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Ranking fuzzy alternatives with consideration of the decision maker's partial fuzzy utility
Abstract
The problems of ranking fuzzy alternatives can be very complex and yet they are encountered in almost every application of fuzzy sets theory. Ranking methods akin to crisp utility models are not sufficient to deal with the vagueness (fuzziness) and imprecise assessment of decision makers' utility values. Also, most indices for ranking fuzzy numbers give unsatisfactory solution because decision maker's utility function is not utilized. It is thus clear that an effective ranking procedure should utilize at least the partial utility information provided by the decision maker and should have a way of processing the vague information. This research has contributed to the discussion of the following three topics. 1. Decision maker's utility function. A partial fuzzy utility model has been proposed for estimating decision maker's utility function. The decision maker is interviewed using natural language. The linguistic terms are then mapped to a set of fuzzy numbers. Based on the piece-wise quadratic utility function and the Extension Principle, partial fuzzy utility functions can be derived. The fuzzy utility function is then defuzzified by using the concept of linguistic average proposed by Zadeh (1975). 2. The concept of utility modifier. Based on decision maker's utility function, the concept of utility modifier has been introduced. All the membership functions of the fuzzy alternatives to be evaluated are modified by the utility modifier. 3. The new ranking methods. New procedures for ranking both single and multiple criteria fuzzy numbers have been developed. Properties of the new index for ranking single criterion fuzzy numbers are investigated. For ranking multi-criteria fuzzy numbers, the fuzzy numbers are projected orthogonally to the one dimensional preference subspace. The fuzzy projections are then evaluated using the proposed index for ranking single criteria fuzzy numbers. A numerical comparison between the proposed and four other commonly used ranking procedures has been conducted. The proposed method has, in general, less shortcomings than the methods compared.
Subject Area
Industrial engineering
Recommended Citation
Li, Huishen, "Ranking fuzzy alternatives with consideration of the decision maker's partial fuzzy utility" (1992). ETD collection for University of Nebraska-Lincoln. AAI9308187.
https://digitalcommons.unl.edu/dissertations/AAI9308187