(Series in Electrical and Computer Engineering) Jie Lu_ Guangquan Zhang_ Da Ruan - Multi-objective G - Multi-Objective Group Decision Making Methods

(Series in Electrical and Computer Engineering) Jie Lu_ Guangquan Zhang_ Da Ruan - Multi-objective G

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Unformatted text preview: Multi-Objective Group Decision Making Methods, Software and Applications With Fuzzy Set Techniques SERIES IN ELECTRICAL AND COMPUTER ENGINEERING Editor: Wai-Kai Chen (University of Illinois, Chicago, USA) Published: Vol. 1: Net Theory and Its Applications Flows in Networks by W. K. Chen Vol. 2: A Mathematical Introduction to Control Theory by S. Engelberg Vol. 5: Security Modeling and Analysis of Mobile Agent Systems by Lu Ma and Jeffrey J. P. Tsai Steven - Multi-Objective.pmd 2 3/12/2007, 2:01 PM S E R I E S I N E L E C T R I C A L A N D vol.6 COMPUTERENGINEERING Multi-Objective Group Decision Making Methods, Software and Applications With Fuzzy Set Techniques Jie Lu . Guangquan Zhang University of Technology, Sydney Australia Da Ruan Belgian Nuclear Research Center (SCK.CEN) & Ghent University, Belgium Fengjie Wu University of Technology, Sydney Australia ICP Inperial College Press Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Series in Electrical and Computer Engineering — Vol. 6 MULTI-OBJECTIVE GROUP DECISION MAKING Methods, Software and Applications with Fuzzy Set Techniques Copyright © 2007 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-1-86094-793-3 ISBN-10 1-86094-793-X Printed in Singapore. Steven - Multi-Objective.pmd 1 3/12/2007, 2:01 PM Foreword Human activities are certainly very diverse, but one of the most important and most frequent activities is decision making. Decision making includes information gathering, data mining, modelling, and analysis. It includes formal calculus as well as subjective attitudes and it has different appearances in different situations and under different circumstances. It is, therefore, not surprising, that several scientific disciplines are concerned with this topic. Logic and Psychology, Management and Computer Sciences, Artificial Intelligence and Operations Research study this phenomenon. Since these disciplines often work independent of each other and very often without any intercommunication it is not surprising that the term ‘decision’ is semantically defined differently in different disciplines and that misunderstandings occur whenever scientists from different areas discuss matters of decision making with each other. For logicians, for instance, and mathematicians a decision is the (timeless) act of selection between different alternatives of actions executed by one (abstract) person and generally guided by one criterion. For a sociologist or empirical decision theoretician a decision is a special, time consuming, goal-oriented information processing act, which may include one person, one organisation, or group of persons and which may be influenced by many explicit and hidden criteria and objectives. This book focuses on one of the most complex decision making structures, in which several persons are involved in the decision making process, of which each has not only one objective function, different from the objective functions of other decision makers, but several. In addition these criteria and objectives are not dichotomous (crisp) but fuzzy, which is usually the case in reality. This represents the combination of three classical areas of decision theory: classical formal and empirical-cognitive decision theory, the theory of multi-criteria and/or multi-objectives decision making and the theory of group decision making. Part I of this book gives an introduction to all three areas. In v vi Multi-Objective Group Decision Making addition this part of the book also offers an introduction to Fuzzy Set Theory and to Decision Support Systems, i.e., computer based systems, which support human decision makers in their activities. Part II of this book combines two components of Part I, namely multiobjective decision making and fuzzy set theory and considers in more detail different models and methods in this area. In analogy to Part I these methods are then moulded in appropriate decision support systems. Building on this Part III turns to fuzzy group decision making. It first describes the methods used to solve this type of decision problems and then describes a web-based decision support system, which is especially designed for group decisions. This is certainly the most advanced type of decision technology that can be found today. This is extended in Part IV to the last stage of sophistication of decision making modelling, namely fuzzy multi-objective group decision making. Of particular interest, not only to practitioners but also to researchers is Part V of this book: applications. A very strong motivation of decision theory has always been, not only to develop theories but to help to improve decision making in practice. The application of theories to real problems is by far not trivial but can often be one of the hardest parts of decision making or problems solving. It is, therefore, particularly valuable for the use of this book, that real applications from very different areas are described in detail. That may not only make other applications easier, but it might also facilitate the understanding of the theories and methods which are the contents of the first four parts of this book. This can only be topped by the enclosed CD, which allows readers to apply the methods themselves and solve problems that they might have or get a deeper understanding of the quite demanding theory which is described in this book. The authors of this book can be congratulated to this exceptional work and it can only be hoped, that many researchers, students and practitioners make use of the material that is offered in this book. Aachen, December 2006 H.