Fuzzy Goal Programming Approach to Chance Constrained Multilevel Programming Problems

This paper presents a fuzzy goal programming (FGP) procedure for solving multilevel programming problems (MLPPs) having chance constraints in large hierarchical decision organizations. In the proposed approach, first the chance constraints of a problem are converted into their respective deterministic equivalent in the decision making context. Then, the objective functions of decision makers (DMs) located at different hierarchical levels are converted into fuzzy goals by introducing an imprecise aspiration level to each of them to make decision in an uncertain environment. In the model formulation, the concept of tolerance membership functions in fuzzy sets for measuring the degree of satisfaction of DMs with regard to achieving the aspired levels of fuzzy goals as well as degree of optimality of the decision vectors controlled by upper-level DMs on the basis of their order of hierarchy in the organizational system. In the solution process, minimization of under deviational variables associated with membership goals defined for the membership functions are considered for achieving the highest membership value (unity) of each of the fuzzy goals to the extent possible on the basis of their weights of importance in the decision making horizon. To illustrate the effectiveness of the proposed approach, a numerical example is solved.