.167], [0.667, 0.800]

[s0.333 , s0.500 ], [0.100, 0.100], [0.600, 0.900]

[s0.306 , s0.388 ], [0.117, 0.200], [0.633, 0.717]

[s0.222 , s0.388 ], [0.117, 0.267], [0.550, 0.717]

[s0.250 , s0.375 ], [0.075, 0.150], [0.625, 0.800]

[s0.033 , s0.100 ], [0.060, 0.140], [0.700, 0.800]

[s0.500 , s0.500 ], [0.000, 0.100], [0.700, 0.900]

[s0.250 , s0.306 ], [0.100, 0.267], [0.533, 0.633]

[s0.361 , s0.528 ], [0.150, 0.217], [0.583, 0.717]

[s0.167 , s0.333 ], [0.125, 0.175], [0.600, 0.825]

[s0.444 , s0.611 ], [0.033, 0.133], [0.633, 0.833]

[s0.111 , s0.222 ], [0.033, 0.200], [0.600, 0.733]

[s0.603 , s0.747 ], [0.550, 0.700], [0.150, 0.233]

[s0.862 , s0.991 ], [0.650, 0.800], [0.100, 0.150]

[s0.689 , s0.747 ], [0.567, 0.767], [0.100, 0.233]

[s0.689 , s0.862 ], [0.650, 0.700], [0.100, 0.250]

[s0.819 , s0.948 ], [0.663, 0.788], [0.125, 0.175]

[s0.862 , s1.000 ], [0.580, 0.780], [0.120, 0.200]

[s0.655 , s0.828 ], [0.600, 0.760], [0.120, 0.220]

[s0.805 , s0.919 ], [0.733, 0.800], [0.067, 0.200]

[s0.517 , s0.689 ], [0.500, 0.700], [0.100, 0.100]

[s0.718 , s0.862 ], [0.617, 0.700], [0.150, 0.267]

[s0.689 , s0.805 ], [0.667, 0.783], [0.083, 0.150]

[s0.647 , s0.732 ], [0.675, 0.750], [0.100, 0.175]

[s0.724 , s0.896 ], [0.660, 0.760], [0.120, 0.220]

[s0.345 , s0.517 ], [0.500, 0.600], [0.200, 0.300]

[s0.747 , s0.919 ], [0.567, 0.700], [0.133, 0.267]

[s0.747 , s0.862 ], [0.650, 0.800], [0.133, 0.183]

[s0.560 , s0.733 ], [0.600, 0.825], [0.100, 0.150]

[s0.459 , s0.632 ], [0.500, 0.633], [0.233, 0.333]

[s0.747 , s0.919 ], [0.633, 0.767], [0.100, 0.167]

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

A4

A3

A2

C2

[s0.887 , s0.961 ], [0.671, 0.829], [0.086, 0.157]

G1

A1

Criteria

C1

Clusters

Suppliers

Table 9.7 Normalized evaluation values by the five clusters

(continued)

9.4 Case Study 221

[s0.667 , s0.786 ], [0.600, 0.757], [0.071, 0.200]

[s0.583 , s0.694 ], [0.583, 0.733], [0.050, 0.200]

[s0.625 , s0.750 ], [0.675, 0.775], [0.100, 0.150]

[s0.889 , s1.000 ], [0.667, 0.767], [0.067, 0.167]

[s0.583 , s0.667 ], [0.650, 0.700], [0.050, 0.200]

[s0.583 , s0.688 ], [0.575, 0.725], [0.088, 0.200]

[s0.633 , s0.767 ], [0.560, 0.700], [0.140, 0.280]

[s0.367 , s0.467 ], [0.660, 0.760], [0.080, 0.180]

[s0.667 , s0.778 ], [0.667, 0.833], [0.100, 0.100]

[s0.833 , s0.833 ], [0.800, 0.900], [0.100, 0.100]

[s0.694 , s0.833 ], [0.633, 0.800], [0.083, 0.183]

[s0.556 , s0.667 ], [0.600, 0.733], [0.167, 0.267]

[s0.458 , s0.625 ], [0.650, 0.775], [0.100, 0.200]

[s0.733 , s0.900 ], [0.600, 0.760], [0.100, 0.180]

[s0.333 , s0.500 ], [0.500, 0.800], [0.100, 0.200]

[s0.694 , s0.806 ], [0.617, 0.767], [0.083, 0.200]

[s0.583 , s0.750 ], [0.667, 0.767], [0.117, 0.217]

[s0.688 , s0.867 ], [0.567, 0.783], [0.133, 0.183]

[s0.673 , s0.852 ], [0.600, 0.750], [0.125, 0.250]

[s0.838 , s0.957 ], [0.767, 0.867], [0.067, 0.133]

[s0.897 , s0.987 ], [0.650, 0.800], [0.050, 0.150]

[s0.740 , s0.897 ], [0.688, 0.800], [0.088, 0.150]

[s0.897 , s0.969 ], [0.640, 0.780], [0.100, 0.180]

[s0.574 , s0.718 ], [0.680, 0.780], [0.140, 0.180]

[s0.538 , s0.718 ], [0.600, 0.733], [0.100, 0.200]

[s0.718 , s0.897 ], [0.800, 0.900], [0.000, 0.100]

[s0.778 , s0.957 ], [0.650, 0.767], [0.083, 0.183]

[s0.598 , s0.688 ], [0.600, 0.750], [0.100, 0.200]

[s0.493 , s0.583 ], [0.625, 0.750], [0.100, 0.200]

[s0.754 , s0.933 ], [0.640, 0.760], [0.100, 0.220]

[s0.359 , s0.359 ], [0.600, 0.700], [0.100, 0.300]

[s0.568 , s0.748 ], [0.583, 0.700], [0.133, 0.217]

[s0.808 , s0.957 ], [0.650, 0.767], [0.150, 0.200]

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

G3

G4

G5

G1

G2

A4

A3

A2

C4

[s0.872 , s1.000 ], [0.714, 0.843], [0.071, 0.129]

G1

A1

Criteria

C3

Clusters

Suppliers

Table 9.7 (continued)

(continued)

[s0.722 , s0.833 ], [0.583, 0.733], [0.100, 0.217]

[s0.472 , s0.639 ], [0.633, 0.700], [0.150, 0.267]

[s0.167 , s0.333 ], [0.700, 0.700], [0.100, 0.300]

[s0.667 , s0.800 ], [0.600, 0.760], [0.120, 0.240]

[s0.375 , s0.542 ], [0.625, 0.775], [0.075, 0.200]

[s0.722 , s0.889 ], [0.650, 0.800], [0.067, 0.167]

[s0.528 , s0.694 ], [0.600, 0.667], [0.133, 0.283]

[s0.833 , s1.000 ], [0.800, 0.800], [0.100, 0.200]

[s0.500 , s0.611 ], [0.600, 0.733], [0.100, 0.267]

[s0.467 , s0.633 ], [0.660, 0.780], [0.100, 0.200]

[s0.800 , s0.967 ], [0.600, 0.780], [0.080, 0.200]

[s0.667 , s0.813 ], [0.663, 0.750], [0.125, 0.225]

[s0.500 , s0.667 ], [0.600, 0.750], [0.100, 0.150]

[s0.667 , s0.667 ], [0.567, 0.700], [0.100, 0.200]

[s0.625 , s0.750 ], [0.575, 0.725], [0.125, 0.225]

[s0.694 , s0.861 ], [0.650, 0.783], [0.100, 0.167]

[s0.667 , s0.786 ], [0.629, 0.757], [0.114, 0.200]

C5

222 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

Suppliers C4 [s0.542 , s0.625 ], [0.600, 0.725], [0.125, 0.225]

[s0.500 , s0.556 ], [0.600, 0.667], [0.167, 0.200]

[s0.500 , s0.667 ], [0.533, 0.667], [0.200, 0.300]

[s0.494 , s0.673 ], [0.725, 0.800], [0.050, 0.175]

[s0.538 , s0.658 ], [0.567, 0.667], [0.167, 0.267]

[s0.658 , s0.838 ], [0.633, 0.800], [0.133, 0.167]

G3

G4

G5

Criteria

C3

Clusters

Table 9.7 (continued)

[s0.667 , s0.722 ], [0.567, 0.767], [0.167, 0.233]

[s0.389 , s0.556 ], [0.533, 0.800], [0.133, 0.200]

[s0.333 , s0.500 ], [0.625, 0.800], [0.050, 0.125]

C5

9.4 Case Study 223

C2 [s0.196 , s0.316 ], [0.092, 0.183], [0.619, 0.756]

[s0.324 , s0.439 ], [0.099, 0.179], [0.621, 0.779]

[s0.256 , s0.350 ], [0.222, 0.330], [0.446, 0.637]

[s0.303 , s0.442 ], [0.091, 0.196], [0.591, 0.741]

C4 [s0.711 , s0.824 ], [0.639, 0.756], [0.068, 0.179]

[s0.702 , s0.779 ], [0.693, 0.826], [0.112, 0.149]

[s0.614 , s0.761 ], [0.615, 0.771], [0.107, 0.208]

[s0.583 , s0.705 ], [0.616, 0.735], [0.122, 0.221]

C1

[s0.971 , s0.903 ], [0.639, 0.783], [0.098, 0.185]

[s0.795 , s0.932 ], [0.639, 0.781], [0.105, 0.191]

[s0.682 , s0.817 ], [0.649, 0.747], [0.113, 0.201]

[s0.682 , s0.839 ], [0.606, 0.761], [0.128, 0.202]

C3

[s0.824 , s0.954 ], [0.694, 0.829], [0.075, 0.145]

[s0.761 , s0.891 ], [1.000, 1.000], [0.000, 0.000]

[s0.660 , s0.794 ], [0.630, 0.756], [0.095, 0.204]

[s0.644 , s0.807 ], [0.635, 0.759], [0.124, 0.197]

C5

[s0.653 , s0.776 ], [0.616, 0.753], [0.108, 0.187]

[s0.723 , s0.882 ], [0.707, 0.779], [0.174, 0.285]

[s0.575 , s0.732 ], [0.624, 0.754], [0.095, 0.221]

[s0.571 , s0.692 ], [0.576, 0.758], [0.134, 0.225]

Suppliers

A1

A2

A3

A4

Suppliers

A1

A2

A3

A4

Suppliers

A1

A2

A3

A4

Table 9.8 The normalized collective evaluation matrix

224 9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

9.4 Case Study

225

Table 9.9 Ranking results of different methods Suppliers

Fuzzy TOPSIS

IF-GRA

ITL-VIKOR

Proposed Method

A1

2

2

2

2

A2

1

1

1

1

A3

3

4

4

3

A4

4

3

3

4

9.4.2 Comparison and Discussion To reveal the effectiveness of the developed GSES model, a comparative study is carried out in this subsection. Based on the same case example, the following green supplier selection approaches are selected for the comparison analysis: the fuzzy TOPSIS (Wang Chen et al. 2016), the intuitionistic fuzzy GRA (IF-GRA) (Bali et al. 2013), and the interval 2-tuple linguistic VIKOR (ITL-VIKOR) (You et al. 2015). Table 9.9 displays the results of the four timber suppliers according to the listed methods. From Table 9.9, it can be observed that the top two green suppliers derived by the three comparative models and the presented method are exactly the same. Therefore, it validates the GSES framework designed in this chapter. Besides, the ranking derived by the proposed approach is consist with the one by the fuzzy TOPSIS method. The fuzzy TOPSIS method adopted trapezoidal fuzzy numbers to evaluate the performance of suppliers. However, it is difficult to give approximate ratings to match the linguistic phrases in the primary expression domain. Moreover, the relative importance of the distances between each alternative to the positive ideal solution and the negative ideal solution is not considered in the TOPSIS method. In addition, there are some differences for the ranking orders obtained by the IF-GRA, the ITL-VIKOR, and the proposed method. According to the proposed method, A3 ranks before A4 while the IF-GRA and the ITL-VIKOR methods give opposite ranking. The reasons for the inconsistence may lie in the weakness of the two methods. For the IF-GRA method, IFSs are denoted as crisp values. In practice, it is difficult to determine membership and non-membership degrees precisely. In addition, the GRA method does not take the grey relation coefficient of each alternative to the negative ideal solution into account. For the ITL-VIKOR method, the VIKOR method does not consider the relative importance of the strategy of maximum group utility and the individual regret. Based on the above comparison analysis, it can be seen that the ranking result derived by the proposed model is more precise and credible. Comparing with the listed methods, the GSES model proposed in this chapter has the distinctive advantages as follows:

226

9 GSES with Large Group Uncertain Linguistic MULTIMOORA Method

• A large group of decision makers are involved to cope with the GSES problem, which is more practical in the real-life situation. By utilizing the ant colony algorithm, large number of decision makers can be clustered into several subgroups rapidly and effectively. • By applying IVIULSs, the uncertainty and vagueness of decision makers’ evaluations can be captured in the proposed model. This makes decision makers to express their opinions more flexibly and the assessment procedure easier to be performed. • The proposed method extends the LINMAP method for determining the objective weights of evaluation criteria. It is useful to deal with conflicting preference relations between alternatives given by decision makers. • The modified MULTIMOORA method under IVIUL environment determines the ranking results from three perspectives (i.e., the ratio system, the reference point method and the full multiplicative form). Thus, a more precise and reliable ranking of green suppliers can be acquired according to this method.

9.5 Chapter Summary In this chapter, we developed a hybrid model to address the GSES problem involving a large group of decision makers. As a new representation of uncertain linguistic information, IVIULSs were utilized for dealing with decision makers’ diversity assessments of suppliers. Ant colony algorithm was utilized to cluster the large number of decision makers into subgroups. An extension of the classical LINMAP method was used for computing the optimal weights of evaluation criteria. Finally, a modified MULTIMOORA approach was applied to rank the alternative green suppliers. A real-life example of a real estate company was implemented to reveal the efficiency of the proposed large group GSES approach. The results showed that the new approach can better reflect the hesitation and fuzziness of experts’ evaluations and obtain a more accurate priority order of the candidate suppliers.

References Asante D, He Z, Adjei NO, Asante B (2020) Exploring the barriers to renewable energy adoption utilising MULTIMOORA- EDAS method. Energy Policy 142:111479 Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96 Bali O, Kose E, Gumus S (2013) Green supplier selection based on IFS and GRA. Grey Syst Theory Appl 3(2):158–176 Brauers WKM, Zavadskas EK (2010) Project management by MULTIMOORA as an instrument for transition economies. Technol Econ Develop Econ 16(1):5–24 Brauers WKM, Zavadskas EK (2011) MULTIMOORA optimization used to decide on a bank loan to buy property. Technol Econ Develop Econ 17(1):174–188

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Nguyen H (2020) A generalized p-norm knowledge-based score function for an interval-valued intuitionistic fuzzy set in decision making. IEEE Trans Fuzzy Syst 28(3):409–423 Qin J, Liu X, Pedrycz W (2017a) An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. Eur J Oper Res 258(2):626–638 Qin J, Liu X, Pedrycz W (2017b) A multiple attribute interval type-2 fuzzy group decision making and its application to supplier selection with extended LINMAP method. Soft Comput 21(12):3207–3226 Sarabi EP, Darestani SA (2021) Developing a decision support system for logistics service provider selection employing fuzzy MULTIMOORA & BWM in mining equipment manufacturing. Appl Comput 98:106849 Srinivasan V, Shocker AD (1973) Linear programming techniques for multidimensional analysis of preferences. Psychometrika 38(3):337–369 Stanujkic D, Zavadskas EK, Smarandache F, Brauers WK, Karabasevic D (2017) A neutrosophic extension of the MULTIMOORA method. Informatica 28(1):181–192 Wan SP, Li DF (2013) Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees. Omega 41(6):925–940 Wang Chen HM, Chou SY, Luu QD, Yu THK (2016) A fuzzy MCDM approach for green supplier selection from the economic and environmental aspects. Math Prob Eng 2016:8097386 Wang J, Li J (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inform 33(1):8–9 Wang LE, Liu HC, Quan MY (2016) Evaluating the risk of failure modes with a hybrid MCDM model under interval-valued intuitionistic fuzzy environments. Comput Ind Eng 102:175–185 Wu SM, You XY, Liu HC, Wang LE (2020) Improving quality function deployment analysis with the cloud MULTIMOORA method. Int Trans Oper Res 27(3):1600–1621 Xu Z, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48(1):246–262 Yazdi M (2020) A perceptual computing–based method to prioritize intervention actions in the probabilistic risk assessment techniques. Qual Reliab Eng Int 36(1):187–213 Yörüko˘glu M, Aydın S (2020) Wind turbine selection by using MULTIMOORA method. Energy Syst. https://doi.org/10.1007/s12667-020-00387-8 You XY, You JX, Liu HC, Zhen L (2015) Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Expert Syst Appl 42(4):1906–1916 Yue W, Liu X, Li S, Gui W, Xie Y (2020) Knowledge representation and reasoning with industrial application using interval-valued intuitionistic fuzzy Petri nets and extended TOPSIS. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-020-01216-1 Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353 Zhang LJ, Liu R, Liu HC, Shi H (2020) Green supplier evaluation and selections: a state-of-the-art literature review of models, methods, and applications. Math Prob Eng 2020:1783421 Zhao H, You JX, Liu HC (2017) Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput 21(18):5355–5367 Zou XY, Chen SM, Fan KY (2021) Multiattribute decision making using probability density functions and transformed decision matrices in interval-valued intuitionistic fuzzy environments. Inf Sci 543:410–425

Chapter 10

GSES with Cloud Model Theory and QUALIFLEX Method

Selecting the optimum green supplier is crucial for green supply chain management, which is a challenging multi-criteria decision making problem. Moreover, while evaluating the performance of alternative suppliers, decision makers tend to determine their assessments using linguistic descriptors due to experts’ vague knowledge and information deficiency. This chapter develops an integrated model based on cloud model and QUALIFLEX (qualitative flexible multiple criteria method) approach to assess the green performance of companies under economic and environmental criteria. For the introduced model, the linguistic terms, expressed in normal clouds, are utilized to assess alternatives against each evaluation criterion. A linear programming model is established to compute the weights of criteria with unknown or incompletely known weight information. An extended QUALIFLEX approach is proposed and used to select the most suitable green supplier. Finally, the proposed GSES method is demonstrated by an empirical example of an auto manufacturer to confirm its rationality and effectiveness.

