The use of possibility theory in the definition of fuzzy Pareto-optimality |
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| Authors: | Ricardo C Silva Akebo Yamakami |
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| Institution: | (1) Department of Economics and Business Management, Yamagata University, 1-4-12, Kojirakawa-cho, 990-8560 Yamagata-shi, Japan;(2) Department of Management Science and Engineering, Akita Prefectural University, 015-0055 Yulihonjo, Japan;(3) Department of Systems Engineering, Northeastern University, 110006 Shenyang, China;(4) School of Information, Central University of Finance and Economics, Beijing, China; |
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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. |
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