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Fuzzy Optimization and Decision Making

, Volume 10, Issue 1, pp 11–30 | Cite as

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

  • Ricardo C. Silva
  • Akebo Yamakami
Article

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.

Keywords

Fuzzy logic Possibility theory Multi-objective optimization Fuzzy Pareto-optimality conditions Fuzzy optimization 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Telematics, School of Electrical and Computer EngineeringUniversity of CampinasCampinasBrazil

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