Approximate Reasoning for Solving Fuzzy Linear Programming Problems
نویسندگان
چکیده
We interpret fuzzy linear programming (FLP) problems (where some or all coefficients can be fuzzy sets and the inequality relations between fuzzy sets can be given by a certain fuzzy relation) as multiple fuzzy reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the objective of the FLP problem. Then the solution process consists of two steps: first, for every decision variable x ∈ R, we compute the maximizing fuzzy set, MAX(x), via sup-min convolution of the antecedents/constraints and the fact/objective, then an (optimal) solution to FLP problem is any point which produces a maximal element of the set {MAX(x) | x ∈ Rn} (in the sense of the given inequality relation). We show that our solution process for a classical (crisp) LP problem results in a solution in the classical sense, and (under well-chosen inequality relations and objective function) coincides with those suggested by [Buc88, Del87, Ram85, Ver82, Zim76]. Furthermore, we show how to extend the proposed solution principle to non-linear programming problems with fuzzy coefficients.
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