SIMILARITY RELATIONS, VAGUE GROUPS, AND FUZZY SUBGROUPS

Kiran R. Bhutani () and John N. Mordeson ()
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Kiran R. Bhutani: Department of Mathematics, The Catholic University of America, Washington, DC 20064, USA
John N. Mordeson: Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA

New Mathematics and Natural Computation (NMNC), 2006, vol. 02, issue 03, 195-208

Abstract: We 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.

Keywords: Vague groups; fuzzy subgroups; similarity relations (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S1793005706000488

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