The use of possibility theory in the definition of fuzzy Pareto-optimality

Authors:
Ricardo C. Silva;Akebo Yamakami
Affiliations:
Department of Telematics, School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil 13083-970;Department of Telematics, School of Electrical and Computer Engineering, University of Campinas, Campinas, Brazil 13083-970
Venue:
Fuzzy Optimization and Decision Making
Year:
2011

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Abstract

Pareto-optimality conditions are crucial when dealing with classic multi-objective optimization problems. 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 definition of 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 mono-objective problems and Karush-Kuhn-Tucker conditions to fuzzy non-dominated solutions. 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.