10.1 Introduction Currently, companies, particularly in the developing nations, have to enhance the effectiveness of their green supply chain management activities to survive in the global marketplace. On the one hand, governments are paying more attention to environmental issues and have issued a series of environmental regulations due to diminishing raw materials, increasing levels of pollution, and deterioration of the environment. Besides, a variety of pressures from consumers are making companies more cautious with regards to the detrimental influences of their business operations on the environment (Rostamzadeh et al. 2015). In this regard, numerous green supplier development programs, such as green purchasing, design for environment, and reverse logistics, have been invested by organizations to enhance their green performance with respect to supply chain (Bai and Sarkis 2010a; Awasthi © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_10

229

230

10 GSES with Cloud Model Theory and QUALIFLEX Method

and Kannan 2016). According to Srivastava (2007), green supply chain management is an approach to the philosophy of management taking environmental concern into account in the supply chain management, which consists of product design, raw material extraction, production processes, product transportation as well as disposing of the end-of-life product. Given the increasing awareness of environmental protection, it is more significant for companies to conduct green supply chain management practices to minimize or eliminate the negative environmental effects of their business operations (Carvalho et al. 2020; Li et al. 2020a; Liu et al. 2020a; Rahman et al. 2020). Within green supply chain management, organizations are required to assess the green performance of their suppliers and select the most appropriate one(s) in different stages of product life cycle (Bai and Sarkis 2010b). Green supplier selection is a challenging multi-dimensional issue in the competitive environment (Sarkis and Dhavale 2015; Banaeian et al. 2018), which can be resolved by multi-criteria decision making (MCDM) methods. The QUALIFLEX (qualitative flexible multiple criteria method) (Paelinck 1978) is an efficient outranking MCDM method that assesses all possible rankings of considered alternatives and finds the optimum one by using the maximum concordance/discordance index. The salient features of the QUALIFLEX method, compared to other MCDM methods, are that: (1) It can simultaneously deal with cardinal and ordinal information in the decision process; (2) It can perfectly address the complex decision making problems with numerous criteria and limited alternatives; (3) It does not require complicated computations in the multiple criteria decision analysis. Over the past decades, researchers have extended the QUALIFLEX method to model and manage MCDM problems within different decision-making environments (Liu et al. 2019b, 2020b; Banerjee et al. 2020; Liang et al. 2020). Moreover, the use of the QUALIFLEX for green supplier selection is practical and has demonstrated satisfactory results (Li and Wang 2017; Peng et al. 2017; Wang et al. 2017). On the other hand, in the process of green supplier evaluation, decision makers may have difficulty in evaluating candidate companies with numerical values due to the uncertainty of input data and the vagueness of human thinking. As is stressed by many researchers (Liu et al. 2019a, 2020c; Ma et al. 2020), it is natural for decision makers to determine their judgments based on linguistic expressions, i.e., inexact and unquantifiable information, in real-life GSES problems. Computing with words is the key to transforming linguistic variables into quantitative values, and the current methods of dealing with linguistic information can be classified into three types, i.e., the linguistic computational model based on membership functions (Zadeh 1975), the linguistic symbolic model based on ordinal scales (Xu 2004) and the 2-tuple linguistic model (Herrera and Martínez 2000). However, as indicated by Wang et al. (2014) the linguistic symbolic model and the 2-tuple linguistic model cannot produce a clear description of either fuzziness or randomness of qualitative information. The linguistic computational model can describe fuzziness but not randomness. However, the cloud model (Li et al. 2009) not only describes the fuzziness and randomness of linguistic terms but also makes the transformation between quantitative values and qualitative concepts much easier and interchangeable. In recent years, the cloud

10.1 Introduction

231

model theory has attracted increasing attention and has been successfully applied in many fields (Hosseini et al. 2020; Li et al. 2020b, c; Wu et al. 2020; Wang et al. 2021). Based on the discussions above, this chapter is aimed at proposing an integrated decision support framework based on cloud model theory and the QUALIFLEX method for the evaluation of qualified green suppliers within linguistic environment. First, the cloud model is introduced for the purpose of handling the fuzziness and randomness of linguistic expressions provided by decision makers. Second, we create an optimization model to obtain the criteria weights that are supposed to be totally unknown or incompletely known. Third, an extended QUALIFLEX algorithm is developed to prioritize the performance of different alternative suppliers and recommend the optimal one(s) for cooperation. In addition, the feasibility and effectiveness of the proposed GSES approach are indicated by a case example concerning an automobile manufacturing company. The remaining part of this chapter is structured as below: Sect. 10.2 introduces some basic concepts related to cloud model theory. Section 10.3 proposes the GSES approach using the cloud model and QUALIFLEX method. In Sect. 10.4, an illustrative example is presented to demonstrate the developed approach. In Sect. 10.5, the conclusions of this chapter are provided.

10.2 Preliminaries 10.2.1 Cloud Model Theory The cloud model is a new cognition model defined by Li et al. (2009) to represent the fuzziness and randomness of qualitative concepts. In this part, some basic concepts and operations related to cloud model theory are introduced. Definition 10.1 (Li et al. 2009) Supposing a qualitative concept T defined on a universe of discourse U, let x, x ∈ U be a random realization of the concept T and μT (x) ∈ [0, 1] be the membership degree of x belonging to T, which corresponds to a random number with a stable tendency. Then the distribution of x in the universe U is called a cloud and every x is called a cloud drop. Definition 10.2 (Li et al. 2009) The characteristics of a cloud y are depicted by three parameters: expectation Ex, entropy En and hyper entropy He. Here, Ex is the center value of the qualitative concept domain, En measures the randomness and fuzziness of the qualitative concept, and He reflects the dispersion degree of the cloud drops and the uncertainty of the membership function. Generally, a cloud can be denoted by y = (E x, En, H e). Definition 10.3 (Wang et al. 2014) Consider any two normal clouds  y1 = y2 = (E x2 , En 2 , H e2 ) in the domain U, the basic operations (E x1 , En 1 , H e1 ) and  of normal clouds are defined as follows:

232

10 GSES with Cloud Model Theory and QUALIFLEX Method

   E x1 + E x2 , En 21 + En 22 , H e12 + H e22 ,    y1 ×  y2 = E x1 E x2 , (En 1 E x2 )2 + (En 2 E x1 )2 ,   2 2 (H e1 E x2 ) + (H e2 E x1 ) ,   √ √ λ y1 = λE x1 , λEn 1 , λH e1 , λ > 0,   √ √  y1λ = E x1λ , λ(E x1 )λ−1 En 1 , λ(E x1 )λ−1 H e1 , λ > 0. 

(1)

(2)

(3) (4)

 y1 +  y2 =

Definition 10.4 (Wang et al. 2014) Let  yi = (E xi , En i , H ei )(i = 1, 2, . . . , n) be n normal clouds in the universe of discourse and w = (w1 , w2 , . . . , wn )T be U, n their associated weights with wi ∈ [0, 1] and i=1 wi = 1, then the cloud weighted averaging (CWA) is defined as: CWAw ( y˜1 , y˜2 , . . . , y˜n ) =

n

wi y˜i =

i=1

⎛ =⎝

n i=1

n

wi (E xi , En i , H ei )

i=1

⎞

n

n



wi E xi ,  wi En i2 ,  wi H ei2 ⎠. i=1

(10.1)

i=1

Definition 10.5 (Wang et al. 2015) Let y˜1 = (E x1 , En 1 , H e1 ) and y˜2 = (E x2 , En 2 , H e2 ) be two arbitrary normal clouds in the domain U, then the distance between them is computed by        (En 1 + H e1 ) (En 2 + H e2 ) E x1 − 1 − E x2 . d( y˜1 , y˜2 ) =  1 − E x1 E x2

(10.2)

Definition 10.6 Let y˜ = (E x, En, H e) be a normal cloud in the domain U, then the signed distance of y˜ from the origin 0˜ is determined by     (En + H e) d y˜ , 0˜ = 1 − E x. Ex

(10.3)

Note that the signed distances from normal clouds to 0˜ are real numbers, which satisfy the law of trichotomy. Definition 10.7 Let y˜1 = (E x1 , En 1 , H e1 ) and y˜2 = (E x2 , En 2 , H e2 ) be two normal clouds in the domain U. Then the comparison of normal clouds is defined as follows:     (1) If d y˜1 , 0˜ > d y˜2 , 0˜ , then y˜1 is better than y˜2 , i.e., y˜1 > y˜2 ;     (2) If d y˜1 , 0˜ < d y˜2 , 0˜ , then y˜1 is worse than y˜2 , i.e., y˜1 < y˜2 ;

10.2 Preliminaries

(3)

233

    If d y˜1 , 0˜ = d y˜2 , 0˜ , then y˜1 is indifferent to y˜2 , i.e., y˜1 = y˜2 .

Definition 10.8 (Wang et al. 2014) Let y˜i = (E xi , En i , H ei )(i = 1, 2, . . . , n) be a set of normal clouds in the universe of discourse U, and  ω = (ω1 , ω2 , . . . , ωn ) be an associated weight vector satisfying ω j ∈ [0, 1] and nj=1 ω j = 1, then the cloud ordered weighted averaging (COWA) is computed by COWAω ( y˜1 , y˜2 , . . . , y˜n ) =

n

ω j y˜σ ( j)

j=1

⎛

n

n ⎝ = ω j E xσ ( j) ,  ω j En 2σ j=1

( j)





n , ω j H e2

j=1

⎞

σ ( j)

⎠,

j=1

(10.4) where y˜σ ( j) = y˜i (i = 1, 2, . . . , n).



E xσ ( j) , En σ ( j) , H eσ ( j)



is the jth largest element of

10.2.2 Laplace Distribution-Based Method Defining the aggregation weight vector ω is one key issue in the theory of the ordered weighted averaging (OWA) operator (Yager 1988). Recently, Mohammed et al. (2016) developed a new method based on the Laplace distribution to calculate the OWA weight vector. This method has the ability to reduce the effect of “false” or “biased” opinions on the decision-making results by assigning higher weights to the median elements of the ordered arguments and lower weights to the tail elements. Definition 10.9 (Mohammed et al. 2016) According to the argument-dependent method based on Laplace distribution, the associated weighting vector of the OWA operator is obtained by 1 − e 2λn

ωj =  n

|i−μn | λn

1 − j=1 2λn e

|i−μn | =  λn

e−

|i−μn | λn

n| n − |i−μ λn j=1 e

,

j = 1, 2, . . . , n,

(10.5)

where n is the number of aggregated arguments, μn is the mean of the number of the argument, and λn is the scale of the Laplace distribution. The parameter μn is calculated by μn =

1 n(1 + n) 1+n = , n 2 2

and the Laplace distribution standard deviation σn is defined as:

(10.6)

234

10 GSES with Cloud Model Theory and QUALIFLEX Method

√ σn = 2λn =



1 n ( j − μn )2 . j=1 n

(10.7)

10.3 The Proposed GSES Methodology In this section, we introduce a new decision support framework by combining cloud model and QUALIFLEX method for addressing the GSES problem with unknown or incomplete weight information. In a nutshell, the proposed methodology is comprised of three phases: assessing the performance of green suppliers based on normal clouds, acquiring the weights of evaluation criteria by a linear programming model, and determining the ranking orders of alternatives with the QUALIFLEX method. The procedure of the proposed GSES approach is depicted in Fig. 10.1, and the detailed explanations are presented as below.

10.3.1 Assess the Performance of Green Suppliers Assume a GSES problem with m feasible alternatives (Ai , i = 1, 2, . . . , m), which are assessed by a committee of l decision makers (DMk , k =  1,2, . . . , l) on the basis   k be the linguistic of n evaluation criteria C j , j = 1, 2, . . . , n . Let D = dikj m×n

decision matrix, where dikj is the suitability assessment of alternative Ai versus criterion Cj provided by the decision maker DMk . Next, the cloud model theory is used to model the linguistic evaluations on alternatives given by the decision makers. Step 1 Obtain the normal cloud decision matrix X k . The proposed GSES approach utilizes the linguistic terms represented by normal clouds to assess the performance of alternative suppliers regarding various evaluation criteria. For instance, these linguistic terms can be represented by the normal clouds shown in Table 10.1. Based on the linguistic ratings of each decision maker, the first step is to transform them into normal clouds as per the scale information to obtain the   linguistic   k k , where x˜i j = E xi j , En i j , H ei j , normal cloud decision matrix X = xi j i = 1, 2, . . . , m; j = 1, 2, . . . , n.

m×n

Step 2 Establish the group normal cloud decision matrix  X. Normally, there may exist “false” or “biased” judgements in the green supplier selection practice. That is to say, some decision makers may give excessively high or excessively low ratings to their preferred or repugnant suppliers. To deal with such cases, the COWA operator is adopted to combine the decision makers’ performance assessments into representative group assessments.

10.3 The Proposed GSES Methodology

235

Fig. 10.1 Flowchart of the proposed GSES approach Table 10.1 Linguistic ratings for alternative suppliers

Linguistic terms

Normal clouds

Very Poor (VP)

(1, 0.45, 0.05)

Poor (P)

(2, 0.45, 0.05)

Medium Poor (MP)

(3, 0.45, 0.05)

Fair (F)

(5, 0.45, 0.05)

Medium Good (MG)

(6, 0.45, 0.05)

Good (G)

(8, 0.45, 0.05)

Very Good (VG)

(9, 0.45, 0.05)

236

10 GSES with Cloud Model Theory and QUALIFLEX Method

By applying the COWA operator, the aggregation of individual cloud matrices  k X = xi j (k = 1, 2, . . . , l) is performed to construct the group normal cloud m×n   , i.e., decision matrix  X = x˜i j k

m×n

l   x˜i j = COWA x˜i1j , x˜i2j , . . . , x˜il j = ω j x˜iσj(h) h=1

⎞ ⎛

l l l  2  2

=⎝ ω j E xiσj(h) ,  ω j En iσj(h) ,  ω j H eiσj(h) ⎠, h=1

h=1

(10.8)

h=1

  where x˜iσj(h) = E xiσj(h) , En iσj(h) , H eiσj(h) is the hth largest element of xikj =   E xikj , En ikj , H eikj (k = 1, 2, . . . , l).

10.3.2 Compute the Weights of Evaluation Criteria The TOPSIS proposed by Hwang and Yoon (1981) is a classical MCDM technique, which selects the most suitable alternative with the shortest distance from the positiveideal solution and the farthest distance from the negative-ideal solution. The aim of this stage is to build an optimization model following the idea of the TOPSIS method for obtaining criteria weights objectively. Suppose w = (w1 , w2 , . . . , wn )T is the weight vector of the criteria C j ( j = 1, 2, . . . , n), which is unknown a priori. In the following section, the detail processes of determining criteria weights are presented. Step 3 Define the positive-ideal and the negative-ideal solutions. Within the cloud environment, the positive-ideal and the negative-ideal solutions, denoted as A+ and A− , can be respectively denoted by 

A+ = x˜ +j

 1×n

=

⎧ ⎨ max x˜i j for benefit criteria, i

⎩ min x˜i j for cost criteria,

(10.9)

i



A− = x˜ −j

 1×n

=

⎧ ⎨ min x˜i j for benefit criteria, i

⎩ max x˜i j for cost criteria.

(10.10)

i

Step 4 Determine the weighted closeness coefficients of alternatives. By using Eq. (10.11), the closeness coefficient of each alternative against the criteria is computed as follows:

10.3 The Proposed GSES Methodology

237

  d x˜i j , x˜ −j    , i = 1, 2, . . . , m, j = 1, 2, . . . , n, Di j =  d x˜i j , x˜ +j + d x˜i j , x˜ −j

(10.11)

    where d x˜i j , x˜ +j d x˜i j , x˜ −j is the distance of Ai from A+ (A− ) concerning the criterion C j . Then the weighted closeness coefficient of alternatives Ai is determined by   d x˜i j , x˜ −j    , i = 1, 2, . . . , m. (10.12) Di = w j Di j = wj  d x˜i j , x˜ +j + d x˜i j , x˜ −j j=1 j=1 n

n

Step 5 Calculate the optimal weights of criteria. The weighted closeness coefficient Dj represents the relative closeness of alternative Ai to the ideal solution; the larger the value of Dj , the better the alternative. Considering all the m alternatives as a whole, the following linear programming model can be created for obtaining criteria weights when the weight information is completely unknown: m m  n   max D(w) = Di = w j Di j i=1 i=1 j=1 ⎧ n (M − 1) ⎨  w = 1, j s.t. j=1 ⎩ w j ≥ 0, j = 1, 2, . . . , n.

(10.13)

By resolving the above model, the optimal solutions are normalized to obtain the weights of criteria as m Di j  m w j = n i=1 j=1

i=1

Di j

.

(10.14)

Furthermore, there are still some cases where the information regarding criteria weights is identified partially. The obtained weight information normally consists of the following five structural forms (Zhang et al. 2015; Liu et al. 2016), for i = j:   (1) A weak ranking: H1 =  wi ≥ w j ;   (2) A strict ranking: H2 = wi − w j ≥ β j β j > 0 ;  (3) A ranking of differences: H3 = wi − w j ≥ w k − wl ( j = k = l); (4) A ranking with multiples: H4 = wi ≥ β j w j 0 ≤ β j ≤ 1 ; (5) An interval form: H5 = {βi ≤ wi ≤ βi + εi } (0 ≤ βi ≤ βi + εi ). For the sake of convenience, H is assumed to be a set of recognized weight information and H = H1 ∪ H2 ∪ H3 ∪ H4 ∪ H5 . For these situations, the single objective optimization model in Eq. (10.15) can be established.

238

10 GSES with Cloud Model Theory and QUALIFLEX Method m m  n   max D(w) = Di = w j Di j i=1 i=1 j=1 ⎧ (M − 2) ⎨ w ∈ H, n s.t.  w j = 1, w j ≥ 0, j = 1, 2, . . . , n. ⎩

(10.15)

j=1

By executing model (M-2), the optimal criteria weights can be obtained as w = (w1 , w2 , . . . , wn )T .

