Theory and approaches of group decision making with uncertain linguistic expressions

Uncertainty and Operations Research Hai Wang Zeshui Xu Theory and Approaches of Group DecisionMaking with Uncertain Linguistic Expressions Uncertainty and Operations Research Editor-in-chief Xiang Li, Beijing University of Chemical Technology, Beijing, China Decision analysis based on uncertain data is natural in many real-world applications, and sometimes such an analysis is inevitable In the past years, researchers have proposed many efficient operations research models and methods, which have been widely applied to real-life problems, such as finance, management, manufacturing, supply chain, transportation, among others This book series aims to provide a global forum for advancing the analysis, understanding, development, and practice of uncertainty theory and operations research for solving economic, engineering, management, and social problems More information about this series at http://www.springer.com/series/11709 Hai Wang Zeshui Xu • Theory and Approaches of Group Decision-Making with Uncertain Linguistic Expressions 123 Hai Wang School of Information Engineering Nanjing Audit University Nanjing, Jiangsu, China Zeshui Xu Business School Sichuan University Chengdu, Sichuan, China ISSN 2195-996X ISSN 2195-9978 (electronic) Uncertainty and Operations Research ISBN 978-981-13-3734-5 ISBN 978-981-13-3735-2 (eBook) https://doi.org/10.1007/978-981-13-3735-2 Library of Congress Control Number: 2018964257 © Springer Nature Singapore Pte Ltd 2019 This work is subject to copyright All rights are reserved 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, express 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 Preface Due to the complexity of problems in hand and the limitation of experts’ cognition, uncertainties are generally inevitable in decision information In the fuzzy linguistic approach, linguistic variables enable a manner to represent uncertain information which is close to human’s cognition It is necessary that, in the traditional way of computing with words, the experts have to represent decision information by means of certain terms However, this is quite difficult when facing complex types of uncertainties Uncertain linguistic expressions, which include more than one possible term in a direct or indirect way, are more consistent with people’s language conventions In order to enable the use of uncertain linguistic expressions in decision-making processes, some fundamental theories and approaches have been developed On the basis of the existing models, this book introduces some linguistic models to represent two types of uncertain linguistic expressions which conform to natural language conventions, i.e., extended hesitant fuzzy linguistic term sets and linguistic terms with weakened hedges, and presents the related fundamental theories and approaches for group decision-making Specifically, the book is organized by five parts as follows: The first part is formed by Chap This chapter introduces the background of computing with words, the focused problems, and some related theory and techniques A brief overview of this related area, such as the current developments of models of uncertain linguistic expressions, the group decision-making approaches, is also given in this chapter The second part is Chap This chapter presents the representational model of the virtual linguistic terms, extend the model of hesitant fuzzy linguistic term sets, and then introduces a new technique to model linguistic hedges Computational models of these techniques, such as order relations, are also presented The third part goes through Chaps 3–5 Chapters and focus on the group decision-making problems with the extended version of hesitant fuzzy linguistic term sets Chapter is under the framework of decision matrices, presents an information fusion based group decision-making approach and a two-phase group v vi Preface decision-making approach Chapter is based on the framework of preference relations, presents some new consistency measures, and then employs them to improve incomplete linguistic preference relations Group decision-making problems and preference relations with hedges are focused in Chap A multigranular group decision-making approach is introduced and some theoretical aspects of the new preference relations are also discussed The fourth part includes Chaps and where group decision-making problems with multiple types of uncertain linguistic expressions are considered Two group decision-making approaches are introduced The first one considers the aspiration levels taking the form of uncertain linguistic expressions and the second one presents descriptive measures for decision makers to understand the effects of uncertain parameters The last part includes Chap A hierarchical model is introduced for the evaluation of big data-based audit platforms The model is solved in the case where the performances take the forms of multiple types of uncertain linguistic expressions, based on the uncertain linguistic expressions approach presented in Chap This book can be used as a reference for engineers, technicians, and researchers who are working in the fields of intelligent computation, fuzzy mathematics, operations research, information science, management science and so on It could also serve as a textbook for postgraduate and senior undergraduate students of