Additive Fuzzy Multiple Goal Programming Model for the Unbalanced Transportation Problem with Hyperbolic Membership Function

This chapter presents a fuzzy goal programming approach to determine an optimal compromise solution for the unbalanced transportation problem with additive multiple fuzzy goals. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.