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Similarity Relations, Vague Groups, And Fuzzy Subgroups

Author

Listed:
  • 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)

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.

Suggested Citation

  • Kiran R. Bhutani & John N. Mordeson, 2006. "Similarity Relations, Vague Groups, And Fuzzy Subgroups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 2(03), pages 195-208.
    • Handle: RePEc:wsi:nmncxx:v:02:y:2006:i:03:n:s1793005706000488
    DOI: 10.1142/S1793005706000488
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