10.3.3 Determine the Ranking of Alternatives Green supplier selection requires multi-dimensional techniques, and the QUALIFLEX method (Paelinck 1978) is a pragmatic and reliable outranking MCDM technique to rank and select alternatives. Thus, in the third phrase of our proposed framework, we extend the classical QUALIFLEX approach to the cloud setting for the generation of ranking of green suppliers. Step 6 Set up all possible permutations of alternatives. For the m alternatives Ai (i = 1, 2, . . . , m), m! permutations of the ranking orders of alternatives exist. Assume that the ρth permutation denoted by Pρ is defined as:   Pρ = . . . , Aχ , . . . , Aη , . . . , ρ = 1, 2, . . . , m!,

(10.16)

where Aξ and Aζ , ξ, ζ = 1, 2, . . . , m, are the suppliers under consideration, and Aξ is ranked larger than or equal to Aζ . Step 7 Acquire the concordance/discordance index. We use the following formula to compute the concordance/discordance index ρ φ j Aξ , Aζ in the ρth permutation against the criterion Cj for each pair of alternatives   Aξ , Aζ .      ρ φ j Aξ , Aζ = d r˜ξ j , 0˜ − d r˜ζ j , 0˜ ,

j = 1, 2, . . . , n.

(10.17)

According to the comparison method of normal clouds introduced in Defini  ρ ρ ρ tion 10.7, φ j Aξ , Aζ > 0, φ j Aξ , Aζ < 0, and φ j Aξ , Aζ = 0 represent concordance, discordance and ex aequo, respectively. Step 8 Determine the weighted concordance/discordance index. Using the weight vector of criteria w = (w1 , w2 , . . . , w n )T acquired in the second  ρ A is determined by , A stage, the weighted concordance/discordance index φ ξ ζ   Eq. (10.18) for the alternatives Aξ , Aζ regarding permutation Pρ .

10.3 The Proposed GSES Methodology

239

n    ρ φ ρ Aξ , Aζ = φ j Aξ , Aζ w j .

(10.18)

j=1

Step 9 Acquire the best ranking of alternative suppliers. For each permutation Pρ , we obtain the comprehensive concordance/discordance index φ ρ through Eq. (10.19).

φρ =

n

 ρ φ j Aξ , Aζ w j .

(10.19)

ξ,ζ =1,2,...,m j=1

A higher comprehensive concordance/discordance index value indicates that the ranking order of the alternatives is better. Hence, the optimum ranking of the considered suppliers can be identified via the comparison of the comprehensive concordance index values φ ρ (ρ = 1, 2, . . . , m!). That is, the permutation with the highest φ ρ value, i.e., P ∗ = max {φ ρ } should be the final ranking of the alternatives. ρ=1,2,...,m!

10.4 Illustrative Example Taking the green supplier selection for an auto manufacturing company as an example, the applicability and efficacy of the proposed GSES model are demonstrated in this section.

10.4.1 Background Description In this case, we consider an auto manufacturing company in Shanghai, China since the green initiatives are expected to be implemented within its operations. To comply with environmental regulations and adapt to social concerns, top management of this company decided to adjust its business strategy and become a company devoted to the public health and environment by committing itself to social responsibility. Currently, determining the qualified green supplier for the automotive component, instrument panel, for improving the company’s supply chain environmental performance is needed. An expert panel including five direct managers (denoted as DM1 , DM2 , …, DM5 ) was established to rate three alternative companies, A1 , A2 , and A3 . Generally, various quantitative and qualitative evaluation criteria must be considered to determine the best green supplier. According to the literature surveys (Igarashi et al. 2013; Govindan et al. 2015) and decision makers’ opinions, green design, green purchasing, green production, green logistics and green recycling are determined as evaluation dimensions for the green supplier selection. Further, several related criteria of each dimension are identified for evaluating the alternative suppliers in more detail

240

10 GSES with Cloud Model Theory and QUALIFLEX Method

Fig. 10.2 Dimensions and criteria for green supplier selection

(see Fig. 10.2). Then, the five decision makers are asked to rate each supplier with regard to the above criteria using the linguistic assessment terms shown in Table 10.1. The completed assessment matrices provided by the expert group are presented in Table 10.2.

10.4.2 Application and Results The GSES problem is solved by applying the proposed model and the implementation procedure is described as follows. Step 1 The linguistic ratings of the five decision makers are transformed into normalclouds  based on Table 10.1 to construct the normal cloud decision matrixes X k = xikj (k = 1, 2, . . . , 5). 3×15

Step 2 The produced normal cloud decision matrixes X k (k = 1, 2, . . . , 5) are aggregated by using  COWA operator to establish the group cloud deci the sion matrix  X = x˜i j 3×15 . The results obtained are presented in Table 10.3. Note that the weighting vector of the COWA operator is determined as ω = (0.068, 0.183, 0.498, 0.183, 0.068) with the Laplace distribution-based method. Step 3 Using Eqs. (10.9) and (10.10), the positive-ideal and the negative-ideal solutions A+ and A− are derived as listed in the last two rows of Table 10.3.

F

P

A2

A3

DM5

DM4

DM3

DM2

G

F

P

A2

A3

F

A3

VG

F

A2

A1

G

MP

A3

A1

MP

A2

F

A3

G

MP

A2

A1

G

A1

C1

A1

DM1

Criteria

Alternatives

Decision makers

MG

P

MP

G

P

MP

MG

P

F

G

MP

MP

MG

P

MP

C2

G

F

G

MG

MG

VG

VG

MG

G

G

MG

G

G

VG

VG

C3

P

VP

P

F

P

VP

MP

P

VP

VP

VP

P

F

P

VP

C4

MG

VP

P

F

VP

VP

G

F

VP

MG

MP

P

F

VP

P

C5

Table 10.2 Linguistic assessments of alternatives provided by the expert group C6

VG

VG

G

G

VG

G

G

VG

VG

VG

G

VG

G

VG

G

C7

G

VG

MP

VG

G

F

VG

VG

F

VG

G

MG

F

VG

F

C8

MG

P

MG

MP

VP

MP

MP

VP

MP

F

P

P

P

P

P

C9

G

P

VG

G

VP

G

G

P

F

F

VP

F

G

P

MG

C10

F

G

MG

G

VG

G

P

VG

G

VG

G

VG

F

G

G

C11

F

G

MG

P

MG

F

F

F

P

MP

MG

F

MP

F

G

C12

MP

F

F

MG

G

MG

F

MG

F

F

G

MG

MG

G

F

C13

MP

F

G

F

F

G

MP

F

VG

F

F

VG

MG

F

VG

C14

G

VP

VP

P

VP

MP

MG

MP

P

F

P

MP

F

VP

P

C15

F

P

VG

F

F

VG

F

MP

VG

P

F

VG

G

F

G

10.4 Illustrative Example 241

242

10 GSES with Cloud Model Theory and QUALIFLEX Method

Table 10.3 The group cloud decision matrix X˜ C1

C2

C3

C4

C5

A1

(8.07, 0.45, 0.05)

(3.14, 0.45, 0.05)

(8.25, 0.45, 0.05)

(1.25, 0.45, 0.05)

(1.75, 0.45, 0.05)

A2

(4.50, 0.45, 0.05)

(2.07, 0.45, 0.05)

(6.14, 0.45, 0.05)

(1.75, 0.45, 0.05)

(1.64, 0.45, 0.05)

A3

(3.25, 0.45, 0.05)

(6.50, 0.45, 0.05)

(7.93, 0.45, 0.05)

(3.18, 0.45, 0.05)

(5.89, 0.45, 0.05)

A+

(8.07, 0.45, 0.05)

(6.50, 0.45, 0.05)

(8.25, 0.45, 0.05)

(3.18, 0.45, 0.05)

(5.89, 0.45, 0.05)

A−

(3.25, 0.45, 0.05)

(2.07, 0.45, 0.05)

(6.14, 0.45, 0.05)

(1.25, 0.45, 0.05)

(1.64, 0.45, 0.05)

C6

C7

C8

C9

C10

A1

(8.25, 0.45, 0.05)

(4.93, 0.45, 0.05)

(2.95, 0.45, 0.05)

(6.32, 0.45, 0.05)

(7.93, 0.45, 0.05)

A2

(8.93, 0.45, 0.05)

(8.75, 0.45, 0.05)

(1.75, 0.45, 0.05)

(1.75, 0.45, 0.05)

(8.25, 0.45, 0.05)

A3

(8.25, 0.45, 0.05)

(8.55, 0.45, 0.05)

(3.50, 0.45, 0.05)

(7.80, 0.45, 0.05)

(5.62, 0.45, 0.05)

A+

(8.93, 0.45, 0.05)

(8.75, 0.45, 0.05)

(3.50, 0.45, 0.05)

(7.80, 0.45, 0.05)

(8.25, 0.45, 0.05)

A−

(8.25, 0.45, 0.05)

(4.93, 0.45, 0.05)

(1.75, 0.45, 0.05)

(1.75, 0.45, 0.05)

(5.62, 0.45, 0.05)

C11

C12

C13

C14

C15

A1

(5.18, 0.45, 0.05)

(5.25, 0.45, 0.05)

(8.75, 0.45, 0.05)

(2.18, 0.45, 0.05)

(8.93, 0.45, 0.05)

A2

(5.89, 0.45, 0.05)

(7.43, 0.45, 0.05)

(5.00, 0.45, 0.05)

(1.32, 0.45, 0.05)

(4.43, 0.45, 0.05)

A3

(3.43, 0.45, 0.05)

(5.12, 0.45, 0.05)

(4.57, 0.45, 0.05)

(5.18, 0.45, 0.05)

(5.00, 0.45, 0.05)

A+

(5.89, 0.45, 0.05)

(7.43, 0.45, 0.05)

(8.75, 0.45, 0.05)

(5.18, 0.45, 0.05)

(8.93, 0.45, 0.05)

A−

(3.43, 0.45, 0.05)

(5.12, 0.45, 0.05)

(4.57, 0.45, 0.05)

(1.32, 0.45, 0.05)

(4.43, 0.45, 0.05)

Step 4 The weighted closeness coefficient is calculated via Eqs. (10.11) and (10.12) for each alternative, and the results are as follows:

D1 = w1 + 0.241w2 + w3 + 0.026w4 + 0.687w8 + 0.756w9 + 0.879w10 + 0.714w11 + 0.059w12 + w13 + 0.224w14 + w15 , D2 = 0.259w1 + 0.258w4 + w6 + w7 + w10 + w11 + w12 + 0.104w13 , D3 = w2 + 0.849w3 + w4 + w5 + 0.947w7 + w8 + w9 + w14 + 0.127w15 .

10.4 Illustrative Example

243

Step 5 The weights of the fifteen criteria are acquired by Eq. (10.14) as: w = (0.06, 0.059, 0.088, 0.06, 0.049, 0.047, 0.092, 0.08, 0.083, 0.089, 0.081, 0.05, 0.052, 0.058, 0.053)T .

Step 6 There are 6 (=3!) permutations of the rankings for the three potential green suppliers, i.e.,

P1 = (A1 , A2 , A3 ), P2 = (A1 , A3 , A2 ), P3 = (A2 , A1 , A3 ), P4 = (A2 , A3 , A1 ), P5 = (A3 , A1 , A2 ), P6 = (A3 , A2 , A1 ). Step Eq. (10.17), we can compute  7 By using   the concordance/discordance index φ ρj Aξ , Aζ for each pair of suppliers Aξ , Aζ in the ρth permutation concerning every criterion Cj . For instance, the calculation results for the permutation P1 are presented in Table 10.4.   ρ Step 8 The weighted concordance/discordance index  φ Aξ, Aζ is acquired by employing Eq. (10.18) for each pair of alternatives Aξ , Aζ (ξ, ζ = 1, 2, 3) and Table 10.5 shows the computational results. Step 9 The comprehensive concordance/discordance indexes φ ρ (ρ = 1, 2, . . . , 6) are determined by utilizing Eq. (10.19) as follows: φ 1 = −0.178, φ 2 = 1.640, φ 3 = −1.818, φ 4 = −1.640, φ 5 = 1.818, φ 6 = 0.178.

Table 10.4 The results of the concordance/discordance index for P1

P1

φ 1j (A1 , A2 )

φ 1j (A1 , A3 )

φ 1j (A2 , A3 )

C1

3.570

4.817

1.247

C2

1.068

−3.366

−4.434

C3

2.115

0.319

−1.796

C4

−0.498

− 1.932

−1.434

C5

0.111

− 4.136

−4.247

C6

−0.681

0.000

0.681

C7

−3.817

−3.613

0.204

C8

1.204

−0.549

−1.753

4.570

−1.477

−6.047

C10

−0.319

2.315

2.634

C11

−0.702

1.749

2.451

C12

−2.179

0.136

2.315

C13

3.749

4.183

0.434

C14

0.864

−3.000

−3.864

C15

4.502

3.932

−0.570

C9

244

10 GSES with Cloud Model Theory and QUALIFLEX Method

Table 10.5 The results of the weighted concordance/discordance indexes P1 φ 1 (A1 , A2 ) φ 1 (A1 , A3 ) φ 1 (A2 , A3 )

P2

0.820

φ 2 (A1 , A3 )

−0.089

φ 2 (A1 , A2 ) φ 2 (A3 , A2 )

−0.909 P4

φ 4 (A2 , A3 ) φ 4 (A2 , A1 ) φ 4 (A3 , A1 )

P3

−0.089

φ 3 (A2 , A1 )

−0.820

0.820

φ 3 (A2 , A3 ) φ 3 (A1 , A3 )

−0.909

0.909 P5

−0.089 P6

−0.909

φ 5 (A

3 , A1 )

0.089

−0.820

φ 5 (A3 , A2 )

0.909

0.089

φ 5 (A1 , A2 )

0.820

φ 6 (A3 , A2 ) φ 6 (A3 , A1 ) φ 6 (A2 , A1 )

0.909 0.089 −0.820

Based on the comprehensive concordance/discordance indexes φ ρ (ρ = 1, 2, . . . , 6), it is clear that P ∗ = max {φ ρ } = φ 5 . Thereby, the ρ=1,2,...,6

optimal ranking of the three alternative companies is A3 A1 A2 , and the most appropriate green supplier is A3 for the vehicle manufacturer.

10.4.3 Discussion Under Incomplete Weight Information The following is the situation where the weight information for the assessment criteria is incompletely known and the given weight information is as follows: ⎧ ⎫ ⎪ ⎨ w1 ≤ 0.04, w2 ≤ w1 , w3 ≤ 0.03, 0.1 ≤ w4 ≤ 0.13, w5 ≥ 0.7w4 , w6 ≥ 0.05,⎪ ⎬ H = 0.1 ≤ w7 ≤ 0.17, 0.06 ≤ w8 ≤ 0.11, w4 − w9 ≥ 0.02, 0.06 ≤ w8 ≤ 0.10, . ⎪ ⎪ ⎩ ⎭ w10 = w11 , 0.008 ≤ w12 ≤ 0.012, w13 ≤ 0.008, w13 = w14 , w15 ≤ w13

Then, using Eqs. (10.9)–(10.12), the following linear programming model is established: max D(w) = 1.2589w1 + 1.2409w2 + 1.8492w3 + 1.2578w4 + 1.0261w5 + w6 + 1.9466w7 + 1.6868w8 + 1.7557w9 + 1.8789w10 + 1.7136w11 + 1.0587w12 + 1.1038w13 + 1.2236w14 + 1.1266w15 ⎧ ⎪ ⎨ w ∈ H, 15 s.t.  w j = 1, w j ≥ 0, j = 1, 2, . . . , 15. ⎪ ⎩ j=1

Based on the above model, the weight vector of the 15 criteria is computed as: w = (0.04, 0.04, 0.03, 0.013, 0.091, 0.05, 0.17, 0.11, 0.11, 0.1, 0.1, 0.008, 0.008, 0.008, 0.005)T .

Accordingly, the comprehensive concordance/discordance indexes φ ρ (ρ = 1, 2, . . . , 6) are computed as φ 1 = −1.921, φ 2 = 0.173, φ 3 = −2.094, φ 4 = −0.173, φ 5 = 2.094, φ 6 = 1.921. Hence, the optimal priority

10.4 Illustrative Example

245

Table 10.6 Ranking results of different methods Alternatives

Fuzzy VIKOR

Fuzzy TOPSIS

Improved GRA

The proposed method

A1

2

2

2

2

A2

2

3

3

3

A3

1

1

1

1

order of the three alternative suppliers is A3 A1 A2 , which is exactly the same as the ranking result earlier. This implies that the proposed decision support framework is also useful for the GSES problems with incomplete criteria weight information.

10.4.4 Comparative Study Next, a comparative analysis is conduced to show the effectiveness of our proposed GSES approach. We base the analysis on the same case example and choose the fuzzy VIKOR (Rostamzadeh et al. 2015), the fuzzy TOPSIS (Uygun and Dede 2016), the improved GRA (Hashemi et al. 2015) to facilitate the comparison analysis. The ranking results of the three alternatives determined by these methods are tabulated in Table 10.6. From Table 10.6, it is seen that the most suitable green supplier for the considered application remains the same, i.e., A3 , according to the proposed approach and the listed methods. Further, the ranking orders of the suppliers with the proposed approach are totally in agreement with the results acquired via the fuzzy TOPSIS and the improved GRA methods. This proves the validity of the proposed GSES model. However, in comparison with the listed methods, the distinct advantages of the approach being proposed in this study are as below: • By using the cloud model theory, the proposed model effectively prevents the loss of information in the semantic transformation and easily completes an interchangeable conversion between qualitative concepts and quantitative information. • The impact of “false” or “biased” assessments of decision makers on the decision result can be decreased by using the COWA operator in aggregating personal judgments into overall assessments. • Against the basic rule of the TOPSIS, the proposed model can be used to manage the green supplier selection problems where the weight information of criteria is completely unknown or partly identified.

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10 GSES with Cloud Model Theory and QUALIFLEX Method

• With the aid of the extended QUALIFLEX algorithm, an accurate and credible ranking of available suppliers can be obtained. In particular, the proposed method is suitable for GSES problems having a large number of criteria but limited alternatives.

10.5 Chapter Summary In this chapter, we presented a practical integrated GSES framework based on the cloud model and QUALIFLEX method to assess and select the most appropriate green supplier considering both economic and environmental criteria. The cloud model was used for representing the linguistic assessments of decision makers with respect to alternative companies, and an extension of the classical QUALIFLEX was applied to generate green supplier rankings. In addition, for the situations where the information of criteria weight is unknown or partly known previously, the proposed approach can derive criteria weights by using a TOPSIS-based optimization model. The proposed GSES method was validated with a real-life case company of the automobile manufacturing industry setup. The results showed that our proposed framework is more expressive in capturing uncertainty and vagueness of decision makers’ judgements and is very useful to yield the best supplier in green supplier management.

