A Fuzzy Goal Programming Approach for Fuzzy Multiobjective Stochastic Programming through Expectation Model

Abstract

In this paper a fuzzy goal programming method for modeling and solving multiobjective stochastic decision making problem involving fuzzy random variables associated with the parameters of the objectives as well as system constraints is developed. In the proposed approach, an expectation model is generated on the basis of the mean of the fuzzy random variables involved with the objectives of the problem. Then the problem is converted into an equivalent fuzzy programming model by considering the fuzzily defined chance constraints. Afterwards, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with the fuzzy parameters of the problem. Now to construct the membership goals of the decomposed objectives under the extended feasible region defined by the decomposed system constraints, the individual optimal values of each objective is calculated in isolation. Then the membership functions are constructed to measure the degree of satisfaction of each decomposed objectives in the decision making environment. The membership functions are then converted into membership goals by assigning unity as the aspiration level of the membership goals. Then a fuzzy goal programming model is developed by minimizing the under deviational variables and thereby obtaining the optimal solution in the decision making environment.