Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters

Abstract

This paper presents an interactive decision making method for multiobjective nonlinear programming problems with fuzzy parameters. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of α-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of fuzzy numbers. In our interactive method, if the decision maker (DM) specifies the degree α of the α-level sets and the reference objective values, a minimax problem is solved 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 α. Then by considering the current values of the objective functions and α as well as the trade-off rates, the DM responds by updating his reference objective values and/or the degree α. In this way the satisfying solution for the DM can be derived efficiently from among an α-Pareto optimal solution set. A numerical example illustrates various aspects of the results developed in this paper.