References Awasthi A, Kannan G (2016) Green supplier development program selection using NGT and VIKOR under fuzzy environment. Comput Ind Eng 91:100–108 Bai C, Sarkis J (2010a) Green supplier development: analytical evaluation using rough set theory. J Clean Prod 18(12):1200–1210 Bai C, Sarkis J (2010b) Integrating sustainability into supplier selection with grey system and rough set methodologies. Int J Prod Econ 124(1):252–264 Banaeian N, Mobli H, Fahimnia B, Nielsen IE, Omid M (2018) Green supplier selection using fuzzy group decision making methods: a case study from the agri-food industry. Comput Oper Res 89:337–347 Banerjee D, Dutta B, Guha D, Martínez L (2020) SMAA-QUALIFLEX methodology to handle multicriteria decision-making problems based on q-rung fuzzy set with hierarchical structure of criteria using bipolar Choquet integral. Int J Intell Syst 35(3):401–431 Carvalho LS, Stefanelli NO, Viana LC, Vasconcelos DSC, Oliveira BG (2020) Green supply chain management and innovation: a modern review. Manag Environ Qual: Int J 31(2):470–482 Govindan K, Rajendran S, Sarkis J, Murugesan P (2015) Multi criteria decision making approaches for green supplier evaluation and selection: a literature review. J Clean Prod 98:66–83 Hashemi SH, Karimi A, Tavana M (2015) An integrated green supplier selection approach with analytic network process and improved grey relational analysis. Int J Prod Econ 159:178–191 Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752 Hosseini F, Safari A, Farrokhifar M (2020) Cloud theory-based multi-objective feeder reconfiguration problem considering wind power uncertainty. Renew Energy 161:1130–1139

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Hwang CL, Yoon K (1981) Multiple attributes decision making methods and applications. Springer, Berlin Igarashi M, de Boer L, Fet AM (2013) What is required for greener supplier selection? A literature review and conceptual model development. J Purch Supply Manag 19:247–263 Li J, Wang JQ (2017) An extended QUALIFLEX method under probability hesitant fuzzy environment for selecting green suppliers. Int J Fuzzy Syst 19:1866–1879 Li DY, Liu CY, Gan WY (2009) A new cognitive model: cloud model. Int J Intell Syst 24(3):357–375 Li G, Li L, Choi TM, Sethi SP (2020a) Green supply chain management in Chinese firms: innovative measures and the moderating role of quick response technology. J Oper Manag 66(7–8):958–988 Li L, Xie Y, Chen X, Yue W, Zeng Z (2020b) Dynamic uncertain causality graph based on cloud model theory for knowledge representation and reasoning. Int J Mach Learn Cybern 11(8):1781– 1799 Li Y, Chen Y, Li Q (2020c) Assessment analysis of green development level based on S-type cloud model of Beijing-Tianjin-Hebei, China. Renew Sustain Energy Rev 133:110245 Liang Y, Qin J, Martínez L, Liu J (2020) A heterogeneous QUALIFLEX method with criteria interaction for multi-criteria group decision making. Inf Sci 512:1481–1502 Liu HC, You JX, Li P, Su Q (2016) Failure mode and effect analysis under uncertainty: an integrated multiple criteria decision making approach. IEEE Trans Reliab 65(3):1380–1392 Liu HC, Quan MY, Li Z, Wang ZL (2019a) A new integrated MCDM model for sustainable supplier selection under interval-valued intuitionistic uncertain linguistic environment. Inf Sci 486:254– 270 Liu HC, Quan MY, Shi H, Guo C (2019b) An integrated MCDM method for robot selection under interval-valued Pythagorean uncertain linguistic environment. Int J Intell Syst 34(2):188–214 Liu J, Hu H, Tong X, Zhu Q (2020a) Behavioral and technical perspectives of green supply chain management practices: empirical evidence from an emerging market. Transp Res Part E: Logist Transp Rev 140:102013 Liu L, Bin Z, Shi B, Cao W (2020b) Sustainable supplier selection based on regret theory and QUALIFLEX method. Int J Comput Intell Syst 13(1):1120–1133 Liu P, Gao H, Fujita H (2020c) The new extension of the MULTIMOORA method for sustainable supplier selection with intuitionistic linguistic rough numbers. Appl Soft Comput. https://doi. org/10.1016/j.asoc.2020.106893 Ma W, Lei W, Sun B (2020) Three-way group decisions under hesitant fuzzy linguistic environment for green supplier selection. Kybernetes 49(12):2919–2945 Mohammed EA, Naugler CT, Far BH (2016) Breast tumor classification using a new OWA operator. Expert Syst Appl 61:302–313 Paelinck JHP (1978) Qualiflex: a flexible multiple-criteria method. Econ Lett 1(3):193–197 Peng JJ, Wang JQ, Yang WE (2017) A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems. Int J Syst Sci 48(2):425–435 Rahman T, Ali SM, Moktadir MA, Kusi-Sarpong S (2020) Evaluating barriers to implementing green supply chain management: an example from an emerging economy. Prod Plan Control 31(8):673–698 Rostamzadeh R, Govindan K, Esmaeili A, Sabaghi M (2015) Application of fuzzy VIKOR for evaluation of green supply chain management practices. Ecol Ind 49:188–203 Sarkis J, Dhavale DG (2015) Supplier selection for sustainable operations: a triple-bottom-line approach using a Bayesian framework. Int J Prod Econ 166:177–191 Srivastava SK (2007) Green supply-chain management: a state-of-the-art literature review. Int J Manag Rev 9(1):53–80 Uygun Ö, Dede A (2016) Performance evaluation of green supply chain management using integrated fuzzy multi-criteria decision making techniques. Comput Ind Eng 102:502–511 Wang JQ, Peng L, Zhang HY, Chen XH (2014) Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf Sci 274:177–191 Wang JQ, Peng JJ, Zhang HY, Liu T, Chen XH (2015) An uncertain linguistic multi-criteria group decision-making method based on a cloud model. Group Decis Negot 24(1):171–192

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Chapter 11

GSES with Heterogeneous Information and MABAC Method

For a manufacturing company, selecting the most suitable green supplier plays an important role in enhancing its green production performance. In this chapter, we develop a new GSES model through the combination of heterogeneous criteria information and an extended multi-attributive border approximation area comparison (MABAC) method. Considering the complexity of decision context, heterogeneous information, including real numbers, interval numbers, trapezoidal fuzzy numbers, and linguistic hesitant fuzzy sets, is utilized to evaluate alternative suppliers with respect to the evaluation criteria. A maximizing consensus approach is constructed to determine the weight of each decision-maker based on incomplete weighting information. Then, the classical MABAC method is modified for ranking candidate green suppliers under the heterogeneous information environment. Finally, the developed GSES model is applied in a case study from the automobile industry to illustrate its practicability and efficiency.

11.1 Introduction Due to the aggravation of global warming and climate change, environmental problems have driven more and more concern from people, stakeholders, and governments. To maintain a competitive edge in the global market, most enterprises have begun to incorporate green development concepts into their daily production and operation management (Mirzaee et al. 2018; Chen 2019). In view of this, green supply chain management (GSCM) with environmental protection concept obtains increasing attention from both researchers and practitioners. The GSCM is a strategy which merges environmental consideration with supply chain practices and can efficiently assist companies in improving their commercial benefits and environmental performance (Liu et al. 2018; Quan et al. 2018; Mishra et al. 2019; Wang et al. 2019). As a significant part of GSCM, green supplier selection is a strategic decision that can enhance the business performance and competitive advantage of a manufacturing © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_11

249

250

11 GSES with Heterogeneous Information and MABAC Method

firm (Shi et al. 2018; Van et al. 2018; Wu et al. 2019). Through selecting appropriate green suppliers, firms can balance economic-based supplier capabilities, as well as social and environmental capabilities. In this context, a growing number of studies have investigated supplier selection problems incorporating sustainability criteria in recent decades (Rashidi et al. 2020; Schramm et al. 2020; Zhang et al. 2020a). In the green supplier evaluation process, different types of performance information (e.g., numerical values, internal values, fuzzy numbers, linguistic terms) may be involved because of the complexity of business context (Mao et al. 2019; Wang et al. 2019). Hence, to reflect the characteristic of each supplier evaluation criterion accurately, the performance evaluation values on different criteria need to be represented in different forms. Trapezoidal fuzzy numbers (TFNs) are a type of fuzzy sets commonly used to describe the vagueness and uncertainty of human preference values. Recently, the concept of linguistic hesitant fuzzy sets (LHFSs) was developed by Meng et al. (2014) to address the qualitative evaluations of decision-makers and reflect their hesitancy and inconsistency. The LHFSs consider the possible membership degrees of linguistic terms and can express linguistic decision information more accurately. Based on its advantages, the LHFS method has been utilized in different fields, such as surrounding rock stability analysis (Gao et al. 2020), risk assessment of seawater pumped hydro storage project (Wu et al. 2020), and university performance management (Zhang et al. 2020b). In this chapter, the green performance values on different criteria are described by heterogeneous information in the forms of LHFSs, TFNs, interval numbers, and real numbers. The TFNs, interval numbers, and real numbers are used to represent quantitative criteria, and the LHFSs are adopted to describe qualitative criteria. Generally, green supplier selection can be regarded as a multi-criteria decisionmaking (MCDM) problem, where a limited number of alternative suppliers are evaluated against multiple conflicting criteria. As a consequence, a number of MCDM methods have been employed for handling green supplier selection problems (Kumari and Mishra 2020; Peng et al. 2020; Pourjavad and Shahin 2020; Rouyendegh et al. 2020). As a new MCDM technique, the multi-attributive border approximation area ´ comparison (MABAC) method was introduced by Pamuˇcar and Cirovi´ c (2015) based on the distance of criteria functions from each of the alternative border approximation areas. The idea of the MABAC method is to make the ranking result as accurate as possible through calculating the potential gains and losses values (Liang et al. 2019). In addition, the methodology has a relatively simple computation procedure and can acquire a robust solution via in-depth comparison and sensibility analyses (Xue et al. 2016; Pamuˇcar et al. 2018; Liang et al. 2019). Because of its features, the MABAC method has been utilized for many practical decision-making problems, which includes circular economy development program selection (Shen et al. 2020), resilient supplier selection (Pamucar et al. 2020), non-traditional machining processes selection assessment (Chakraborty et al. 2020), occupational health and safety risk assessment (Liu et al. 2020b), undergraduate teaching audit and evaluation (Gong et al. 2020), and public evaluation of shared bicycle (Liu et al. 2020a). Consequently, it is reasonable to adopt the MABAC method to derive the ranking of green suppliers including multiple criteria and limited alternatives.

11.1 Introduction

251

According to the above discussions, we aim to develop an extended MABAC model to determine the best green supplier with heterogeneous criteria information. In this model, LHFSs, TFNs, interval numbers, and real numbers are jointly employed to express the performance evaluations of alternative green suppliers with respect to different criteria. A maximizing consensus technique is constructed to compute the weights of decision-makers in terms of incomplete weighting information. Further, an extended MABAC method is developed for determining the priority of alternative green suppliers within the heterogeneous information environment. The remainder of this chapter is organized as follows: Sect. 11.2 introduces the basic concepts of LHFSs, TFNs, and interval numbers. Section 11.3 presents the details of the developed GSES model. In Sect. 11.4, a case study in the automobile industry is utilized to illustrate the developed model, which is followed by a discussion of managerial implications in Sect. 11.5. Finally, concluding remarks are outlined in Sect. 11.6.

11.2 Preliminaries The concept of LHFSs was first proposed by Meng et al. (2014) to describe the complexity of uncertain environment and the vagueness of human cognition. Definition 11.1 (Meng et al. 2014) Let S = { si |i = 1, 2, . . . , 2t + 1} be a linguistic term set. AN LHFS LH on S is a set whose element is a combination of h i and lh i . AN LHFS LH is denoted as. L H = { h i , lh i |h i ∈ S, i = 1, 2, . . . , l L H },

(11.1)

where h i  represents the  linguistic terms, lh i =  r1 , r2 , . . . , r|lh i | r1 ≤ r2 ≤ · · · ≤ r|lh i | is a set of the possible membership degrees of the element h i ∈ S to the LHFS LH, |lh i | is the amount of real numbers in lh i , and l L H is the count of linguistic terms in LH with lh = 0. The possible membership degrees of lh i are lie in the interval [0, 1]. Definition 11.2 (Meng et al. 2014) Suppose that |h } { h and L H L H = , lh ∈ S, i = 1, 2, . . . , l = 1 i i i A 2    = l . Let l h q , lh q h q ∈ S, i = 1, 2, . . . , l B are two LHFSs, where A B   q r ij ∈ lh i ( j = 1, 2, . . . , |lh i |) and rk ∈ lh q k = 1, 2, . . . , lh q  be the jth and the kth linguistic term set possible membership degrees in lh i and lh q for the i is a subscript function. Then the LHFSs L H1 and L H2 , respectively; f (si ) = 2t+1 operational laws of LHFSs are defined as follows: (1)

L H1 ⊕ L H2 = ∪(h i ,lh i )∈L H1 ,(h q ,lh q )∈L H2

   q S f (h i )+ f (h q ) , ∪r ij ∈lh i ,rkq ∈lh q 1 − 1 − r ij 1 − rk ;

252

(2) (3) (4)

11 GSES with Heterogeneous Information and MABAC Method



 q L H1 ⊗ L H2 = ∪(h i ,lh i )∈L H1 ,(h q ,lh q )∈L H2 S f (h i ) f (h q ) , ∪r ij ∈lh i ,rkq ∈lh q r ij rk ;

 λ 

λL H1 = ∪(h i ,lh i )∈L H1 Sλ f (h i ) ∪r ij ∈lh i 1 − 1 − r ij , λ ∈ [0, 1];

 L H1λ = ∪(h i ,lh i )∈L H1 S f (h i )λ ∪r ij ∈lh i r λj , λ ∈ [0, 1].

Definition 11.3 (Meng et al. 2014) Suppose that LH = { h i , lh i |h i ∈ S, i = 1, 2, . . . , l L H } is an LHFS, its expected function and variance function can be described as follows: E(L H ) =

 lL H  f (h i ) 1  , l L H i=1 |lh i |

(11.2)

⎤2 ⎡ lL H  1  f (h ) i ⎣ V (L H ) = ri − E(L H )⎦ . l L H i=1 |lh i | r ∈lh i

(11.3)

i

Definition 11.4 (Meng et al. 2014) Suppose that L H1 and L H2 are two LHFSs, the comparison method can be defined below: (1) (2) (3)

If E(L H1 ) > E(L H2 ), then L H1 is superior to L H2 , denoted by L H1 > L H2 ; If E(L H1 ) < E(L H2 ), then L H1 is inferior to L H2 , denoted by L H1 < L H2 ; If E(L H1 ) = E(L H2 ), then (a) (b)

if V (L H1 ) < V (L H2 ), L H1 is superior to L H2 , denoted by L H1 > L H2 ; if V (L H1 ) = V (L H2 ), L H1 is equal to L H2 , denoted by L H1 = L H2 .

Definition 11.5 (Dong et al. 2017) Suppose that |h } { h and L H L H = , lh ∈ S, i = 1, 2, . . . , l = i i i  A 2   1 i is a subscript h q , lh q h q ∈ S, i = 1, 2, . . . , l B are two LHFSs, f (si ) = 2t+1 function. The distance between L H1 and L H2 is computed by ⎧ ⎡ ⎪ ⎨1 1 ⎢ d(L H1 , L H2 ) = ⎣ ⎪ ⎩ 2 lA

    min  h q ,lh q )∈L H2  (  (h i ,lh i )∈L H1 

f (h i ) |lh i |



|lh i | j=1

|lh i | j=1

jr ij



j

  f (h q ) |lh q | q   k=1 krk 1  |lh q | + min  −  |lh q | (h i ,lh i )∈L H1  lB  (h q ,lh q )∈L H2 k=1 k 

−

f (h i ) |lh q |

f (h i ) |lh i |

 2 q   kr k  k=1  |lh q |   k=1 k

 lh | q|



 2 ⎤⎫ 21 ⎬ jr ij  ⎪  ⎥  ⎦ ,  ⎪ j  ⎭

|lh i | j=1

|lh i | j=1

(11.4)    q where λ > 0, rk ∈ lh q k = 1, 2, . . . , lh q  represent the kth possible membership degree of the qth linguistic term in LHFS, and k is a position weight associated with q rk .

11.2 Preliminaries

253

Definition 11.6 (Meng et al. 2014) Suppose that L Hi (i = 1, 2, . . . n) is a set of LHFS, the linguistic hesitant fuzzy weighted averaging (LHFWA) operator is defined as: LHFWA(L H1 , L H2 , . . . , L Hn ) =

∪ (sθ (1) ,lh (sθ (1) ))∈L H1 ,...,(sθ (n) ,lh (sθ (n) ))∈L Hn " $$ " n #   w i n 1 − r(i) si=1 , (11.5) 1− ∪ wi θ(i) , r(1) ∈lh (sθ (1) ),...,r(n) ∈lh (sθ (n) ) i=1

n wi = 1. where wi is the weight of the LHFS L Hi which satisfies wi > 0 and i=1 TFN is the most generic class of fuzzy numbers with liner membership function. It is conceptually and computationally sample. % is a fuzzy set defined on Definition 11.7 (Dubois and Prade 1978) Suppose that A the universal set of real numbers R. It is regarded as a fuzzy number if its membership function satisfies the following characteristics: (1) (2) (3) (4)

μ A% : R → [0, 1] is continuous; μ A%(x) = 0 for all x ∈ (−∞, a] ∪ [b, +∞); μ A%(x) strictly increasing on [a, b] and strictly decreasing on [b, c]; μ A%(x) = 1 for all x ∈ [b, c], where a < b < c < d.

% = (a, b, c, d) can be Definition 11.8 (Dubois and Prade 1978) A fuzzy number A seen as a TFN if its membership function μ A% : R → [0, 1] is defined as. ⎧ (x − a)/(b − a), a ≤ x ≤ b ⎪ ⎪ ⎨ 1, b≤x ≤c μ A% = ⎪ (d − x)/d − c, c ≤ x ≤ d ⎪ ⎩ 0, others.

