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A solution concept for fuzzy multiobjective programming problems based on convex cones. (English) Zbl 1076.90070
Summary: A solution concept for fuzzy multiobjective programming problems based on ordering cones (convex cones) is proposed in this paper. The notions of ordering cones and partial orderings on a vector space are essentially equivalent. Therefore, the optimality notions in a real vector space can be elicited naturally by invoking a concept similar to that of the Pareto-optimal solution in vector optimization problems. We introduce a corresponding multiobjective programming problem and a weighting problem of the original fuzzy multiobjective programming problem using linear functionals so that the optimal solution of its corresponding weighting problem is also the Pareto-optimal solution of the original fuzzy multiobjective programming problem.

MSC:
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming
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