Fuzzy mathematical programing approach for solving multi objective fuzzy stochastic programming problem

Most of the real world decision making problems involve uncertainty, which arise due to incomplete information or linguistic information on data. Stochastic programming and fuzzy programming are two powerful techniques to solve such type of problems. Fuzzy stochastic programming is concerned with optimization problems in which some or all parameters are treated as fuzzy random variables. In this paper, a multi-objective chance constrained programming problem has been considered when coefficients are fuzzy random variables. By using the conceptα- cut, the fuzzy stochastic problem is converted into an equivalent deterministic non-linear programming problem. Then the fuzzy programming technique has been applied to obtain a compromise solution. A numerical example is also presented to illustrate the methodology.

Keywords:

Chance constrained programming , Normal distribution , Fuzzy programming , Hyperbolic membership function