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Interval-valued fuzzy n-ary subhypergroups of n-ary hypergroups

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Abstract

This paper provides a continuation of ideas presented by Davvaz and Corsini (J Intell Fuzzy Syst 18(4):377–382, 2007). Our aim in this paper is to introduce the concept of quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set. This concept is a generalized concept of quasicoincidence of a fuzzy point within a fuzzy set. By using this new idea, we consider the interval-valued (∈, ∈ ∨q)-fuzzy n-ary subhypergroup of a n-ary hypergroup. This newly defined interval-valued (∈, ∈ ∨q)-fuzzy n-ary subhypergroup is a generalization of the usual fuzzy n-ary subhypergroup. Finally, we consider the concept of implication-based interval-valued fuzzy n-ary subhypergroup in an n-ary hypergroup; in particular, the implication operators in £ukasiewicz system of continuous-valued logic are discussed.

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Acknowledgments

The authors are highly grateful to referees and Professor John Maclntyre, Editor-in-Chief, for their valuable comments and suggestions for improving the paper.

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Authors and Affiliations

  1. Department of Mathematics, Yazd University, Yazd, Iran

    B. Davvaz

  2. Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

    Osman Kazancı & S. Yamak

Authors
  1. B. Davvaz
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  2. Osman Kazancı
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  3. S. Yamak
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Correspondence to Osman Kazancı.

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Davvaz, B., Kazancı, O. & Yamak, S. Interval-valued fuzzy n-ary subhypergroups of n-ary hypergroups. Neural Comput & Applic 18, 903–911 (2009). https://doi.org/10.1007/s00521-008-0207-1

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  • DOI: https://doi.org/10.1007/s00521-008-0207-1

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