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Duality of fuzzy \(MC^ 2\) linear programming: A constructive approach. (English) Zbl 0843.90130

Summary: 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 (MC\(^2\)) linear programming problem. For a given MC\(^2\) problem, both its fuzzy primal and dual programs are defined as the problems with fuzzy optimal objectives. We first use the MC\(^2\)-simplex method to locate sets of potential solutions of maximum and minimum MC\(^2\) 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.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C05 Linear programming
90C29 Multi-objective and goal programming
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