(11.6)

% = (a1 , b1 , c1 , d1 ) and Definition 11.9 (Dubois and Prade 1978) Suppose that A % B = (a2 , b2 , c2 , d2 ) are two TFNs. Then, the operational laws of TFNs can be defined as follows: (1) (2) (3) (4)

%+ % A B = (a1 + b1 , a2 + b2 , a3 + b3 , a4 + b4 ); %⊗ % A B = (a1 × b1 , a2 × b2 , a3 × b3 , a4 × b4 ); % = (λa1 , λa2 , λa3 , λa4 ); λA   %λ = a1λ , a2λ , a3λ , a4λ . A

% = (a1 , b1 , c1 , d1 ) and Definition 11.10 (Dubois and Prade 1978) Suppose that A % % B is given as follows: B = (a2 , b2 , c2 , d2 ) are two TFNs. The distance between A and % & ' 4  ' 1 % % d A, B =( (ai − bi )2 . 4 i=1 

(11.7)

254

11 GSES with Heterogeneous Information and MABAC Method

*   ) Definition 11.11 (Yue 2011) Let a = a L , a U = x|0 < a L ≤ x ≤ a U , then a is defined as an interval number. The values a L and a U represent for the lower bound and upper bound of a, respectively. * ) * ) Definition 11.12 (Yue 2011) Suppose that a = a L , a U and b = b L , bU are two interval numbers. The operational laws of two interval numbers can be defined as below: (1) (2) (3) (4)

a + b = [a L + b L , a U + bU ]; a ⊗ b = [a L × b L , a U × bU ]; U λa = )[λa L , λa * ]; λ λ λ a = a L , aU . Besides, the distance between a and b is defined as: + , 2  2 1  L d(a, b) = a − a U + b L − bU . 2

(11.8)

11.3 The Proposed GSES Model This section develops an extended MABAC model to evaluate green suppliers and select the optimal one under the heterogeneous information environment. In this model, LHFSs, TFNs, interval numbers, and real numbers are utilized to represent the green performance of alternative suppliers regarding different criteria. A maximizing consensus technique is adopted to determine the weights of decision-makers based on incomplete weighting information. Then, an extended MABAC method is applied to rank candidate green suppliers with heterogeneous evaluation data. The flowchart of the proposed GSES model is displayed in Fig. 11.1. For a GSES problem, assume that there are m alternatives Ai (i = 1, 2, . . . , m), n criteria C j ( j = 1, 2, . . . , n) and l decision-makers DMk (k = 1, 2 . . . , l). The heterogeneous performance evaluation matrix , - of alternative suppliers given by decision.

k

maker DMk is denoted as P = pˆ ikj

m×n

, where pˆ ikj is the evaluation of supplier

Ai for criterion C j provided by decision-maker DMk . The evaluation value pˆ ikj is considered by four different forms of information in this study, i.e., real numbers (N 1 ), interval numbers (N 2 ), TFNs (N 3 ), and LHFSs (N 4 ). In general, the criterion C j is evaluated by using one of the four distinct information,forms. If-j ∈ N1 , then is expressed pˆ ikj = xikj is expressed as a real number; if j ∈ N2 , then pˆ ikj = aikjL , aikU j , as an interval number; if j ∈ N3 , then pˆ ikj = aikj , bikj , cikj , dikj is expressed as TFNs; 

 i jk i jk  i jk if j ∈ N4 , then pˆ ikj = h a , lh a h a ∈ S is expressed as LHFSs. The weight  of criterion C j is given as w j , which satisfies w j > 0 and nj=1 w j = 1. Then, the proposed GSES model is explained below.

11.3 The Proposed GSES Model

255

Fig. 11.1 Flowchart of the proposed GSES model

Step 1 Obtain the normalized heterogeneous evaluation matrixes. Generally, benefit and cost criteria are included in a green supplier selection .

k

process. Therefore, the heterogeneous evaluation matrixes P (k = 1, 2, ..., l) need k normalized to establish the normalized heterogeneous evaluation matrixes P = * )to be pikj m×n (k = 1, 2, . . . , l), in which: ⎧ jk ⎪ xikj /xmax ⎪ ⎪ ⎪ jk ⎪ ⎪ 1 − xikj /xmax ⎪ ⎪ , ⎪ ⎪ jkU jkU k L ⎪ a /amax , a kU /amax ⎪ i j i j ⎪ ⎪ , ⎪ ⎪ jkU jkU kL kU ⎪ ⎪ ⎨ 1 − ai j /amax , 1 − ai j /amax  jk jk jk jk %ikj = k k k k P ⎪ ai j /dmax , bi j /dmax , ci j /dmax , di j /dmax ⎪  ⎪ ⎪ jk jk jk jk ⎪ ⎪ 1 − dikj /dmax , 1 − cikj /dmax , 1 − bikj /dmax , 1 − aikj /dmax ⎪  ⎪

 ⎪ ⎪ i jk i jk  i jk ⎪ h a , lh a h a ∈ S ⎪ ⎪ ⎪ 

 ⎪

 ⎪ ⎪ k  i jk ∈ S

 ⎪ h i jk 1 − ri j h a ⎩ ∪ h i jk ,lh i jk ∈ pk i jk , ∪ k r ∈lh (2t+1)− f h a

a

ij

a

ij

a

i f j ∈ N1B i f j ∈ N1C i f j ∈ N2B i f j ∈ N2C i f j ∈ N3B (11.9) i f j ∈ N3C i f j ∈ N4B i f j ∈ N4C

256

11 GSES with Heterogeneous Information and MABAC Method

where NqB (q = 1, 2, 3, 4) is a set of benefit criteria and NqC (q = 1, 2, 3, 4) is jk jkU a set of cost criteria. Besides, xmax = maxi xikj ( j ∈ N1 , k ∈ l), amax = jk maxi aikU ( j ∈ N2 , k ∈ l), and dmax = maxi dikj ( j ∈ N3 , k ∈ l). j Step 2 Calculate the weights of decision-makers using maximizing consensus approach. The maximizing consensus approach (Xu and Wu 2013) can be used to calculate the weights of decision-makers based on incomplete weighting information. The basic idea of this method is to maximize the consensus level among the individual evaluation matrixes (Zhang and Xu 2015). If the consensus of a decision-maker’s evaluation matrix is considerably greater than the consensus of other decisionmakers’ evaluation matrixes, then the decision-maker should be assigned a bigger weight. According to the maximizing consensus method, we can construct the following programming model for calculating the weights of decision-makers λk (k = 1, 2, . . . , l): ⎛

⎞  l m  n      1 1 ⎝ 1 − d pikj , piuj ⎠ λk max F(λk ) = n × m × − 1) 2 (l k=1 u=1,u=k i=1 j=1 ⎧ l ⎨ λ = 1, s.t. k=1 k (11.10) ⎩ λk ∈ W, λk ≥ 0, l 

where pikj and piuj are the elements of the normalized heterogeneous evaluation k

u

matrixes P and P , respectively, and W is the partial weight information given by decision-makers. Then, the solution set of the programming goal model is relative weights of the l decision-makers. Step 3 Rank alternative green suppliers by the MABAC method. In this step, the MABAC method is extended and utilized to derive the ranking of the evaluation alternatives with heterogeneous information. The procedural steps of the MABAC approach are depicted as follows. % Step 3.1 Construct the collective heterogeneous evaluation matrix P. Based on the weighted averaging operators of LHFSs, TFNs, interval numbers, and real numbers, we can aggregate the normalized heterogeneous evaluation k matrixes P (k ) =* 1, 2, . . . , l) to construct an collective heterogeneous evaluation % = p˜ i j . For example, the collective evaluation values of LHFSs can matrix P m×n be computed by

11.3 The Proposed GSES Model

257 l

p˜ i j = ⊕ λk pikj .

(11.11)

k=1

.

Step 3.2 Establish the weighted collective evaluation matrix P . Based on ,the -weights of evaluation criteria, an weighted collective evaluation % = p˜ i j is established by matrix P m×n

p˜ i j = w j p˜ i j

(11.12)

% Step 3.3 Derive the border approximation area vector G. The border approximation area for the jth criterion can be determined through the following formula: g˜ j =

m # 

p˜ i j

1/m

, j = 1, 2, . . . , n.

(11.13)

i=1

Based on the values g˜ j ( j = 1, 2, . . . , n) of all the evaluation criteria, * the border ) % = g˜ 1 , g˜ 2 , . . . , g˜ n approximation area vector can be established as G Step 3.4 Establish the distance matrix D. By calculating the distance between each of the m alternatives ) * and the border approximation area, we can obtain the distance matrix D = di j m×n . That is, ⎧

 ⎨ d p˜ , g˜ j i f p˜ i j ≥ g˜ j ,

i j  di j = ⎩ −d p˜ , g˜ j i f p˜ < g˜ j . ij ij

(11.14)

Based on the distances di j , the belonging of alternative Ai to the approximation area is obtained as follows: ⎧ + ⎨ G i f di j > 0, (11.15) Ai ∈ G i f di j = 0, ⎩ − G i f di j < 0. Then, the area containing the ideal green suppliers (A+ ) is defined as the upper approximation area (G + ), while the area containing the anti-ideal green suppliers (A− ) is defined as the lower approximation area (G − ) (see Fig. 11.2). Step 3.5 Determine the optimum green supplier. If the candidate green supplier Ai belongs to G + , then it is close or equal to the ideal green supplier. In contrast, if the candidate green supplier Ai belongs to G − , it

258

11 GSES with Heterogeneous Information and MABAC Method

Fig. 11.2 Upper (G+ ), lower (G− ) and border (G) approximation areas

is close or equal to the anti-ideal green supplier. Thus, the values of criteria functions for all green suppliers can be computed by adding the distances between candidate suppliers and the border approximation areas. Through computing the sum of row elements of the distance matrix D, the priority values of the alternative green suppliers can be obtained as: P Vi =

n 

di j , i = 1, 2, . . . , m.

(11.16)

j=1

The bigger the value of PV i , the better the green supplier Ai . Consequently, we can obtain the ranking of the considered m green suppliers based on the descending order of their priority values P Vi (i = 1, 2, . . . , m). The largest PV i corresponds to the best green supplier.

11.4 Case Study

259

11.4 Case Study 11.4.1 Implementation In this section, the developed GSES model is applied in an automobile manufacturing company located in Shanghai, China, to illustrate its applicability and efficacy. Under the green development concept, the company insisted on manufacturing green and environmentally friendly products. The transmission is one of the most important parts of a car, which affects its driving experience and fuel consumption. This company needs to select a suitable green supplier for purchasing transmissions to increase its economic and environmental performance. In this case, five potential suppliers (Ai , i = 1, 2, . . . , 5) were considered as alternatives for further assessment and selection. Three decision-makers invited to evaluate each green supplier with eight criteria (DM k , k = 1, 2, 3) were   C j , j = 1, 2, . . . , 8 , including product quality (C1 ), technological level (C2 ), flexibility (C3 ), delivery time (C4 ), and price (C5 ), financial situation (C6 ), innovation ability (C7 ), and environmental performance (C8 ). Among them, criterion C5 is a cost criterion and the other seven criteria are benefit criteria. The linguistic term set S is used for describing the evaluation information from decision-makers using LHFSs. 3 S=

4 s1 = V er y poor, s2 = Poor, s3 = Slightly poor, s4 = Fair, s5 = Slightly good, . s6 = Good, s7 = V er y good

The weight vector of the eight evaluation criteria is given as w = (0.1, 0.2, 0.1, 0.1, 0.15, 0.15, 0.1, 0.1). To accurately and flexibly evaluate the alternative suppliers, four forms of information, including LHFSs, TFNs, interval numbers, and real numbers, are adopted to assess the candidate suppliers according to the characteristics of the eight evaluation criteria. Specifically, the evaluations of green suppliers on the three qualitative criteria C1 , C3 , and C8 are represented by LHFSs due to the uncertainty of the production process. For the criteria C2 and C7 , the decision-makers tend to provide the lower and upper limits and the most possible values; thus, their assessments are represented by TFNs. Because C4 and C6 are quantitative criteria, we use interval numbers to express them. The assessments for the criterion C5 can be represented by real numbers. The heterogeneous evaluation information of candidate green suppliers from the three decision-makers is shown in Table 11.1. In what follows, the sustainability ranking of the five green suppliers is determined with the aid of our proposed GSES approach. Step 1 According to the heterogeneous evaluation information of Table 11.1, the ) * k normalized heterogeneous evaluation matrices P = pikj 5×8 (k = 1, 2, 3) are constructed using Eq. (11.9) and presented in Table 11.2. Step 2 In this case study, the weight information about decision-makers is assumed to be incompletely known, and the known weight information is given as: λ =

DM3

DM2

{(S5 , 0.6)}

(6, 7, 8, 9) {(S4 , 0.3)} {(S3 , 0.6), (S4 , 0.3)} (50, 60, 75, 85) {(S4 , 0.3, 0.5)}

(2, 3, 4, 5) {(S4 , 0.5), (S5 , 0.4)} {(S4 , 0.4)} (50, 60, 75, 85) {(S4 , 0.2)}

(70, 90, 91, 92)

{(S4 , 0.7)}

[65, 88]

118

[0.81, 0.90]

(3, 4, 5, 6)

{(S4 , 0.6), (S5 , 0.4)}

{(S5 , 0.8)}

(80, 85, 90, 95)

{(S3 , 0.6)}

[75, 88]

118

[0.78, 0.86]

(5, 6, 7, 8)

{(S5 , 0.6)}

{(S5 , 0.3, 0.6)}

(72, 80, 90, 95)

{(S4 , 0.3)}

[75, 89]

C2

C3

C4

C5

C6

C7

C8

C1

C2

C3

C4

C5

C6

C7

C8

C1

C2

C3

C4

[82, 90]

[0.74, 0.82]

116

[87, 90]

[0.76, 0.83]

116

[87, 90]

{(S6 , 0.4, 0.6)} (30, 80, 85, 90)

{(S4 , 0.5), (S5 , 0.3)}

C1

DM1

A2

Green suppliers

A1

Criteria

Decision makers

Table 11.1 Heterogeneous evaluation of green suppliers given by decision makers

[78, 86]

{(S5 , 0.4)}

(74, 80, 82, 85)

{(S4 , 0.8)}

{(S4 , 0.3)}

(3, 4, 5, 6)

[0.72, 0.83]

120

[45, 58]

{(S2 , 0.4)}

(30, 80, 85, 90)

{(S4 , 0.7)}

{(S3 , 0.4, 0.6)}

(5, 6, 7, 8)

[0.74, 0.85]

120

[45, 58]

{(S4 , 0.3, 0.7)}

(50, 60, 75, 85)

{(S5 , 0.6)}

A3

[66, 78]

{(S4 , 0.8)}

(65, 70, 78, 81)

{(S5 , 0.5), (S6 , 0.2)}

{(S3 , 0.3)}

(2, 3, 4, 5)

[0.76, 0.81]

115

[66, 87]

{(S5 , 0.6, 0.8)}

(75, 80, 85, 95)

{(S2 , 0.4, 0.6)}

{(S4 , 0.3)}

(1, 2, 3, 4)

[0.74, 0.82]

115

[70, 90]

{(S5 , 0.4)}

(75, 80, 85, 95)

{(S2 , 0.6), (S3 , 0.5)}

A4

[65, 90]

{(S3 , 0.7)} (continued)

(82, 84, 89, 92)

{(S3 , 0.4)}

{(S6 , 0.7)}

(6, 7, 8, 9)

[0.78, 0.85]

110

[89, 95]

{(S6 , 0.8)}

(70, 90, 91, 92)

{(S6 , 0.8)}

{(S5 , 0.6), (S6 , 0.4)}

(5, 6, 7, 8)

[0.79, 0.85]

110

[92, 95]

{(S3 , 0.2, 0.5)}

(80, 85, 90, 95)

{(S3 , 0.7)}

A5

260 11 GSES with Heterogeneous Information and MABAC Method

Decision makers

(3, 5, 6, 7) {(S4 , 0.3, 0.6)}

(5, 6, 7, 8)

{(S6 , 0.4)}

C7

C8

116

[0.79, 0.88]

[0.76, 0.85]

118

A2

C6

A1

Green suppliers

C5

Criteria

Table 11.1 (continued)

{(S3 , 0.4)}

(4, 5, 6, 7)

[0.73, 0.84]

120

A3

{(S3 , 0.5)}

(4, 5, 6, 7)

[0.75, 0.82]

115

A4

{(S5 , 0.6)}

(6, 7, 8, 9)

[0.80, 0.86]

110

A5

11.4 Case Study 261

DM3

DM2

{(S5 , 0.6)}

(0.67, 0.78, 0.89, 1.00) {(S4 , 0.3)} {(S3 , 0.6), (S4 , 0.3)} (0.53, 0.63, 0.79, 0.90) {(S4 , 0.3, 0.5)}

(0.22, 0.33, 0.44, 0.56) {(S4 , 0.5), (S5 , 0.4)} {(S4 , 0.4)} (0.53, 0.63, 0.79, 0.89) {(S4 , 0.2)}

(0.74, 0.95, 0.96, 0.97)

{(S4 , 0.7)}

[0.68, 0.93]

0.02

[0.90, 1.00]

(0.33, 0.44, 0.56, 0.67)

{(S4 , 0.6), (S5 , 0.4)}

{(S5 , 0.8)}

(0.84, 0.90, 0.95, 1.00)

{(S3 , 0.6)}

[0.79, 0.93]

0.02

[0.91, 1.00]

(0.56, 0.67, 0.78, 0.89)

{(S5 , 0.6)}

{(S5 , 0.3, 0.6)}

(0.76, 0.84, 0.95, 1.00)

{(S4 , 0.3)}

[0.83, 0.99]

C2

C3

C4

C5

C6

C7

C8

C1

C2

C3

C4

C5

C6

C7

C8

C1

C2

C3

C4

[0.91, 1.00]

[0.86, 0.95]

0.03

[0.92, 0.95]

[0.84, 0.92]

0.03

[0.92, 0.95]

{(S6 , 0.4, 0.6)} (0.32, 0.84, 0.90, 0.95)

{(S4 , 0.5), (S5 , 0.3)}

C1

DM1

A2

Green suppliers

A1

Criteria

Decision makers

Table 11.2 Normalized heterogeneous evaluation of green suppliers

[0.87, 0.96]

