Decision-making with a fuzzy preference relation |
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Authors: | SA Orlovsky |
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Institution: | Computing Centre of the U.S.S.R. Academy of Sciences, 117333 Moscow, U.S.S.R. |
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Abstract: | In most decisio-making problems a preference relation in the set of alternatives is of a fuzzy nature, reflecting for instance on the fuzziness of experts estimates of the preferences. In this paper, the corresponding fuzzy equivalence and strict preference relations are defined for a given fuzzy non-strict preference relation in an unfuzzy set of alternatives which are used to introduce in a natural way the fuzzy set of nondominated alternatives. Two types of linearity of a fuzzy relation are introduced and the equivalence of the unfuzzy nondominated alternatives is studied. It is shown that unfuzzy nondominated solutions to the decision-making problem exist, provided the original fuzzy relation satisfies some topological requirements. A simple method of calculating these solutions is indicated. |
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