Abstract

The structure of fuzzy binary relations of indifference and preference is studied. The full description of fuzzy equivalence relations in terms of fuzzy partitions is given. All possible logical relations between various transitivity properties of fuzzy preferences are established. These relations permit to choose the notion of a fuzzy quasi-order relation which is an analog of a corresponding crisp relation. The possible approaches to the fuzzy choice are outlined. Finally, the general notion of a relative ‘degree of fuzziness’ is defined in connection with a study of the quantitative description of preservation properties under fuzzy mappings.

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