Fuzzy programming approach to multi-objective stochastic linear programming problems

This paper presents an application of fuzzy programming approach to the multi-objective stochastic linear programming problem. After converting the proposed stochastic programming problem into a deterministic problem (which may be linear or non-linear), fuzzy programming approach is applied to find the compromise solution. Assuming the coefficients of the decision variables in the objective functions and in the constraints, and the right-hand-side parameters in the constraints as normal random variables, a methodology is presented to convert the probabilistic problem into a deterministic problem. Then fuzzy programming is applied using linear as well as non-linear membership functions. The method leads to an efficient solution as well as an optimal compromise solution. A numerical example is also presented to illustrate the methodology.