Study of possibility programming in stochastic fuzzy multiobjective linear fractional programming problem

The concept of ranking method is an efficient approach to rank fuzzy numbers. In this paper, we have studied stochastic fuzzy multiobjective linear fractional programming problem (SFMOLFPP) where SFMOLFPP is transformed to its equivalent deterministic-crisp multiobjective linear programming problem (MOLPP). To study SFMOLFPP, a SFMOLFPP is presented in which the fuzzy coefficients and scalars in the linear fractional objectives and the fuzzy coefficients are characterised by triangular or trapezoidal fuzzy numbers. The left hand side of the stochastic fuzzy constraints are characterised by triangular or trapezoidal fuzzy numbers, while the right hand sides are assumed to be independent random variable with known distribution function. We have modify Iskander´s approach [16] to transform the suggested problem to its equivalence deterministic-crisp MOLPP. We have also used ranking function in SFMOLFPP to find the pareto optimal solution of the reduced multiobjective linear fractional programming problem (MOLFPP). One numerical example is presented to demonstrate two methodologies.