Interactive fuzzy programming for two-level 0-1 programming problems with fuzzy parameters through genetic algorithms

In this paper, an interactive fuzzy programming method using genetic algorithms has been proposed for two-level 0-1 programming problems with fuzzy parameters. According to the proposed technique, the decision maker in each level establishes his fuzzy goals related to the objective functions, using linear membership functions. After that the upper level decision maker establishes, subjectively, the minimal acceptable degree of the degree of satisfaction for the membership functions and, simultaneously, considers the ratio of satisfaction degrees between the levels; if necessary, the decision maker updates his minimal acceptability degree interactively. In so doing, a satisfactory solution is produced by taking into consideration also the achievement balance of the overall satisfaction degree, while respecting the upper-level decision maker's decision. The feasibility and validity of the proposed method was demonstrated through a numerical example for a two-level 0-1 programming problem with fuzzy parameters. The algorithm proposed in this paper can be extended to multilevel problems.