the relevant professional institutions of higher learning The first author would like to thank Dr Xiao-Jun Zeng at the University of Manchester for his insightful ideas and great suggestions This work was supported in part by the National Natural Science Foundation of China under Grant 71571123 and Grant 71601092, and the Key University Science Research Project of Jiangsu Province (No 16KJA520002, 18KJB413006) and the China Scholarship Council Nanjing, China September 2018 Hai Wang Zeshui Xu Contents Part I Introduction Backgrounds and Literature Review 1.1 Linguistic Decision-Making in Qualitative Setting 1.2 Focused Problems 1.2.1 Novel CWW Models Based on ULEs 1.2.2 Preference Relations Based on ULEs 1.2.3 GDM Approaches Based on ULEs 1.2.4 Modelling Complex Problems Under Uncertainties 1.3 Recent Advances of the Focused Problems 1.3.1 Review of Modelling ULEs and Decision-Making Approaches 1.3.2 Review of Lingustic Hedges 1.3.3 Review of Group Decision-Making Approaches Under Uncertainty 1.3.4 A Summary of the Contributions and Limitations 1.4 Aims and Focuses of This Book References Part II 3 6 7 14 15 20 22 24 35 35 36 37 43 44 45 45 Theory and Models of Uncertain Linguistic Expressions Representational Models and Computational Foundations of Some Types of Uncertain Linguistic Expressions 2.1 Virtual Linguistic Model 2.1.1 Preliminaries 2.1.2 Syntax and Semantics of VLTs 2.1.3 Computational Model of VLTs 2.2 Extended Hesitant Fuzzy Linguistic Term Sets 2.2.1 Fuzzy Linguistic Approach and HFLTS 2.2.2 Representational Model of EHFLTSs vii viii Contents 2.2.3 Basic Operations of EHFLTSs and Their Properties 2.2.4 A Partial Order of EHFLTSs 2.3 Total Orders of EHFLTSs 2.3.1 Existing Order Relations of EHFLTSs 2.3.2 Total Orders of EHFLTSs: A Generation Approach 2.4 Linguistic Terms with Weakened Hedges 2.4.1 Respresentational Model of LTWHs 2.4.2 Linguistic Computational Model Based on LTWHs 2.5 A Comparative Analysis on Similar Models of ULEs 2.5.1 Compared with the Existing Techniques of Modeling Hedges 2.5.2 LTWHs Versus ULTs and HFLTSs 2.5.3 Compared with Other Techniques 2.6 Concluding Remarks References Part III 46 48 48 49 50 55 56 63 66 66 67 69 70 70 75 75 76 77 79 79 83 86 89 90 92 Group Decision-Making Based on a Single Type of Uncertain Linguistic Expressions Group Decision-Making Based on EHFLTSs Under the Framework of Decision Matrix 3.1 A Framework of Multiple Groups Decision-Making 3.1.1 Mathematical Description of MGDM 3.1.2 Process of MGDM 3.2 A MGDM Approach Based on Information Fusion 3.2.1 Some Aggregation Operators of EHFLTSs 3.2.2 Properties of the Aggregation Operators 3.2.3 Implementation of the MGDM Processes 3.2.4 Applications 3.2.5 Comparative Analysis 3.3 A Two-Phase GDM Approach Based on Admissible Orders 3.3.1 Defining the EHFLOWA Operator Based on Admissible Orders 3.3.2 The Two-Phase GDM Approach 3.3.3 Application in Evaluations of Energy Technologies 3.3.4 Comparisons and Further Discussions 3.4 Conclusions References 92 95 97 100 104 104 Preference Analysis and Applications Based on EHFLTSs 4.1 Some Consistency Measures of EHFLPRs 4.1.1 The Concept of EHFLPRs 4.1.2 Preference Relation Graphs 107 108 108 109 Contents 4.1.3 Additive Consistency for EHFLPRs 4.1.4 Selective Algorithm for Reducing EHFLPRs to LPRs Based on Additive Consistency 4.1.5 Weak Consistency for EHFLPRs 4.1.6 Broken Circle Algorithm for Reducing EHFLPRs to LPRs Based on Weak Consistency 4.1.7 Comparative Analyses 4.2 Improving Incomplete LPRs Based on Consistency Measures of EHFLPRs 4.2.1 Incomplete LPRs and Their Consistency Measures 4.2.2 An Interactive Algorithm to Reach Weak Consistency of Incomplete LPRs 4.2.3 A Consistency-Based Interactive Algorithm to Complete Incomplete LPRs 4.2.4 The Interactive Algorithm with Self-adaptive Evolution to Complete Incomplete LPRs 4.2.5 An Example Regarding the Evaluation of Energy Channels 4.2.6 Comparisions and Discussions 4.3 Conclusions References Preference Analysis and Group Decision-Making Based on LTWHs 5.1 Multi-granular Linguistic Decision-Making with LTWHs 5.1.1 The Framework of MGLDM Problems 5.1.2 Constructing Multi-granular Linguistic Model Based on Hedges 5.1.3 An Approach for MGLDM with LTWHs 5.1.4 An Application of Evaluating the Non-financial Performance of Banks 5.1.5 Compared with Similar MGLDM Approaches 5.2 Consistency Measures of Linguistic Preference Relations with Hedges 5.2.1 Some Basic Operations and Order Relations of LTWHs 5.2.2 Linguistic Preference Relations with Weakened Hedges 5.2.3 Consistency Measures of LHPRs 5.2.4 Weak Consistency of LHPRs 5.2.5 Additive Consistency of LHPRs 5.2.6 Consistency Improving of LHPRs 5.3 Conclusions References ix 112 113 116 117 118 122 123 124 127 131 134 137 139 140 141 141 141 143 144 145 147 150 151 152 154 156 158 162 167 168 ... those of traditional variables, © Springer Nature Singapore Pte Ltd 2019 H Wang and Z Xu, Theory and Approaches of Group Decision- Making with Uncertain Linguistic Expressions, Uncertainty and Operations... 44 45 45 Theory and Models of Uncertain Linguistic Expressions Representational Models and Computational Foundations of Some Types of Uncertain Linguistic Expressions 2.1 Virtual Linguistic. .. problems, and some related theory and techniques A brief overview of this related area, such as the current developments of models of uncertain linguistic expressions, the group decision- making approaches,