Fuzzy potential solutions in multi-criteria and multi-constraint level linear programming problems

Abstract Given a multi-criteria and multi-constraint level (MC 2 ) linear programming problem, we can use an MC 2 -simplex method to find a set of potential solutions. Each potential solution optimizes the MC 2 problem under a certain range of decision parameters, namely the criteria weight vector and the constraint level weight vector. In this paper, we extend the potential solution to a fuzzy potential solution for a given fuzzy MC 2 problem. With a certain range of the decision parameters, a membership function of the MC 2 problem is first constructed. Then, for such a parameter range, a fuzzy potential solution is determined in terms of the membership function and a primal potential basis. Based on the theoretical analysis, we propose a heuristic algorithm to systematically and effectively locate all fuzzy potential solutions for all possible changes of the decision parameters. A numerical example is used to illustrate the algorithm.

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