A Fuzzy Solution Approach to a Fuzzy Linear Goal Programming Problem

Abstract

In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM) who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from the past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets and a lot of fuzzy approaches to multiobjective programming have been developed.Many decisors might follow a satisfaction criterion rather than the criterion of maximizing an objective function; and the satisfaction criterion leads to the concept of goal. Goal programming (GP) is an appropriate approach to the problem and when attributes and/or goals are in an imprecise environment and they cannot be stated with precision, we work in fuzzy goal programming.This paper presents a fuzzy solution to a GP problem when all the parameters may be fuzzy numbers. The method relies on á-cuts of the fuzzy solution to generate the possibility distribution of the objective functions. Ideas are illustrated with a numerical example.