Exponential membership function in stochastic fuzzy goal programming

Considering the stochastic fuzzy goal programming, this paper provides a study of four known fuzzy goal programming models. This study is considered in the case of stochastic fuzzy goal programming. The chance-constrained approach and the exponential membership function are utilized to transform Iskander’s structure of stochastic fuzzy goal program [M.G. Iskander, A fuzzy weighted additive approach for stochastic fuzzy goal programming, Applied Mathematics and Computation 154 (2004) 543–553] to its equivalent deterministic-crisp, according to each one of the four models. The exponential membership function is considered with increasing rate of change and with decreasing rate of change. The decision-maker should precisely set his goals relative weights in two models, and his preemptive priority structure in the other two. A numerical example is given for illustration.