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This monograph is intended for a graduate course ofengineering and management science, as well as for personswho want an introductory and a capsule look into thetheories and methodologies of multiple attribute decisionmaking under a fuzzy environment. Moving from classical MADMintroduces a great deal of complexity to the decisionanalysis. In a fuzzy environment, the decision analysis isextended to not only consider the aggregation of performancescores (which are fuzzy) but also the comparison of fuzzynumbers which cannot be easily compared as in the case ofreal numbers. Chapter II gives an overview of the classicalMADM. Chapter III presents the basic concepts and themathematical operations of fuzzy set theory with figures andsimple numerical examples in a easy-to-read andeasy-to-follow manner. Chapter IV deals with the fuzzyranking methods. Fuzzy ranking methods are widely used inmany aspects of fuzzy applications (especially fuzzyoptimization procedure). A systematic classification ofnearly two dozens of existing ranking methods is presented.In chapter IV, a system for classifying over one dozen fuzzyMADM methods is presented. The concept, algorithm, and thecharacteristics of each method are discussed. Thecomputational procedure of each method is illustrated bysolving a simple numerical example.
Contenu
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.