Similarity Relations, Vague Groups, And Fuzzy Subgroups
AbstractWe define vague groups in terms of similarity relations rather than fuzzy equalities. This yields a bijection between the set of all right-invariant similarity relations on a group and the set of all fuzzy subgroups of the group. Under this bijection, right-invariant and left-invariant similarity relations correspond to normal fuzzy subgroups. We show how this bijection allows for the transfer of results between vague groups and fuzzy subgroups. In particular, certain numerical invariants that characterize fuzzy subgroups of an Abelian group can be used to characterize vague groups.
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.
Volume (Year): 02 (2006)
Issue (Month): 03 ()
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Web page: http://www.worldscinet.com/nmnc/nmnc.shtml
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