INTERACTIVE DECISION MAKING FOR MULTI-OBJECTIVE LINEAR FRACTIONAL PROGRAMMINGPROBLEMS WITH FUZZY PARAMETERS

This paper focuses on multiobjective linear fractional programming problems with fuzzy parameters and presents a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method.

Abstract

Abstract In this paper, we focus on multiobjective linear fractional programming problems with fuzzy parameters and present a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of a-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of the fuzzy numbers. In our interactive decision making method, in order to generate a candidate for the satisficing solution which is also a-Pareto optimal, if the DM specifies the degree α of the a-level sets and the reference objective values, the minimax problem is solved by combined use of the bisection method and the linear programming method and the DM is supplied with the corresponding α-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the degree a. Then by considering the current values of the objective functions and a as well as the trade-off rates, the DM acts on this solution by updating his/her reference objective values and/or degree a. In this way the satisficing solution for the DM can be derived efficiently from among an a-Pareto optimal solution set. A numerical example illustrates various aspects of the results developed in this paper.