Solving multi-objective fuzzy probabilistic 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 order to capture randomness and fuzziness under one roof. A method for solving multi-objective fuzzy probabilistic programming problem is proposed in this paper. The uncertain parameters are considered as fuzzy log-normal random variables. Since the existing methods are not enough to solve fuzzy probabilistic programming problem directly, therefore the mathematical programming model is transformed to an equivalent multi-objective crisp model. Finally, a fuzzy programming technique is used to solve the multi-objective crisp model. The resulting model is then solved by standard non-linear programming methods. In order to illustrate the methodology a numerical example is provided.