A priority based fuzzy programming approach for multiobjective probabilistic linear fractional programming

This paper deals with a fuzzy goal programming methodology for solving multiobjective linear fractional chance constrained programming problems containing fuzzy numbers and exponentially distributed fuzzy random variables associated with the system constraints. In model formulation process, the problem is converted into an equivalent fuzzy programming model by applying chance constrained programming technique in a fuzzily defined probabilistic decision making situation. Then using the concept of α-cut for fuzzy numbers and by considering the tolerance level of fuzzy numbers the problem reduces to an equivalent sub problem with interval coefficients. In this method the convex combination of each interval is used and the problem is reduced to a nonlinear programming problem. Finally the model is solved by converting nonlinear model into its equivalent multiobjective linear programming model by using Taylor series; and a priority based fuzzy goal programming method is used for achievement of the highest membership degree. To demonstrate the efficiency of the proposed technique an illustrative example, studied previously, is solved and the solution is compared with the existing methodology.