Primal fuzzy programming and inverse fuzzy programming problems

Fuzzy variable is a function from a possibility space to the real line. In this paper, two classes of fuzzy programming problems with fuzzy variable coefficients are presented. The first one is called primal fuzzy programming problem whose objective is a chance function defined by possibility measure, while the second one is called inverse fuzzy programming problem whose objective is a critical value function. Generally, the difficulties of solving the two fuzzy programming problems are different. Thus, to solve the problems effectively, we prove two main results which show solving one of the problems is equivalent to solving its counterpart.