{(S5 , 0.4)}

(0.78, 0.84, 0.86, 0.89)

{(S4 , 0.8)}

{(S4 , 0.3)}

(0.33, 0.44, 0.56, 0.67)

[0.84, 0.97]

0.00

[0.47, 0.61]

{(S2 , 0.4)}

(0.32, 0.84, 0.90, 0.95)

{(S4 , 0.7)}

{(S3 , 0.4, 0.6)}

(0.56, 0.67, 0.78, 0.89)

[0.82, 0.94]

0.00

[0.47, 0.61]

{(S4 , 0.3, 0.7)}

(0.53, 0.63, 0.79, 0.90)

{(S5 , 0.6)}

A3

[0.73, 0.87]

{(S4 , 0.8)}

(0.68, 0.74, 0.82, 0.85)

{(S5 , 0.5)}

{(S3 , 0.3)}

(0.22, 0.33, 0.44, 0.56)

[0.88, 0.94]

0.04

[0.69, 0.92]

{(S5 , 0.6, 0.8)}

(0.79, 0.84, 0.90, 1.00)

{(S2 , 0.4, 0.6)}

{(S4 , 0.3)}

(0.11, 0.33, 0.33, 0.44)

[0.82, 0.91]

0.04

[0.74, 0.95]

{(S5 , 0.4)}

(0.79, 0.84, 0.90, 1.00)

{(S2 , 0.6), (S3 , 0.5)}

A4

[0.72, 1.00]

{(S3 , 0.7)} (continued)

(0.86, 0.88, 0.94, 0.97)

{(S3 , 0.4)}

{(S6 , 0.7)}

(0.67, 0.78, 0.89, 1.00)

[0.91, 0.99]

0.08

[0.94, 1.00]

{(S6 , 0.8)}

(0.84, 0.90, 0.95, 1.00)

{(S6 , 0.8)}

{(S5 , 0.6), (S6 , 0.4)}

(0.56, 0.67, 0.78, 0.89)

[0.88, 0.94]

0.08

[0.97, 1.00]

{(S3 , 0.2, 0.5)}

(0.84, 0.90, 0.95, 1.00)

{(S3 , 0.7)}

A5

262 11 GSES with Heterogeneous Information and MABAC Method

Decision makers

(0.33, 0.56, 0.67, 0.78) {(S4 , 0.3, 0.6)}

(0.56, 0.67, 0.78, 0.89)

{(S6 , 0.4)}

C7

C8

0.03

[0.90, 1.00]

[0.86, 0.97]

0.02

A2

C6

A1

Green suppliers

C5

Criteria

Table 11.2 (continued)

{(S3 , 0.4)}

(0.44, 0.56, 0.67, 0.78)

[0.83, 0.95]

0.00

A3

{(S3 , 0.5)}

(0.44, 0.56, 0.67, 0.78)

[0.85, 0.93]

0.04

A4

{(S5 , 0.6)}

(0.67, 0.78, 0.89, 1.00)

[0.91, 0.98]

0.08

A5

11.4 Case Study 263

264

11 GSES with Heterogeneous Information and MABAC Method

{0.25 ≤ λ1 ≤ 0.40, 0.20 ≤ λ2 ≤ 0.35, λ3 ≤ λ2 ≤ λ1 }. Based on Eq. (11.10), we can establish the following linear programming model: max F(λk ) = 0.95λ1 + 0.94λ2 + 0.94λ3 ⎧ ⎪ 0.25 ≤ λ1 ≤ 0.40 ⎪ ⎪ ⎪ ⎪ ⎨ 0.2 ≤ λ2 ≤ 0.35 s.t. λ2 ≤ λ1 ⎪ ⎪ ⎪ ⎪ λ3 ≤ λ2 ⎪ ⎩λ + λ + λ = 1 1 2 3 By solving the above model, the weight vector of the three decision-makers is obtained as λ = (0.4, 0.3, 0.3). Step 3 In this step, the alternative green suppliers are ranked by using the MABAC method. Step 3.1 According to corresponding weighted ) * averaging operators, the collective % = p˜ i j is established as shown in Table heterogeneous evaluation matrix P 5×8 11.3. % ,Step- 3.2 Using Eq. (11.12), the weighted collective evaluation matrix P = is constructed and presented in Table 11.4. p˜ i j 5×8

Step 3.3 By Eq. (11.13), the border approximation areas of the eight evaluation % as criteria are calculated to construct the border approximation area vector G follows: % = [{(S0.40 , 0.084, 0.088, 0.091, 0.094), (S0.42 , 0.078, 0.080, 0.086)}, G (0.130 0.163 0.1780.190), {(S0.406 , 0.068, 0.700, 0.073, 0.076, 0.078, 0.079, 0.081)}, [0.077 0.090],0.000, [0.130 0.144], (0.043 0.055 0.066 0.077), {(S0.410 , 0.058, 0.063, 0.066), (S0.429 , 0.054, 0.058, 0.061)}].

Step 3.4 The distances between the five green suppliers and the border approx% are computed through Eq. (11.14). Then, the distance matrix imation G * ) vector D = di j 5×8 is established and displayed in Table 11.5. Step 3.5 The priority value for each green supplier P Vi (1 = 1, 2, . . . 5) is obtained by using Eq. (11.16). The computation results are also displayed in Table 11.5. Based on the descending sequence of the priority values P Vi (1 = 1, 2, . . . 5), the ranking result of the five green suppliers is obtained as: A5 > A1 > A4 > A3 > A2 . Thus, the green supplier A5 is the most desirable green supplier for the given case study.

(0.43, 0.58, 0.69, 0.80)

{(S4.0 , 0.37, 0.49), (S4.3 , 0.33, 0.47)} {(S3.3 , 0.37, 0.44)} {(S3.4 , 0.39)}

[0.76, 0.95]

0.020

[0.90, 1.00]

(0.47, 0.58, 0.69, 0.80)

{(S4.9 , 0.53), (S5.3 , 0.47)}

C5

C6

C7

C8

[0.86, 0.94]

0.030

[0.91, 0.96]

{(S4.4 , 0.42, 0.47)}

{(S3.7 , 0.58)}

C4

(0.46, 0.57, 0.68, 0.79)

[0.83, 0.95]

0.000

[0.59, 0.71]

(0.24, 0.36, 0.47, 0.58)

[0.85, 0.93]

0.040

[0.72, 0.91]

{(S3.7 , 0.36, 0.55)} {(S4.7 , 0.59)}

(0.76, 0.81, 0.87, 0.96)

C3

(0.54, 0.76, 0.84, 0.91)

(0.44, 0.72, 0.83, 0.92)

A5

{(S5.3 , 0.63), (S5.7 , 0.59)}

(0.62, 0.73, 0.84, 0.96)

[0.90, 0.97]

0.080

[0.89, 1.00]

{(S3.9 , 0.61, 0.67)}

(0.82, 0.91, 0.95, 0.98)

{(S2.90 , 0.52, 0.57), (S3.3 , 0.47, 0.53)} {(S3.9 , 0.67)}

A4

(0.77, 0.90, 0.95, 0.99)

A3

C2

A2

{(S4.60 , 0.58, 0.64), (S5 , 0.52, 0.59)} {(S4.5 , 0.47, 0.55), (S4.8 , 0.37, 0.47)} {(S4.4 , 0.70)}

C1

A1

Criteria Green suppliers

Table 11.3 Collective heterogeneous evaluation matrix

11.4 Case Study 265

0.003

[0.135, 0.150]

(0.047, 0.058, 0.069, 0.080)

{(S0.49 , 0.073), (S0.53 , 0.061)} {(S0.40 , 0.045, 0.066), (S0.43 , 0.039, 0.061)} {(S0.33 , 0.045, 0.057)} {(S0.34 , 0.048)}

C5

C6

C7

C8

(0.043, 0.058, 0.069, 0.080)

[0.128, 0.142]

0.005 (0.046, 0.057, 0.068, 0.079)

[0.124, 0.143]

0.000

[0.059, 0.071]

(0.024, 0.036, 0.047, 0.058)

[0.127, 0.139]

0.006

[0.072, 0.091]

{(S0.37 , 0.044, 0.076)} {(S0.47 , 0.086)}

[0.076, 0.095]

C4

[0.091, 0.096]

{(S0.44 , 0.053, 0.062)}

{(S0.37 , 0.083)}

C3

(0.152, 0.162, 0.175, 0.191)

(0.088, 0.143, 0.166, 0.183)

(0.108, 0.152, 0.169, 0.182)

{(S0.29 , 0.070, 0.081),

{(S0.44 , 0.114)}

(S0.33 , 0.062, 0.073)}

A4

A3

(0.155, 0.180, 0.190, 0.197)

(S0.48 , 0.045, 0.061)}

{(S0.45 , 0.061, 0.076),

{(S0.46 , 0.083, 0.098),

(S0.5 , 0.071, 0.086)}

A2

A1

C2

C1

Criteria Green suppliers

Table 11.4 Weighted collective evaluation matrix

{(S0.53 , 0.095), (S0.57 , 0.084)}

(0.062, 0.073, 0.084, 0.096)

[0.134, 0.145]

0.012

[0.089, 0.100]

{(S0.39 , 0.089, 0.106)}

(0.163, 0.181, 0.189, 0.196)

{(S0.39 , 0.106)}

A5

266 11 GSES with Heterogeneous Information and MABAC Method

0.026

A5

0.020

0.011

− 0.001 0.013

0.033

− 0.017

A4

− 0.019

− 0.014

0.035

A3

− 0.024

0.004

A2

0.024

C3

0.017

C2

0.008

C1

A1

Green suppliers

0.011

− 0.003

− 0.018

0.011

0.012

0.006

0.000

0.005

C5 0.003

C4 − 0.003

Table 11.5 Distance matrix D and the ranking of green suppliers 0.006

0.003

− 0.004

− 0.004

− 0.002

C6

0.002

0.002

0.003

0.019

− 0.019

C7

0.018

0.029

− 0.004

− 0.002

− 0.002

C8

0.132

0.017

− 0.016

− 0.025

0.076

PV i

Ranking

1

3

4

5

2

11.4 Case Study 267

268

11 GSES with Heterogeneous Information and MABAC Method

Fig. 11.3 Ranking results of green suppliers by different methods

11.4.2 Comparisons and Discussion To illustrate the effectiveness and usefulness of the proposed GSES model, a comparison analysis with the fuzzy GRA (Banaeian et al. 2018), the intuitionistic fuzzy TOPSIS (Memari et al. 2019), the picture fuzzy VIKOR (Meksavang et al. 2019), and the linguistic Z-number AQM (Duan et al. 2019) methods is performed in this part. The sorting results of the five green suppliers obtained by the selected methods are shown in Fig. 11.3. As visualized in Fig. 11.3, the top two green suppliers derived by the proposed model, the fuzzy GRA, the picture fuzzy VIKOR and the linguistic Z-number AQM are identical. Besides, the ranking order of A2 obtained by the proposed model, the fuzzy GRA, the intuitionistic fuzzy TOPSIS, and the picture fuzzy VIKOR are exactly the same. Therefore, the effectiveness of our developed model for dealing with the GSES problem can be demonstrated. On the other hand, there are some differences in the rankings derived by the proposed model and the four compared methods. By comparing with the fuzzy GRA and the picture fuzzy VIKOR, we can find that A4 is ranked before A3 in the proposed model; the fuzzy GRA and the picture fuzzy VIKOR give an opposite ranking. According to the proposed model, A4 ranks third and A2 ranks fifth; but the linguistic Z-number AQM gives an inverse result. What is more, the results obtained by the proposed model and the intuitionistic fuzzy TOPSIS are quite different. For the proposed model, the optimal green supplier is A5 , while the best green supplier obtained by the intuitionistic fuzzy TOPSIS is A1 . The reasons for the inconsistent ranking orders can be summarized below: Firstly, in the four listed methods, the

11.4 Case Study

269

alternative suppliers are evaluated by only one type of information, whereas the evaluations of green suppliers in our proposed model are described by different forms of information based on the characteristics of evaluation criteria. In addition, the proposed model adopted the LHFSs to express decision-makers’ hesitancy, inconsistency, and uncertainty in the supplier evaluation process. Secondly, the weights of decision-makers are not considered or given subjectively in the four compared methods. This may cause the loss of information in the aggregation process of decision-makers’ judgments. Thirdly, the priority determination mechanisms of the five methods are different. In the compared methods, the GRA, the TOPSIS, the VIKOR, and the AQM methods are used for evaluating and selecting the best green supplier, respectively. In contrast, the MABAC method is modified to derive the ranking of alternatives in the proposed model, which determines the ranking result of green suppliers through calculating the potential gains and losses values.

11.5 Managerial Implications The empirical results of the case example by the proposed GSES model are summarized in Table 11.5. These results give the priority values of the five considered suppliers, along with their respective rankings. Supplier A5 was ranked as the top supplier with a priority value of 0.132. Even though A5 is selected as the optimal supplier amongst the candidate group, and is recommended for contracting by the automobile manufacturer, there are some evaluation criteria that had low ratings for the supplier. The results for the suppliers’ evaluation can be used by the company to improve the performance of their suppliers. The automobile manufacturer may require specific post-selection negotiations with the selected supplier for possible improvements in these lower-rated performance criteria using the other suppliers as benchmarks. From the theoretical point of view, the GSES model being developed in this chapter contributes the following advantages. • The evaluation values on different criteria with different features are handled by heterogeneous information. This is more suitable to complex GSES features and also allows decision-makers to express their judgments flexibly in the types of information they prefer. • A maximizing consensus approach based on an optimization model is proposed to determine the weight of each decision-maker. It can deal with the situations in which information about expert weights is incompletely known a priori. • An extended MABAC method is employed to rank and select the most preferred green supplier. As depicted in the comparison analysis, the proposed GSES approach does not require considerable computations but still yields a reasonable and credible solution result.

270

11 GSES with Heterogeneous Information and MABAC Method

11.6 Chapter Summary This chapter proposed a new approach based on the MABAC method to select suppliers within heterogeneous information environment. In this model, the evaluation values of candidate suppliers with respect to different criteria were represented in four types of information, i.e., TFNs, interval numbers, and real numbers. Then, the classical MABAC method was extended and integrated with the maximizing consensus approach to rank candidate suppliers. To demonstrate the efficiency of our proposed GSES model, an empirical example from the automobile industry was provided together with a comparison analysis with the extent methods. The results show that the underlying principle behind the proposed model is acceptable to managers and decision-makers, which is more suitable to reflect decision features and more in line with experts’ preferences in the real GSES process.

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Chapter 12

GSSOA Using Double Hierarchy Hesitant Linguistic Sets and Decision Field Theory

With the increasing pressure from global competition, manufacturers have realized that green production is significant in supply chain management. Green supplier selection and order allocation (GSSOA) play a distinct and critical role for organizations to achieve green development and build competitive advantage. In this chapter, we develop a GSSOA model for selecting the most suitable green suppliers and determining the optimal order sizes among them. First, double hierarchy hesitant linguistic term sets (DHHLTSs) are adopted to deal with uncertainty in evaluating the green performance of alternative suppliers. Then, an extended decision field theory is proposed to choose efficient green suppliers dynamically. Considering quantity discount, a multi-objective linear programming model is established to allocate reasonable order quantities among the selected suppliers. The applicability and effectiveness of the developed model are illustrated through its application in the electronic industry and a comparative analysis with other methods.

12.1 Introduction With the increasing awareness of environmental protection, more and more enterprises have integrated green thinking into their daily production and operation management (Liu et al. 2019a; Stevi´c et al. 2020). In such context, the green supply chain management (GSCM) concept emerged, which aims to improve the economic, environmental, and social performance while reducing environmental pollution and eliminating the waste of resources in procurement, manufacturing, distribution, and sales (Quan et al. 2018; Meksavang et al. 2019). Many enterprises have recognized the necessity of adopting green development measures and started to change their practices to achieve green development (Lo et al. 2018; Liu et al. 2019b; Wang et al. 2019). Selecting qualified green suppliers and determining optimal order quantities play a pivotal role in improving the performance of a green supply chain, as companies are held responsible not only for their own actions, but for the adverse © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 H.-C. Liu and X.-Y. You, Green Supplier Evaluation and Selection: Models, Methods and Applications, https://doi.org/10.1007/978-981-16-0382-2_12

273

274

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

environmental impacts of their partners (Wang et al. 2017; Shi et al. 2018). Recently, many researchers have tried to integrate green supplier selection with order allocation to help enterprises enhance their green performance (Alegoz and Yapicioglu 2019; Duan et al. 2019b; Esmaeili-Najafabadi et al. 2019; Bektur 2020; Jia et al. 2020; You et al. 2020). For a GSES problem, the green performance of alternative suppliers is often evaluated based on multiple criteria. To handle ambiguity information in the green supplier selection, many uncertainty theories have been utilized in the literature, such as fuzzy sets (Jain et al. 2020), hesitant fuzzy sets (Liu et al. 2019b), intuitionistic fuzzy sets (Kumari and Mishra 2020), cloud mode (Li et al. 2019), and interval type-2 fuzzy sets (Mousavi et al. 2020b). However, these methods are insufficient to describe complex evaluation information in detail. Besides, decision makers’ evaluation information may be lost in the information transform process. To address these issues, Gou et al. (2017) proposed the double hierarchy hesitant linguistic term sets (DHHLTSs), which are composed of two hierarchy linguistic term sets. In a DHHLTS, the first hierarchy is a classical feature linguistic labels and the second hierarchy is the characteristic or detailed supplementary for the first hierarchy. Using the DHHLTSs, the complicated evaluation information from decision makers can be described more detail. In addition, decision makers can utilize DHHLTSs to express their opinions comprehensively. Given these advantages, many researchers have adopted the DHHLTSs to handle complex uncertain linguistic information in various decision-making problems (Duan et al. 2019a; Krishankumar et al. 2020a, b; Wang et al. 2020; Liu et al. 2021). Generally, green supplier selection is regarded as a multi-criteria decision making (MCDM) problem. Therefore, a number of MCDM methods have been suggested to solve the GSES problems (Mohammed 2020; Mousavi et al. 2020a; Peng et al. 2020; Zeng et al. 2020; Zhang et al. 2020). The decision field theory (DFT) proposed by Busemeyer and Townsend (1993) is a dynamic MCDM approach that can better simulate decision making process under uncertain environment. Besides, the DFT method can formulate the change of decision makers’ preference intensity over time (Lee et al. 2008). Recently, the DFT has been utilized for decision making in different fields. For example, Lee and Son (2020) proposed an extended DFT with social learning for modeling and analyzing human behaviors in social networks. Song et al. (2019) proposed a hesitant fuzzy DFT for the route selection of the arctic northwest passage. Hao et al. (2017) developed an intuitionistic fuzzy decisionmaking framework based on DFT and applied it to address investment decision making problems. In addition, Abad et al. (2014) estimated expected human attention weights based on the DFT and Qin et al. (2013) analyzed park-and-ride decision behavior by using the DFT. According to the above discussions, this chapter first proposes a new green supplier selection model by combining DHHLTSs and DFT to select qualified green suppliers. Further, a multi-objective linear programming (MOLP) model is constructed for obtaining suitable order quantities for the selected green suppliers. More specifically, the DHHLTSs are applied for evaluating the green performance of suppliers with respect to each evaluation criterion. An extended weighting method

12.1 Introduction

275

is developed to compute the weights of evaluation criteria according to comparative importance evaluations of decision makers. Then, the DFT is used to choose the best portfolio of green suppliers among alternatives. Finally, a MOLP model based on quantity discount is constructed to obtain suitable order sizes for the appropriate green suppliers. The remainder of this chapter is structured as follows. Section 12.2 presents the basic concepts of DHHLTSs. The developed GSSOA model is described in Sect. 12.3. In Sect. 12.4, an illustrative case application in the electronic industry is utilized to demonstrate the proposed model. Section 12.5 provides conclusions of this chapter.