-J. Zimmermann Preface This book presents what a multi-objective group decision-making problem is and how a decision support system can support reaching a solution in practice. In this book, both fuzzy set theory and optimisation method are the key techniques to solve a multi-objective group decision-making problem under an uncertain environment. We offer several advantages here: • It combines decision making theories, tools and applications effectively. For each issue of fuzzy multi-objective decision making, fuzzy multi-criteria decision making, fuzzy group decision making, multi-objective group decision-making, fuzzy multi-objective group decision-making presented in this book, we discuss their models and methods in great details with the related software systems and cases studies. • It is designed as a unified whole in which each chapter relates its content to what went before and is, in turn, related to what will follow. Some case based examples such as product planning are discussed in different chapters for different decision situations, individual and group decision makers, and the use of different decision support systems to get desired solutions. • It doesn’t attempt to provide exhaustive coverage of every fact or research result that exists. It mainly reflects our last ten years research results in this field and what is more related, and also assumes about what the readers have already studied. • As the technology is up-to-date throughout some results come from ours and other authors’ recent publications. Our potential readers could be organisational managers and practicing professionals, who can use the provided methods and software to solve their real decision problems; researchers in the areas of multi-objective decision making, multi-criteria decision making, group decision making, vii viii Multi-Objective Group Decision Making fuzzy set applications and decision support systems; students at the advanced undergraduate or master’s level in management or business administration programs; and students at the advanced undergraduate or master’s level in information systems and application of computer science programs. This book is organised as follows. The first part, from Chapters 1 to 5, covers concepts and frameworks of decision making, multi-objective and multi-attribute decision making, group decision making, decision support systems, and fuzzy systems in general. Readers will learn how to model a decision problem and go through all phases of decision making process as well as the characteristics of multi-objective decision making and the components of a decision support system. The second part of the book, from Chapters 6 to 8, presents fuzzy multi-objectives decision making, including its model, several methods, and an implemented decision support system. The third part, from Chapters 9 to 11, is about group decision making within an uncertain environment. The fourth part, from Chapters 12 to 13, covers the framework, methods and systems of fuzzy multi-objective group decision making, which applies the results developed in the first two parts of the book. The last part, from Chapters 14 to 16, focuses on applications of the decision methods and systems presented in previous chapters. These applications include power market, team situation awareness and logistic management. Most of the chapters, from Part 2 to Part 5, have real case based examples and illustrate how to use the provided decision support techniques. Within five decision support systems presented in this book, a CD-ROM included in this book has two of them, called fuzzy multiobjective decision support system (FMODSS) and fuzzy group decision support system (FGDSS). Examples illustrated in the book are mainly screenshots from using those two systems. Readers are encouraged to practice with the two systems with real world decision problems. We wish to thank Australian Research Council (ARC) as the work presented in this book was partially supported under ARC discovery grants DP0211701, DP0557154 and DP0559213; co-workers who have advised and conducted some research results of this book with us; many researchers who have worked in multi-objective decision making, group decision making, fuzzy set application, decision support systems and Preface ix related areas over the past several decades, for which we have added their significant insight in the book and well-known publications in the reference list; the researchers and students at University of Technology Sydney (UTS) who suffered through several versions of the decision support systems shown in this book and whose comments improved it substantially; and Steven Patt, Editor at World Scientific, who helped us to ensure the book was as good as we were capable of making it. Jie Lu, UTS, Sydney Guangquan Zhang, UTS, Sydney Da Ruan, SCK•CEN, Mol and UGent, Gent Fengjie Wu, UTS, Sydney December 2006 This page intentionally left blank Contents Foreword v Preface vii Part I: Decision Making, Decision Support Systems, and Fuzzy Sets........... 1 1. Decision Making .................................................................................... 1.1 Decision and Decision Makers...................................................... 1.2 Decision Making Process .............................................................. 1.3 Problem Modelling and Optimisation ........................................... 1.4 Computerised Decision Support.................................................... 3 3 5 10 13 2. Multi-Objective and Multi-Attribute Decision Making ......................... 2.1 Criteria, Objectives, and Attributes............................................... 2.2 MODM Models............................................................................. 2.3 MODM Methods........................................................................... 2.3.1 Classifications ................................................................... 2.3.2 Weighting method ............................................................. 2.3.3 Goal programming ............................................................ 2.3.4 A case-based example ....................................................... 2.4 MADM Models............................................................................. 2.5 MADM Methods........................................................................... 2.5.1 TOPSIS ............................................................................. 2.5.2 AHP................................................................................... 2.5.3 A case-based example ....................................................... 2.6 Summary ....................................................................................... 17 17 19 21 21 25 25 28 29 31 32 34 35 37 3. Group Decision Making ......................................................................... 3.1 Decision Groups............................................................................ 3.2 Characteristics ............................................................................... 