Abstract
In this paper, by considering the experts'fuzzy understanding of the nature of the parameters in the problemformulation process, we formulate multiobjective nonconvex nonlinear programming problems with fuzzy numbers and present an interactive fuzzy satisficing method through floating point genetic algorithms. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced. After determining the fuzzy goals of the decision maker, if the decision maker specifies the degree α and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems for which the floating point genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, we propose the revised GENOCOP III by introducing a method for generating an initial feasible point and a bisection method for generating a new search point efficiently. Then an interactive fuzzy satisficing method is presented together with an illustrative numerical example.
