Duality of Fuzzy MC2 Linear Programming: A Constructive Approach

Based on decision makers′ goal-seeking and compromise behavior, this paper proposes a constructive approach to duality of a fuzzy multiple criteria and multiple constraint level (MC2) linear programming problem. For a given MC2 problem, both its fuzzy primal and dual programs are defined as the problems with fuzzy optimal objectives. We first use the MC2-simplex method to locate sets of potential solutions of maximum and minimum MC2 problems for primal and dual programs, respectively. Then, we construct separate membership functions for primal and dual programs. For each program, a set of fuzzy potential solutions is determined in terms of the membership function and "primal" potential bases with certain ranges of decision parameters. Finally, using the primal and dual membership functions, we construct several fuzzy weak duality functions for any pair of primal and dual fuzzy potential solutions.