Fuzzy goal programming in the case of exponential membership functions with quasiconcave piecewise linear exponents

Fuzzy goal programming has been the subject of numerous studies. A few contributions have examined the situation in which the membership functions of the fuzzy goals are exponential. This paper considers the fuzzy goals when their membership functions are natural exponential with quasiconcave/quasiconvex piecewise linear exponents. The proposed approach is also applicable to the case of concave or convex piecewise linear exponents. Two main forms of exponential membership functions are used. According to each form, two types of fuzzy goal programming models are presented. The lexicographic weighted maxmin model and the pre-emptive priority structure model. The two models take the form of a mixed zero-one nonlinear goal program. A numerical example illustrates the implementation and comparison of the two models.