An interactive fuzzy satisficing method for multiobjective nonconvex programming problems with fuzzy numbers through coevolutionary genetic algorithms

In this paper, by considering the experts' fuzzy understanding of the natur e of the parameters in the problem-formulation process, multiobjective nonc onvex nonlinear programming problems with fuzzy numbers are formulated and an interactive fuzzy satisficing method through coevolutionary genetic algo rithms is presented. Using the alpha -levei sets of fuzzy numbers, the corr esponding nonfuzzy alpha -programming problem is introduced. After determin ing the fuzzy goals of the decision maker, if the decision maker specifies the degree alpha and the reference membership values, the corresponding ext ended Pareto optimal solution can be obtained by solving the augmented mini max problems for which the coevolutionary genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, the revised GENOCOP III is proposed by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method fur derivi ng a satisficing solution for the decision maker efficiently from an extend ed Pareto optimal solution set is presented together with an illustrative n umerical example.