Fuzzy multiobjective optimization modeling with Mathematica
نویسنده
چکیده
In the real situations, decision makers are often faced to a plurality of objectives and constraints in a world of imprecise data about the preferences of agents, the local constraints and the global environment. In a fuzzy environment, fuzzy linear programming (FLP) and fuzzy goal programming (FGP) problems incorporate fuzzy objective functions and constraints, fuzzy parameters and variable sets. Mathematical operators are used to aggregate the fuzzy objective functions and constraints. The optimal solution corresponds to the maximum degree of the membership function in the decision set. The resolution of the multiobjective FLP consists in reducing the vector optimization of objective functions to a single objective. Weighted goal programming problems consider the relative importance of objectives. This contribution surveys essential techniques with numerical applications to simple economic problems. The computations are carried out using the software Mathematica 7.0.1 and the subpackage Fuzzy Logic 2, from which selected primitives are proposed.
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