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Multiple Attribute Decision Making M e t h o d s a n d a p p l i c a t i o n s

Multiple Attribute Decision Making M e t h o d s a n d a p p l i c a t i o n s Gwo-Hshiung Tzeng Jih-Jeng Huang

CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2011 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper Version Date: 20110513 International Standard Book Number: 978-1-4398-6157-8 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copy- right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro- vides licenses and registration for a variety of users. For organizations that have been granted a pho- tocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

Contents Preface.......................................................................................................................xi Authors ................................................................................................................... xiii Chapter 1 Introduction ..........................................................................................1 Profile of Multiple Criterion Decision Making .........................1 1.1 1.2 Historical Development of Multiple Attribute Decision Making ......................................................................................2 1.3 Historical Development of Multiple Objective Decision 1.4 Making ......................................................................................4 Introduction to Fuzzy Sets .........................................................7 1.4.1 Basic Concepts .............................................................7 1.4.2 Fuzzy Arithmetic Operations .......................................9 1.4.3 Extension Principle ......................................................9 1.4.4 α-Cut Arithmetic ....................................................... 10 1.4.5 Ranking Fuzzy Numbers ........................................... 11 1.5 Outline of this Book ................................................................ 11 part I Concepts and Theory of MadM Chapter 2 Analytic Hierarchy Process ................................................................ 15 2.1 Eigenvalue Method .................................................................. 15 2.2 Geometric Mean Method ........................................................20 2.3 Linear Programming Method ..................................................22 Fuzzy Lambda-Max Method ...................................................25 2.4 Chapter 3 Analytic Network Process and Fuzzy Analytic Network Process ..... 29 3.1 Analytic Network Process ....................................................... 29 3.2 Fuzzy Analytic Network Process ............................................ 35 3.3 Matrix Method for Fuzzy Analytic Network Process .............44 Chapter 4 Simple Additive Weighting Method ................................................... 55 4.1 4.2 4.3 Simple Additive Weighting Method ........................................ 55 Fuzzy Simple Additive Weighting ........................................... 57 Fuzzy Simple Additive Weighting for the Best Plan: Example of an Environment-Watershed Plan ..........................60 4.3.1 Building a Hierarchical Structure of Environment-Watershed Evaluation Criteria.............. 61 v

vi Contents 4.3.1.1 Determining the Evaluation Criteria Weights ....................................................... 62 4.3.2 Fuzzy Numbers .......................................................... 63 4.3.3 Linguistic Variables ...................................................64 4.3.4 Fuzzy Analytic Hierarchy Process .............................65 Fuzzy Multiple Criteria Decision-Making ..............................66 4.4 Chapter 5 TOPSIS and VIKOR ..........................................................................69 5.1 TOPSIS ....................................................................................69 5.2 VIKOR ..................................................................................... 71 5.3 Comparing VIKOR and TOPSIS ............................................ 75 5.4 Fuzzy TOPSIS ......................................................................... 76 Chapter 6 ELECTRE Method ............................................................................. 81 6.1 ELECTRE I ............................................................................. 81 6.2 ELECTRE II ........................................................................... 82 6.3 ELECTRE III ..........................................................................86 6.4 ELECTRE IV ..........................................................................90 Chapter 7 PROMETHEE Method ......................................................................95 7.1 The Notion of the PROMETHEE Method ..............................95 7.2 PROMETHEE I, II, III, IV .....................................................96 7.2.1 PROMETHEE I..........................................................98 7.2.2 PROMETHEE II ........................................................99 7.2.3 PROMETHEE III .......................................................99 7.2.4 PROMETHEE IV ..................................................... 100 7.3 Example for House Selection ................................................ 102 Chapter 8 Gray Relational Model ..................................................................... 103 8.1 Concepts of Gray System and Gray Relation ........................ 103 8.2 Gray Relation Model ............................................................. 104 8.3 Gray Relation for Multiple Criteria Evaluation ..................... 105 8.4 Example for Car Selection ..................................................... 107 Chapter 9 Fuzzy Integral Technique ................................................................. 109 9.1 Fuzzy Integral ........................................................................ 109 9.2 Hierarchical Fuzzy Integral ................................................... 114 Chapter 10 Rough Sets ........................................................................................ 123 10.1 10.2 Information System ...............................................................124 Indiscernible Relation ............................................................124

Contents vii 10.3 Approximation of Sets and Approximation of Accuracy ...... 125 10.4 Reduction of Attributes ......................................................... 126 10.5 Decision Table and Decision Rules ....................................... 126 10.6 The Analytical Procedure of Data Analysis .......................... 127 Chapter 11 Structural Model .............................................................................. 131 Interpretive Structural Modeling Method ............................. 131 11.1 11.2 DEMATEL Method............................................................... 134 11.3 Fuzzy Cognition Maps .......................................................... 138 part II applications of MadM Chapter 12 AHP: An Application ....................................................................... 143 12.1 Introduction ........................................................................... 143 12.2 Planning and Design Alternatives Evaluation Model ........... 144 12.2.1 Building Hierarchical Structure of Evaluation Criteria ...................................................................... 144 12.2.2 Determining the Evaluation Criteria Weights .......... 144 12.3 Case of Selecting the Engineering Service for Public Buildings ................................................................................ 146 12.3.1 Weights Calculation of the Evaluation Criteria ........ 146 12.3.2 Estimating the Performance Matrix ......................... 152 12.3.3 Ranking the Alternatives ......................................... 154 12.4 Discussions ............................................................................ 154 12.5 Conclusion ............................................................................. 156 Chapter 13 VIKOR Technique with Applications Based on DEMATEL and ANP ........................................................................................... 157 Introduction ........................................................................... 157 13.1 13.2 Novel Hybrid Multiple Criteria Decision Making model ...... 158 13.2.1 DEMATEL ............................................................... 158 13.2.2 Analytic Network Process ........................................ 161 13.2.3 VIKOR Method ........................................................ 164 13.3 Numerical Example with Applications ................................. 166 13.4 Discussions and Comparisons ............................................... 169 13.5 Conclusions ............................................................................ 171 Chapter 14 TOPSIS and VIKOR: An Application ............................................. 173 14.1 Alternative Solutions ............................................................. 174 14.2 Evaluation Criteria ................................................................. 177 14.2.1 Establishing the Evaluation Criteria ......................... 177

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