Publisher Description

This monograph is intended for graduate courses in engineering and management science, as well as readers who want an introduction to the theories and methologies of Multiple Attribute Decision Making (MADM) in a fuzzy environment. Classical MADM introduces a great deal of complexity to the decision analysis. In a fuzzy environment, the decision analysis is extended to consider not only the aggregation of performance scores (which are fuzzy) but also the comparison of fuzzy numbers which cannot be easily compared as in the case of real numbers. Chapter 2 gives an overview of classical MADM. Chapter 3 presents the basic concepts and the mathematical operations of fuzzy set theory with figures and simple numerical examples in an easy-to-read and easy-to-follow manner. Chapter 4 deals with fuzzy ranking methods, which are widely used in many fuzzy applications (especially fuzzy optimization procedure). A systematic classification of nearly two dozen existing ranking methods is presented, and a system for classifying over one dozen fuzzy MADM methods is concept, algorithm and the characteristics of each method are discussed, and the computational procedure of each method is illustrated by solving a simple numerical example.

Table of Contents

I. Introduction.- II. Multiple Attribute Decision Making — An Overview.- 2.1 Basics and Concepts.- 2.2 Classifications of MADM Methods.- 2.3 Description of MADM Methods.- III. Fuzzy Sets and their Operations.- 3.1 Introduction.- 3.2 Basics of Fuzzy Sets.- 3.3 Set-Theoretic Operations with Fuzzy Sets.- 3.4 The Extension Principle and Fuzzy Arithmetics.- 3.5 Conclusions.- IV. Fuzzy Ranking Methods.- 4.1 Introduction.- 4.2 Ranking Using Degree of Optimality.- 4.3 Ranking Using Hamming Distance.- 4.4 Ranking Using ?-Cuts.- 4.5 Ranking Using Comparison Function.- 4.6 Ranking Using Fuzzy Mean and Spread.- 4.7 Ranking Using Proportion to The Ideal.- 4.8 Ranking Using Left and Right Scores.- 4.9 Ranking with Centroid Index.- 4.10 Ranking Using Area Measurement.- 4.11 Linguistic Ranking Methods.- V. Fuzzy Multiple Attribute Decision Making Methods.- 5.1 Introduction.- 5.2 Fuzzy Simple Additive Weighting Methods.- 5.3 Analytic Hierarchical Process (AHP) Methods.- 5.4 Fuzzy Conjunctive/Disjunctive Method.- 5.5 Heuristic MAUF Approach.- 5.6 Negi's Approach.- 5.7 Fuzzy Outranking Methods.- 5.8 Maximin Methods.- 5.9 A New Approach to Fuzzy MADM Problems.- VI. Concluding Remarks.- 6.1 MADM Problems and Fuzzy Sets.- 6.2 On Existing MADM Solution Methods.- 6.3 Critiques of the Existing Fuzzy Methods.- 6.4 A New Approach to Fuzzy MADM Problem Solving.- 6.5 Other Multiple Criteria Decision Making Methods.- 6.6 On Future Studies.- VII. Bibliography.

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Long Description

This monograph is intended for an advanced undergraduate or graduate course as well as for researchers, who want a compilation of developments in this rapidly growing field of operations research. This is a sequel to our previous works: "Multiple Objective Decision Making--Methods and Applications: A state-of-the-Art Survey" (No.164 of the Lecture Notes); "Multiple Attribute Decision Making--Methods and Applications: A State-of-the-Art Survey" (No.186 of the Lecture Notes); and "Group Decision Making under Multiple Criteria--Methods and Applications" (No.281 of the Lecture Notes). In this monograph, the literature on methods of fuzzy Multiple Attribute Decision Making (MADM) has been reviewed thoroughly and critically, and classified systematically. This study provides readers with a capsule look into the existing methods, their characteristics, and applicability to the analysis of fuzzy MADM problems. The basic concepts and algorithms from the classical MADM methods have been used in the development of the fuzzy MADM methods. We give an overview of the classical MADM in Chapter II. Chapter III presents the basic concepts and mathematical operations of fuzzy set theory with simple numerical examples in a easy-to-read and easy-to-follow manner. Fuzzy MADM methods basically consist of two phases: (1) the aggregation of the performance scores with respect to all the attributes for each alternative, and (2) the rank ordering of the alternatives according to the aggregated scores.

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