12.2 Preliminaries The DHHLTSs were proposed by Gou et al. (2017) based on double hierarchy linguistic term sets (DHLTSs) to represent decision makers’ evaluation information more precisely and completely. Definition 12.1 (Gou et al. 2017) Suppose that S = { st |t = −τ, . . . , −1, 0, 1, . . . , τ } and O = { ok |k = −ς, . . . , −1, 0, 1, . . . , ς } are two independent linguistic term sets, where S is the first hierarchy and O is the second hierarchy. A DHLTS SO is defined as follows:    SO = st t ∈ [−τ, τ ]; k ∈ [−ς, ς ] ,

(12.1)

where ok represents the second hierarchy linguistic term when the first hierarchy linguistic term is st , and st is called the double hierarchy linguistic term (DHLT). Definition 12.2 (Gou et al. 2017) Suppose that SO =   st t = −τ, . . . , −1, 0, 1, . . . , τ ; k = −ς, . . . , −1, 0, 1, . . . , ς is a DHLTS. Then, HSO is a DHHLTS on X and it can be defined as:    HSO = < xi , hSO (xi ) >xi ∈ X ,

(12.2)

where hSO (xi ) is a collection of some values in SO , and expressed as:   hSO (xi ) = sφl (xi )sφl ∈ SO ; l = 1, 2, . . . , L; φl = −τ, . . . , −1, 0, 1, . . . , τ ; ϕl = −ς, . . . , −1, 0, 1, . . . ς }

(12.3)

Here, L is the number of linguistic terms in hSO and sφl in each hso (xi ) is the continuous terms in So ; hso (xi ) expresses the possible degree of the linguistic variable xi to So and it is named as double hierarchy hesitant linguistic element (DHHLE).  Definition 12.3 (Gou et al. 2017) Let SO = { st t = −τ, . . . , −1,0, 1, . . . , τ ;  k = −ς, . . . , −1, 0, 1, . . . , ς } be a DHLTS, hSO = { sφl sφl ∈

276

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

SO ; l = 1, 2, . . . , L; φl = [−τ, τ ]; ϕl = [−ς, ς ]} be a DHHLE, and hγ = { γl |γl ∈ [0, 1]; l = 1, . . . , L} be a hesitant fuzzy element. The subscript φl < ϕl > of the DHLT sφl and the membership degree γl expresses equivalent information. They can be transformed into each other by the following functions: f : [−τ, τ ] × [−ς, ς ] → [0, 1]  ϕl +(τ +φl )ς = γl if φl = −τ 2ςτ f (φl , ϕl ) = ϕl = γ if φl = −τ l, 2ςτ f −1 : [0, 1] → [−τ, τ ] × [−ς, ς ], ⎧ sτ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ s[2τ γ −τ ] f −1 (γl ) = s0 ⎪ ⎪ ⎪ s[2τ γ −τ ]+1 ⎪ ⎪ ⎩ sτ

(12.4)

if γ = 1 if 1 ≤ 2τ γ − τ ≤ τ if − 1 ≤ 2τ γ − τ ≤ 1 if − τ ≤ 2τ γ − τ ≤ −1

(12.5)

if γ = −1

Furthermore, the transformation between the DHHLE hSO and the hesitant fuzzy element hγ can be determined by  

  F hSO = F sφl sφl ∈ SO ; l = 1, . . . , L; φl ∈ [−τ, τ ]; ϕl ∈ [−ς, ς ] = { γl |γl = f (φl , ϕl )} = hγ ,

(12.6)

 F −1 hγ = F −1 ({ γl |γl ∈ [0, 1]; l = 1, . . . , L})  

 = sφl φl < oϕl >= f −1 (γl ) = hSO .

(12.7)

Definition 12.4 (Gou et al. 2017) Suppose that So =   st t = −τ, . . . , −1, 0, 1, . . . , τ ; k = −ς, . . . , −1, 0, 1, . . . , ς be a DHLTS, hSO1 and hSO2 are two DHHLEs, λ is a real number. The basic operations of DHHLEs are defined below: ⎞ ⎛ (1)

(2)



⎜ hSO1 ⊗ hSO1 = F −1 ⎝

λ hSO = F −1





η1 ∈F hSO



η∈F (hSO )

  ,η2 ∈F hSO

1   λ η .

⎟ {η1 η2 }⎠;

2

 = = { st t Definition 12.5 (Gou et al. 2017) Let SO −τ, . . . , −1, 0, 1, . . . ,τ ; k = −ς, . . . , −1, 0, 1, . . . , ς } be a DHLTS,   hSO = sφl sφl ∈ SO ; l = 1, 2, . . . , L; φl = [−τ, τ ]; ϕl = [−ς, ς ] be a DHHLE. Then, the expected value of hSO is computed by

12.2 Preliminaries

277 L 

 1 E hSO = F sφl . L

(12.8)

l=1

Definition 12.6 (Gou et al. 2018) Suppose that SO   st t = −τ, . . . , −1, 0, 1, . . . , τ ; k= −ς, . . . , −1, 0, 1, . . . , ς 12 1n is a DHLTS.HS1O and HS2O = h11 SO , hSO , . . . , hSO  21 22  1j 2n h , h , . . . , hSO are two DHHLTSs, where hSO

SO SO    1j 1j 1j sφl sφl ∈ SO ; l = 1, 2, . . . , #hSO (j = 1, 2, . . . , n) 1j is the #hSO

 2j 2j sφl sφl

number

DHLTS in and  2j ∈ SO ; l = 1, 2, . . . , #hSO (j = 1, 2, . . . , n) while

number of DHLTS in

2j hSO .



d HS1O , HS2O =



of

1j hSO

Then, the distance between

HS1O

and

HS2O

 2 1   1j  2j F sφl − F sφl  L L

2j hSO 2j #hSO

= = = while = is the

is defined by

 21 ,

(12.9)

l=1

where L is the maximum number of linguistic terms in HS1O and HS2O .   Definition 12.7 Suppose that HSO = hSO1 , hSO2 , . . . hSOn is a collection of DHHLEs, then the double hierarchy hesitant weighted geometric (DHHWG) operator is defined as: ⎞ ⎛  n   w ⎟ ⎜   w

n

γi i ⎟ DHHWG hSO1 , hSO2 , . . . hSOn = ⊗ hSOi i = F −1 ⎜ ⎠. ⎝ i=1  γi ∈F hSO

i=1

i

(12.10)

12.3 The Developed GSSOA Model This section proposes an integrated GSSOA model for selecting qualified green suppliers and optimally allocating reasonable order sizes to meet different procurement criteria. To sum up, three stages are included in the proposed model, which include computing the weights of evaluation criteria based on the PIPRCIA (pivot pairwise relative criteria importance assessment) method (Stanujkic et al. 2017), determining the ranking of candidate green suppliers by an extended DFT, and allocating reasonable order sizes to the selected suppliers using a MOLP model. Figure 12.1 displays a flow chart of the proposed GSSOA model. For a GSSOA problem, suppose that there are m candidate suppliers Ai (i = 1, 2, . . . , m), n considered criteria Cj (j = 1, 2, . . . , n) and g decision

278

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

Fig. 12.1 Flowchart of the developed SSS&OA model

  g makers DMg (g = 1, 2 . . . , q). Assume that H g = hSO ij

m×n

is the double hierg

archy hesitant linguistic (DHHL) evaluation matrix of DMg , where hSO = ij  

g g sφij sφij ∈ SO is a DHHLE denoting the evaluation for supplier Ai with ij ij respect to Cj based on the linguistic term sets S = { st |t = −τ, . . . , −1, 0, 1, . . . , τ } . . . , ς}. The decision makers’ weights are and O = { ok |k = −ς, . . . , −1, 0, 1, q assumed as νg (g = 1, 2, . . . , q) with g=1 νg = 1 and 0 < νg < 1. Next, the detailed procedure of the developed GSSOA model is described. Stage 1 Determine criteria weights by the PIPRCIA method. The PIPRCIA method, developed by Stanujkic et al. (2017), is a new subjective weighting method to determine criteria weights according to the judgements of decision makers. This method allows decision makers to evaluate criteria when the expected criteria importance ranking is difficult or impossible to reach a consensus (Stevi´c et al. 2018). It enables decision makers to easily involve in the evaluation process and can improve reliability of the collected data. Hence, the PIPRCIA method is adopted to obtain subjective weights for the n evaluation criteria. The detailed steps are given as follows:

12.3 The Developed GSSOA Model

279

Step 1.1 Rank the evaluation criteria in descending order. This step is to determine the order of the n evaluation criteria Cj (j = 1, 2, . . . , n) in descending order based on their importance. Since the consensus on the expected importance of criteria is not easy to reach in an actual GSES problem, decision makers are allowed to evaluate the criteria comparative importance with regard to their preliminary ordering. Step 1.2 Determine the comparative importance of criteria.

g = hSO is the DHHL comparative importance Suppose ψ g Cj , Cj+1 jj+1 by decision maker DM between criteria Cj and Cj+1 provided   g using the     t = −τ and O = = s , . . . , −1, 0, 1, . . . , τ linguistic term sets S t     ok k = −ς  , . . . , −1, 0, 1, . . . , ς  , for j = 1, 2, . . . , n−1; g = 1, 2, . . . , q. Then, the aggregated comparative importance of criteria can be determined by  vg q g

 q 2 ψ Cj , Cj+1 = DHHWG h1 SOjj+1 , hSOjj+1 , . . . hSOjj+1 = ⊗ hSOjj+1 g=1 ⎞ ⎛ ⎧ ⎫ q ⎨ ⎬⎟ ⎜  v ⎟ ⎜ (12.11) =F −1 ⎜ γg g ⎟. ⎭⎠ ⎝ !⎩ g=1 g Ojj+1

γj ∈F hS

Step 1.3 Compute the relative weights of evaluation criteria. The relative weight of each criterion wj (j = 1, 2, . . . , n) is calculated through the following formula:  wj =

1 wj+1 2(1−γ (Cj ,Cj+1 ))

j = n, j < n.

(12.12)



 where γ Cj , Cj+1 is the membership degree of ψ Cj , Cj+1 determined by Eq. (12.4). Step 1.4 Calculate the normalized weights of evaluation criteria. The normalized weights of the n evaluation criteria w¯ j (j = 1, 2, . . . , n) are determined by w¯ j =

wj . n  wj

(12.13)

j=1

Stage 2 Select qualified green suppliers by the DFT. The DFT, developed by Busemeyer and Townsend (1993), is a dynamic decisionmaking approach. It describes how decision makers’ preferences evolve over time until a decision is reached. In this section, we extended the DFT with DHHLTSs to determine the ranking of green suppliers.

280

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

Step 2.1 Aggregate the decision makers’ evaluations. In this step, the individual DHHL matrixes of decision makers H g (g = 1, 2,. . . ,q) are aggregated to construct a collective DHHL evaluation , where matrix H = hSOij m×n

 q g vg q hSOij = DHHWG h1SO , h2SO , . . . hSO = ⊗ hSO ij ij ij ij g=1 ⎞ ⎛ ⎧ ⎫ q ⎜  ⎨ ⎬⎟ v ⎟ ⎜ =F −1 ⎜ γg g ⎟ ⎭⎠ ⎝ !⎩ g=1 γi ∈F

by

g hS O

(12.14)

ij

˙ Step 2.2 Calculated the distance % & matrix D between green suppliers. ˙ ˙ The distance matrix D = diu m×m between the m green suppliers can be obtained

d˙ iu =

n   d hSOij , hSOuj , i, u = 1, 2, . . . , m.

(12.15)

j=1

˙ Step 2.3 Determine the feedback matrix F. % & ˙ ˙ The feedback matrix F = fij m×n describes the memorizing effect of the competitive relationship between different green suppliers, in which diagonal elements represent the self-impact of a supplier, while non-diagonal elements express the competitive effects between suppliers. The feedback matrix F˙ is determined by ˙2 F˙ = I − ϕ · e−δ·D ,

(12.16)

where I is an identity matrix. The parameter δ describes the discriminable capability and it lies in the interval [0.01,1000] (Hao et al. 2017), and parameter ϕ represents the competitive impact between suppliers and belongs to [0,1] (Berkowitsch et al. 2014). ˙ Step 2.4 Determine the contract % & matrix C. ˙ The contract matrix C = c˙ ij m×n is determined as follows: ' c˙ ij =

1 if i = j, 1 − n−1 if i = j.

(12.17)

Step 2.5 Obtain the ranking of green suppliers. Suppose P(t)=(˙p1 (t), p˙ 2 (t), . . . , p˙ m (t)) is a preference vector of green suppliers at the time t, where p˙ i (t) represents the preference value of Ai at the time t and can be calculated by

12.3 The Developed GSSOA Model

p˙ i (t) =

n 

281

 w¯ j E hSOij , i = 1, 2, . . . , m.

(12.18)

j=1

Then, the preference vector P(t + h) at the time t + h is calculated by ˙ P(t + h) = FP(t) + V (t + h)

(12.19)

where h represents an arbitrary short time step and P(t + h) will approximate the diffusion process when h approaches zero. V (t + h) is the DHHL valence vector and it can be computed by V (t + h) = C˙ ⊗ H  ⊗ w¯ j (t + h)   where H  = E hSOij

m×n

(12.20)

, w¯ j (t + h) is the considered criteria weights at time t +

h, and w¯ j (t + h) is randomly generated in the interval [w¯ j − 0.05, w¯ j + 0.05]. The final decision results are concluded when the decision time t reaches the threshold criteria (Hao et al. 2017). The ranking of the m green suppliers is determined according to the decreasing order of the p˙ i (t + h)(i = 1, 2, . . . , m) values and the largest p˙ i (t + h) corresponds to the best supplier. Stage 3 Allocate order sizes to the qualified green suppliers. In this stage, we establish an MOLP model with quantity discount to determine the order size for each selected green supplier. The objectives of the developed model include minimizing the total cost of purchasing, minimizing the total defect quantity of product, minimizing the total delay delivery quantity of product, and maximizing the total green value of purchasing simultaneously. The developed MOLP model is given below. Step 3.1 Define related indexes and parameters. Indexes • p: Index of products p, p = 1, 2, . . . , λ . • i: Index of supplier i, i = 1, 2, . . . , m. • r: Index of discount intervals, r = 1, 2, . . . , R. Parameters: • Opi : Ordering cost of product p offered by green supplier. • Ppir : Purchase price of product p offered by green supplier i in discount interval r • Bpir : Lower quantity bound of the discount interval r in product p provided by supplier i. • Tpi : Unit transportation cost of product p offered by green supplier i. • Hp : Unit holding cost of product p. • Dp : Demand of product p. • Cpi : Capacity of pth product for ith green supplier. • Qpi : Defective rate of product p offered by green supplier i.

282

• • • •

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

Qp : Maximum defective rate of product p can be accepted. Lpi : Delay rate of supplier p in product i. Lp : Maximum acceptable delay rate of product p. Pi : Priority value of green supplier i obtained by the DFT.

Decision variables: • Xpir : Order size of product p purchased from green supplier i at discount interval r. • Ypir : Binary variable (=1) if product p is offered by green supplier i at discount interval r, 0 otherwise. Step 3.2 Construct an MOLP model considering multiple objectives. To allocate order for each selected green supplier, the following MOLP model can be established: min z1 =

n  m 

Ppir Xpir

(12.21)

Qpi .Xpir

(12.22)

k=1 i=1

min z2 =

n  m  p=1 i=1

min z3 =

n  m 

Lpi Xpir

(12.23)

p=1 i=1

max z4 =

n 

Pi∗ Xpir

(12.24)

i=1

Subject to: n 

Xpir ≥ Dp ∀i

(12.25)

Xpir < Cpi ∀p, i

(12.26)

Bpir ≤ Xpir ≤ Bpir+1 ∀p, i, r

(12.27)

p=1

R 

Ypir ≤ 1 ∀p, i

(12.28)

r=1 n  m  p=1 i=1

Qpi Xpir ≤ Qp Dp

(12.29)

12.3 The Developed GSSOA Model

283

n  m 

Lpi Xpir ≤ Lp Dp

(12.30)

p=1 i=1

Xpir ≥ 0 ∀p, i

(12.31)

The objective function Eq. (12.21) is established for minimizing the entire cost of purchasing. Equations (12.22) and (12.23) are the measure of defective quantity and delayed delivery quantity of product, respectively. The objective function of Eq. (12.24) maximizes the total green value of purchasing. Constraint sets in Eq. (12.25) state that the total purchase number of each product must satisfy the demand quantity of the product. The capacity constraint sets described in Eq. (12.26) show that the total quantity of product p purchased from the ith supplier should not exceed its capacity. Equations (12.27) and (12.28) are the constraints of discount interval, where the product is allowed to purchase at a certain price value. The constraint sets in Eq. (12.29) represent that the total defective amount of product p must be lower than the maximum acceptable defective amount. The total delayed delivery number of product p cannot exceed the maximum acceptable delayed amount as given in Eq. (12.30). Step 3.3 Determine optimum order quantities of the selected suppliers. In the MOLP model, all goals may not be realized under system constraints simultaneously. Thus, the priority and importance of objectives need to be considered. In this chapter, the LP-metrics method (Mohammed et al. 2018) is utilized to solve the established MOLP model. Suppose zb∗ (b = 1, 2, 3, 4) are the optimal solutions of four objective functions subject to Eqs. (12.25–12.31), respectively. Let ωb (b = 1, 2, 3, 4) be the relative importance offour objective functions given by decision makers, satisfying 0 ≤ ωb ≤ 1 and 4b=1 ωb = 1. The MOLP model constructed in the last step can be transformed into a single objective programming by ) ( z1 − z1∗ z2 − z2∗ z3 − z3∗ z4 − z4∗ . + ω2 + ω3 − ω4 minz = ω1 z1∗ z2∗ z3∗ z4∗

(12.32)

Through solving this single objective programming model, the order quantity of each selected green supplier can be determined.

