The complete decision set of the generalized Symmetrical Fuzzy Linear Programming problem

The generalized Symmetrical Fuzzy Linear Programming problem is defined in this paper as involving both fuzzy and nonfuzzy constraints of which fuzzy constraints are represented by linear and nonlinear membership functions. Fuzzy intervals are proposed to represent fuzzy equality constraints. The general form of fuzzy constraints is proposed. By defining the membership function μD as an explicit function of minZ rather than an explicit function of the solution set x, the complete solution set and its existence criterion are studied. The improvement of objective values based on the obtained complete solution set is also discussed. A truck fleet problem presented in the literature is cited to explain the proposed method and to prove the correctness of the solution.