3.3 Models........................................................................................... 3.4 Process .......................................................................................... 3.5 Methods......................................................................................... 3.6 Group Support Systems and Groupware ....................................... 3.7 Summary ....................................................................................... 39 39 40 42 44 46 49 51 4. Decision Support Systems...................................................................... 4.1 Concepts........................................................................................ 4.2 Characteristics ............................................................................... 53 53 55 xi xii Multi-Objective Group Decision Making 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 Types............................................................................................. Multi-Objective DSS..................................................................... Multi-Attribute DSS...................................................................... Group DSS .................................................................................... Intelligent DSS .............................................................................. Web-Based DSS............................................................................ Components .................................................................................. Summary ....................................................................................... 56 59 63 65 67 70 73 75 5. Fuzzy Sets and Systems ......................................................................... 5.1 Fuzzy Sets ..................................................................................... 5.1.1 Definitions......................................................................... 5.1.2 Operations and properties.................................................. 5.1.3 Decomposition theorem and the extension principle ........ 5.2 Fuzzy Relations............................................................................. 5.3 Fuzzy Numbers ............................................................................. 5.4 Linguistic Variables ...................................................................... 5.5 Fuzzy Linear Programming........................................................... 5.5.1 Zimmermann’s model ....................................................... 5.5.2 Fuzzy parameters .............................................................. 5.6 Summary ....................................................................................... 77 77 77 79 80 81 83 87 89 90 91 91 Part II: Fuzzy Multi-Objective Decision Making .......................................... 93 6. Fuzzy MODM Models ........................................................................... 6.1 A Problem ..................................................................................... 6.2 Fuzzy Parameter-Based MOLP Models........................................ 6.2.1 A general FMOLP model.................................................. 6.2.2 An FMOLPα model ........................................................... 6.3 Solution Transformation Theories................................................. 6.3.1 General MOLP transformation.......................................... 6.3.2 Weighted MOLP transformation....................................... 6.3.3 Constrained MOLP transformation ................................... 6.3.4 Weighted maximum MOLP transformation...................... 6.4 Fuzzy Multi-Objective Linear Goal Programming Models .......... 6.5 Summary ....................................................................................... 95 95 97 97 100 102 102 111 114 116 119 121 7. Fuzzy MODM Methods ......................................................................... 7.1 Related Issues................................................................................ 7.2 Fuzzy MOLP................................................................................. 7.2.1 Method description............................................................ 7.2.2 A numeral example ........................................................... 7.3 Fuzzy MOLGP .............................................................................. 7.3.1 Method description............................................................ 123 123 126 126 130 136 137 Contents xiii 7.3.2 A numeral example ........................................................... Interactive FMOLP ....................................................................... 7.4.1 Method description............................................................ 7.4.2 A numeral example ........................................................... Summary ....................................................................................... 141 146 146 152 159 8. Fuzzy Multi-Objective DSS ................................................................... 8.1 System Configuration.................................................................... 8.2 System Interface............................................................................ 8.3 A Model-Base and Model Management ....................................... 8.4 A Method-Base and Solution Process ........................................... 8.4.1 Fuzzy MOLP..................................................................... 8.4.2 Fuzzy MOLGP .................................................................. 8.4.3 Interactive FMOLP ........................................................... 8.5 Case-Based Examples ................................................................... 8.6 Summary ....................................................................................... 161 161 163 164 167 167 167 170 173 185 7.4 7.5 Part III: Fuzzy Group Decision Making ........................................................ 187 9. Fuzzy MCDM ........................................................................................ 9.1 A Problem ..................................................................................... 9.2 Models........................................................................................... 9.3 Fuzzy TOPSIS..........
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