A Fuzzy Goal Programming Approach for Solving Multiobjective Fuzzy Stochastic Programming Problems

This article presents a fuzzy goal programming (FGP) procedure for solving a stochastic multiobjective decision making (MODM) problem having the finite probabilistic aspiration levels for achievement of the chance constrained goals. In the proposed approach, the different chance parameters involved with the stochastically defined goal constraints are considered continuously distributed independent random variables. In the model formulation, first the membership functions of the fuzzy probablistic goals are constructed by defining the tolerance limits for achievement of the goals in the decision situation. Then, the defined membership functions are converted into their deterministic equivalent according to the prescribed distribution function of the random parameters. In the solution process, achievement of the membership goals defined for the deterministic membership functions to the highest value (unity) to the extent possible on the basis of the weights of importance of achieving the goals is considered. Two numerical examples are solved to illustrate the approach.