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Some Results On Fuzzy Coverings And Partitions | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 17, Issue 2, 2006, Pages 74-85 | ||
| Author | ||
| Abstract | ||
| The aim of this paper is briefly analyze, and we recall how coverings and crisp partitions can be described in terms of resemblance and equivalence relations. Also natural extensions to the fuzzy case of concepts as covering and w-resemblance relation are given. Also we shows how, from each covering Σ of a fuzzy set μ, a w-resemblance relation RΣ on μ can be constructed; and conversely. The concepts of pre-class and class of a wresemblance relation are introduced. Also,w-similarity relations are studied as a significant particular case of fuzzy w-resemblance relations. We introduce a necessary and sufficient conditions for R to be a wsimilarity relation and connections between w-similarity classes and classes in the sense of section 2 are analyzed. Then a fuzzy partition π is defined as a covering that has a w-similarity relation associated being π the set of w-similarity classes of R. Finally, notions of quotient–set and canonical mapping are properly extended to the fuzzy case thus the analogy between the fuzzy partition theory presented in this paper and classical (crisp) is clearly manifest. | ||
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