Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach

Abstract

In this paper, a fuzzy goal programming (FGP) approach is considered for solving stochastic fuzzy multi-level multi-objective fractional programming (ML-MOFP) problem. In the developed stochastic fuzzy ML-MOFP model the fractional objective function coefficients and scalars are represented by fuzzy parameters. Moreover, in the constraints, the right-hand sides are independent random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered to be fuzzy parameters. Therefore, the chance-constrained approach with dominance possibility criteria and the α-cut approach are utilized to transform the stochastic fuzzy ML-MOFP problem to its equivalent deterministic-crisp problem. Then, the membership functions for the defined fuzzy goals are setup. Also, in the proposed FGP model, a linearization procedures for the membership goals of the objective functions is developed. Hence, the FGP approach is used to achieve the highest degree of each of the membership goals by minimizing the sum of the negative deviational variables. Finally, an algorithm to clarify the developed FGP approach, as well as Illustrative numerical example, are presented.