In this paper, a fuzzy goal programming (FGP) approach is considered for
solving stochastic fuzzy multi-level multi-objective fractional programming (MLMOFP)
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 chanceconstrained
approach with dominance possibility criteria and the a-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. |
