Interactive fuzzy programming for two-level nonconvex programming problems with fuzzy parameters through genetic algorithms

Abstract

This paper formulates two-level nonconvex programming problems with fuzzy parameters by considering the experts’ vague or fuzzy understanding of the nature of the parameters in the problem-formulation process, and presents an interactive fuzzy programming method through genetic algorithms. Using the level sets of fuzzy parameters characterized as fuzzy numbers, the corresponding nonfuzzy two-level nonconvex programming problem is introduced. The fuzzy goals of the decision makers for the nonconvex objective functions at both levels are quantified by eliciting the corresponding membership functions. In our interactive method, having specified the level sets of the fuzzy parameters, by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels, an overall satisfactory solution is derived efficiently through genetic algorithms which are effective for nonconvex programming problems. An illustrative numerical example for two-level nonconvex programming problems with fuzzy parameters is provided to demonstrate the feasibility and efficiency of the proposed method.