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

Given a multi-criteria and multi-constraint level (MC²) linear programming problems, the authors cna use an MC²-simplex method to find a set of potential solutions. Each potential solution optimizes the MC² problem under a certain range of decision parameters, namely the criteria weight vector and the constraint level weight vector. In this paper, the authors extend the potential solution to a fuzzy potential solution for a given fuzzy MC² problem. With a certain range of the decision parameters, a membership function of the MC² 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, the authors 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.