Definition of Fuzzy Pareto-Optimality by Using Possibility Theory
نویسندگان
چکیده
Pareto-optimality conditions are crucial when dealing with classic multi-objective optimization problems because we need to find out a set of optimal solutions rather than only one optimal solution to optimization problem with a single objective. Extensions of these conditions to the fuzzy domain have been discussed and addressed in recent literature. This work presents a novel approach based on the use of possibility theory as a comparison index to define a fuzzily ordered set with a view to generating the necessary conditions for the Pareto-optimality of candidate solutions in the fuzzy domain. Making use of the conditions generated, one can characterize fuzzy efficient solutions by means of carefully chosen singleobjective problems. The uncertainties are inserted into the formulation of the studied fuzzy multi-objective optimization problem by means of fuzzy coefficients in the objective function. Some numerical examples are analytically solved to illustrate the efficiency of the proposed approach. Keywords— Possibility theory, multi-objective optimization, fuzzy Pareto-optimality conditions, fuzzy mathematical programming.
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