Abstract
Abstract A new approach to Cartesian product, relations and functions in fuzzy set theory is established. A concept of fuzzy Cartesian product is introduced using a suitable lattice. A fuzzy relation is then defined as a subset of the fuzzy Cartesian product analogously to the crisp case. Fuzzy equivalence relations are introduced and investigated. Results corresponding to those on ordinary equivalence relations are proved for fuzzy equivalence relations. Finally, the notion of a fuzzy function is introduced, as a special type of fuzzy relations, and is then investigated. This fuzzy function generalizes Zadeh's definition of functions in the fuzzy context.
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