Fuzzy Cartesian product, fuzzy relations and fuzzy functions

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 r...

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Bibliographic Details
Published in:Fuzzy sets and systems 1991-06, Vol.41 (3), p.299-315
Main Authors: Dib, K.A., Youssef, Nabil L.
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Fuzzy Cartesian product
fuzzy cutting
fuzzy equivalence class
fuzzy equivalence relation
fuzzy function
fuzzy partial order
fuzzy partition
fuzzy relation
fuzzy total order
Mathematics
Sciences and techniques of general use
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Summary: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.
ISSN:0165-0114
1872-6801
DOI:10.1016/0165-0114(91)90134-C