Synopses & Reviews
This monograph is intended for a graduate course of engineering and management science, as well as for persons who want an introductory and a capsule look into the theories and methodologies of multiple attribute decision making under a fuzzy environment. Moving from classical MADM introduces a great deal of complexity to the decision analysis. In a fuzzy environment, the decision analysis is extended to not only consider 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 II gives an overview of the classical MADM. Chapter III presents the basic concepts and the mathematical operations of fuzzy set theory with figures and simple numerical examples in a easy-to-read and easy-to-follow manner. Chapter IV deals with the fuzzy ranking methods. Fuzzy ranking methods are widely used in many aspects of fuzzy applications (especially fuzzy optimization procedure). A systematic classification of nearly two dozens of existing ranking methods is presented. In chapter IV, a system for classifying over one dozen fuzzy MADM methods is presented. The concept, algorithm, and the characteristics of each method are discussed. The computational procedure of each method is illustrated by solving a simple numerical example.
Synopsis
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.