12.4 Case Study In this section, we first present an example to illustrate the performance of the proposed GSSOA model, and then conduct further analysis to compare the proposed model with other methods.

284

12 GSSOA Using Double Hierarchy Hesitant Linguistic Sets …

12.4.1 Illustration of the Proposed Model This section applies the developed GSSOA model to an electronics manufacturing firm located in Shanghai, China. The company’s products include semiconductors, sensors, electronic components, and industrial control products. Under great competitive pressure from the global electronics market, the company decided to manufacture green and environment friendly products to improve its performance of green supply chain management. Selecting qualified green suppliers and allocating optimal orders are two significant activities to solve this problem. In this case, five potential suppliers Ai (i = 1, 2, . . . , 5) are selected for the further evaluation. These green suppliers are evaluated according to ten criteria Cj (j = 1, 2, . . . , 10) from three different dimensions (see Table 12.1). Then, five decision makers DMg (g = 1, 2, . . . , 5) are involved in the evaluation process based on the linguistic term sets S and O defined below. The relative importance of criteria is evaluated by utilizing the linguistic term sets S  and O . Due to their different backgrounds and expertise, the weight vector of the five decision makers is given as v = (0.3, 0.2, 0.2, 0.15, 0.15).  S=  O=  

S =

 s−3 = very poor, s−2 = poor, s−1 = slightly poor, s0 = fair, , s1 = slightly good , s2 = good , s3 = very good

 o−3 = far from, o−2 = only a little, o−1 = a little, o0 = just right, , o1 = much, o2 = very much, o3 = extremely

  = very unimportant, s = unimportant, s = slightly unimportant, s−3 −2 −1 , s0 = equally important, s1 = slightly important, s2 = important, s3 = very important   o−3 = extremely, o−2 = very much, o−1 = much, o0 = just right, O = . o1 = a little, o2 = only a little, o3 = far from

The DHHL comparative importance information of the ten criteria assessed by the decision makers is displayed in Table 12.2. Moreover,  we can obtain the DHHL g g evaluation matrixes of the five decision makers H = hSO (g = 1, 2, . . . , 5). ij

5×10

For example, the evaluation information of the first decision maker DM1 is shown in Table 12.3. In what follows, the developed GSSOA model is adopted to choose qualified green suppliers and allocate suitable order sizes among them. Stage 1 Determine criteria weights by the PIPRCIA method. Step 1.1 Based on their estimated importance to supplier green performance, the 12 criteria are ranked in descending order as: C1  C5  C3  C2  C4  C6  C8  C10  C9  C7 . Step 1.2 Through Eq. (12.11), the comparative importance evaluation information of criteria is aggregated and the result is given in Table 12.2.

12.4 Case Study

285

Table 12.1 Green supplier selection criteria Dimension

Criteria

Definition

Supplier performance

Product quality (C1 )

Ensure the quality of products in accordance with ISO 19000, QS9000 and other relevant requirements and specifications

Green manufacturing (C2 )

Committed to the production of clean and environmentally friendly products

Service flexibility (C3 )

Products need to meet customer requirements and can ensure on-time delivery when orders are changed

Environmental performance (C4 )

The ability of environmental protection and to observe environmental supervision for products and reduce waste as much as possible

Innovation ability (C5 )

Innovative product design to ensure the product detachable, recyclable and sustainable

Green logistic (C6 )

The ability to reduce transportation cost and pollution through logistics planning

Labor intensive (C7 )

The extent to which a supplier relies on labor in productive activities

Financial stability (C8 )

The financial status and financial stability of supplier

Supplier reputation (C9 )

The reputation of supplier in the industry, as well as past cooperation experience

Information safety (C10 )

Suppliers’ ability to protect product information

Environmental protection

Supplier risk

Step 1.3 Using Eq. (12.12), the relative weights of criteria wj (j = 1, 2, . . . , 10) are computed as shown in Table 12.4. Step 1.4 According to Eq. (12.13), the normalized weights of criteria w¯ j (j = 1, 2, . . . , 10) are calculated and displayed in Table 12.4. Stage 2 Select qualified green suppliers by the DFT.   Step 2.1 By Eq. (12.14), the collective DHHL evaluation matrix H = hSOij 5×10

is established as shown in Table 12.5. ˙ is Step 2.2 Via Eq. (12.15), the distance matrix of the five green suppliers D computed as follows:

0

0

−2 >

1



0

 s1

2

 s0





−1



  s−1

−1

DM2

   s1 , s2 0 −1

  s2 −1

  s1 −2

  s1 −2

  s1 −2

  s−1 −1

   s1 , s2

DM1

  s1 −1

   s1 , s2 −2 0

  s0 1

   s−1 , s0 −2 0

  s0 3

  s0 2

  s2

Decision makers

(C9 , C7 ) s  , s  0 1

 s2

 s1

 s−2

 s0

 s0 s j , if and only if i > j; Negation operator: neg(si ) = s j , if i + j = 2t.

The linguistic scale functions have the advantage of assigning different semantic values to linguistic terms in different situations (Peng and Wang 2017). Hence, it is an effective quantitative tool for converting nature language into numerical values. Definition 13.1 (Peng and Wang 2017) Let S = {s0 , s1 , . . . , s2t } be a linguistic term set. If θi ∈ [0, 1] is a numerical value, then the linguistic scale function is a mapping from si to θi (i = 0, 1, . . . , 2t), and it is defined as follows: F : si → θi (i = 0, 1, . . . , 2t),

(13.1)

where 0 ≤ θ0 ≤ θ1 ≤ . . . ≤ θ2t ≤ 1. The function F is a monotone increasing function with respect to the subscript i and the symbol θ i expresses the decision makers’ preferences when they are utilizing linguistic term si . Many linguistic scale functions have been introduced in the literature and the following are representative ones (Wang et al. 2016; Liu and Liu 2017): (1)

The first function is derived based on the subscript function, and it is expressed as: F1 (θi ) = θi =

(2)

i (0 ≤ i ≤ 2t), 2t

(13.2)

The second function is defined based on the exponential scale, and it is denoted as:

300

13 GSSOA Using Linguistic Z-Numbers and AQM

 F2 (θi ) = θi =

a t −a t−i 2a t −2 a t +a i−t −2 2a t −2

(0 ≤ i ≤ t) , (t + 1 ≤ i ≤ 2t)

(13.3)

where the value of parameter a can be obtained based on experimental study and it generally lies in the interval [1.36, 1.4]. The linguistic Z-numbers were proposed by Wang et al. (2017a) to depict uncertain linguistic decision making information and reduce information loss in the decision making process. Definition 13.2 (Wang et al. 2017a) Let X be a universe of discourse, S = {s0 , s1 , . . . , s2t } and S  = s0 , s1 , . . . , s2t  be two linguistic term sets. Then, let Aφ(x) ∈ S and Bϕ(x) ∈ S  . A linguistic Z-number set Z in X can be denoted in a function form as: Z=



  x, Aφ(x) , Bϕ(x) |x ∈ X .

(13.4)

where Aφ(x) is a fuzzy restriction on the values that the uncertain linguistic variable x is allowed to take, and Bϕ(x) is a measure of reliability of Aφ(x) .     Definition 13.3 (Wang et al. 2017a) Let z i = Aφ(i) , Bϕ(i) and z j = Aφ( j) , Bϕ( j) be two linguistic Z-numbers; let f ∗ and g ∗ be two different linguistic scale functions and their inverse functions are f ∗−1 and g ∗−1 , respectively. Then, the operational laws on linguistic Z-numbers are defined below:  ∗−1  ∗ 

   f  f Aφ(i) + f ∗ Aφ( j) , ∗ ∗ ∗ ∗ ; (1) z i ⊕ z j = f ( Aφ(i) )×g ( Bϕ( j) )+ f ( Aφ( j) )×g ( Bϕ( j) ) g ∗−1 f ∗ ( Aφ(i) )+ f ∗ ( Aφ( j) )      (2) λz i = f ∗−1 λ f ∗ Aφ(i) , Bϕ( λ ≥ 0; j) , where   ∗ λ ∗−1 ∗  λ λ ∗−1 g Bϕ(i) , where λ ≥ 0. f Aφ(i) , g (3) z i = f   Definition 13.4 (Wang et al. 2017a) Let z i = Aφ(i) , Bϕ(i) be a linguistic Z-number. Then the score function S(z i ) of z i is given below:     S(z i ) = f ∗ Aφ(i) × g ∗ Bϕ(i) ,

(13.5)

The accuracy function A(z i ) of z i can be defined as follows:      A(z i ) = f ∗ Aφ(i) × 1 − g ∗ Bϕ(i) .

(13.6)

    Definition 13.5 (Wang et al. 2017a) Let z i = Aφ(i) , Bϕ(i) and z j = Aφ( j) , Bϕ( j) be two linguistic Z-numbers. Then, their comparative laws are defined below: (1)

If Aφ(i) > Aφ( j) and Bϕ(i) > Bϕ( j) , then zi is strictly great than zj , denoted by zi > z j ;

13.2 Preliminaries

301

    If S(z i ) ≥ S z j and A(z i ) > A z j , then zi is greater than zj , denoted by zi z j ;     (3) If S(z i ) = S z j and A(z i ) = A z j , then zi is equivalent to zj , denoted by zi ∼ z j ;       (4) If S(z i ) = S z j and A(z i ) < A z j or S(z i ) < S z j , then zi is less than zj , denoted by z i ≺ z j .   Definition 13.6 Let z i = Aφ(i) , Bϕ(i) (i = 1, 2, . . . , n) be a collection of linguistic Z-numbers. Then, the linguistic Z-numbers weighted average (LZWA) operator is defined as: (2)

LZWA(z 1 , z 2 , . . . , z n ) = ⎛ ⎜ ∗−1 =⎜ ⎝f

n 

wi z i

i=1

⎛ n     ⎞⎞

wi f ∗ Aφ(i) g ∗ Bϕ(i) ⎜ i=1 ⎟⎟   ⎟⎟, wi f ∗ Aφ(i) , g∗−1 ⎜ n ⎝ ⎠⎠    i=1 wi f ∗ Aφ(i)

 n 

(13.7)

i=1

and the linguistic Z-numbers weighted geometric average (LZWGA) operator is defined as: n

LZWGA(z 1 , z 2 , . . . , z n ) = ⊗ (z i )wi i=1   n

 n

    wi wi ∗−1 ∗ ∗−1 ∗ = f f Aφ(i) g Bϕ(i) ,g , i=1

(13.8)

i=1

wn ) is the weight vector of z i (i = 1, 2, . . . , n) with the where w = (w1 , w2 , . . . , n wi = 1. condition wi ∈ [0, 1] and i=1

13.3 The Proposed GSSOA Model In this section, we developed a hybrid three-phase model to select qualified green suppliers and determine their optimal order quantity. Specifically, linguistic Znumbers are utilized to evaluate the green suppliers based on economic and environmental performance, criteria weights are computed by the SWARA method, and a modified AQM is adopted to rank the alternative green suppliers. Then, a MOLP model is established to allocate the order quantity for each qualified supplier with the objectives to maximize the total green purchase value and minimize the total purchase cost. Flowchart of the developed GSSOA model is shown in Fig. 13.1. For a GSSOA problem with m alternative green suppliers Ai (i = 1, 2, . . . , m), n criteria C j ( j = 1, 2, . . . , n) and l decision makers DMh (h = 1, 2 . . . , l), let R h =

302

13 GSSOA Using Linguistic Z-Numbers and AQM

Fig. 13.1 Flowchart of the proposed GSSOA model

  rihj

be the performance evaluation matrix from the hth decision maker. In the   matrix R , rihj = Aφ(i j h) , Bϕ(i j h) is the linguistic Z-number evaluation of supplier Ai against criterion C j provided by DMhbased on the linguistic term sets S =  m×n

h

{s0 , s1 , . . . , s2t } and S  = s0 , s1 , . . . , s2t  . The weight of DMh is defined as λh  which satisfies λh > 0 and lh=1 λh = 1. Next, the proposed GSSOA method is described in detail in the following subsections.

13.3.1 Suppliers Selection Stage 1 Determine criteria weights by the SWARA method.

13.3 The Proposed GSSOA Model

303

The SWARA method is a new weighting method proposed by Keršulien˙e et al. (2010). The main characteristic of this method is that it is uncomplicated, straightforward and involves less comparisons in contrast to other weighing methods (Kiani Mavi et al. 2018; Ghenai et al. 2020). Hence, the SWARA method is utilized here to obtain the weights of green evaluation criteria. The detailed procedure is presented as follows. Step 1.1 Rank green evaluation criteria in descending order. The n green evaluation criteria C j ( j = 1, 2, . . . , n) are sorted in descending order according to their expected importance. The new ranked criteria are denoted as Cj ( j = 1, 2, . . . , n). Step 1.2 Evaluate the comparative importance among criteria. Starting from the second criterion, the decision makers assess the relative importance of Cj to Cj−1 ( j = 2, 3, . . . , n) using the linguistic term set S˙ = {˙s0 , s˙1 , . . . , s˙2t˙}. Then, the LZWA operator is used to aggregate the relative impor tance vectors by all the decision makers E h = e2h , e3h , . . . , enh to obtain the collective relative importance vector E = [e2 , e3 , . . . , en ]. That is, l    e j = LZWA e1j , e2j , . . . , elj = λh ehj

 =

f ∗−1

h=1

 l    

∗   Aφ( j h) g ∗ Bϕ( j h) h=1 λh f ∗ ∗−1 λh f Aφ( j h) , g ,   l ∗ A φ( j h) h=1 λh f h=1

 l 

j = 2, 3, . . . , n.

(13.9)

Step 1.3 Determine the criteria importance coefficients c j ( j = 1, 2, . . . , n) by the following formula:  cj =

1  j =1 . S ej + 1 j > 1

(13.10)

Step 1.4 Compute the recalculated criteria weights v j ( j = 1, 2, . . . , n) by  vj =

1 c j−1 cj

j =1 . j >1

(13.11)

Step 1.5 Compute the final criteria weights wj ( j = 1, 2, . . . , n) by wj =

vj . n  vj

(13.12)

j=1

Finally, the weight vector of the evaluation criteria C j ( j = 1, 2, . . . , n) w = (w1 , w2 , . . . , wn ) can be derived by rearranging the weights wj ( j = 1, 2, . . . , n).

304

13 GSSOA Using Linguistic Z-Numbers and AQM

Stage 2 Rank alternative green suppliers by the linguistic Z-number AQM. The AQM is a relatively new MCDM method proposed by Gou et al. (2016). This method can easily and intuitively generate the ranking of alternatives through precedence relationship matrix and directed graph (Liu et al. 2019b). In this part, we extend the AQM with linguistic Z-numbers and used the linguistic Z-number AQM to obtain the ranking of alternative green suppliers. The detail steps for ranking green suppliers are as follows. Step 2.1 Aggregate the performance evaluations of decision makers. By using the LZWGA operator to aggregate the individual performance evaluation matrices R h (h  1, 2, . . . , l), we can obtain the collective performance evaluation  = matrix R = ri j m×n , where   l  wh ri j = LZWGA ri1j , ri2j , . . . , ril j = ⊗ ril j h=1   l

 l

      w w h h = f ∗−1 f ∗ Aφ(i j h) g ∗ Bϕ(i j h) , g ∗−1 . h=1

(13.13)

h=1

Step 2.2 Compare alternative suppliers with respect to each criterion. Based on the collective performance evaluation matrix R, the 0–1 precedence  j with respect to Cj can be established. For the relationship matrix P j = piu m×m

j

j

alternative pair (Ai , Au ), if ri j ru j on the jth criterion, then piu = 1 and pui = 0, and they are denoted as (Ai Au ) j and (Ai ≺ Au ) j , respectively. If ri j = ru j , then j j j j piu = pui = 1; if Ai and Au cannot be compared, then piu = pui = 0. The two situations are both denoted as (Ai ≈ Au ) j . Step 2.3 Compute the overall weight for each pair of alternative suppliers. The overall pros weight w(Ai Au ) of all alternative pairs (Ai Au )(i, u = 1, 2, . . . , m) can be computed by adding up all the weights of (Ai Au ) j regarding the criterion C j . That is, w(Ai Au ) =



wj.

(13.14)

j∈( Ai Au ) j

Analogously, the overall cons weight w(Ai ≺ Au ) and the overall indifference weight w(Ai ≈ Au ) can be computed. Step 2.4 Calculate the overall pros and cons indicated value for each pair of alternative suppliers. The overall pros and cons indicated values about all alternative pairs I (Ai Au )(i, u = 1, 2, . . . , m) are computed by I (Ai , Au ) =

w(Ai Au ) + ϕw(Ai ≈ Au ) , w(Ai ≺ Au ) + ϕw(Ai ≈ Au )

(13.15)

13.3 The Proposed GSSOA Model

305

where ϕ ∈ [0, 1] denoting the importance degree of w(Ai ≈ Au ). Step 2.5 Find the precedence relationships among alternative suppliers. Given the threshold value τ > 1, the relationships among the m alternative suppliers can be computed as follows: ⎧ (Ai , Au ) ≥ τ ⎨ Ai Au , I  A ≈ Au , 1 τ < I (Ai , Au )