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

Original Article

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.

Keywords

Hypergroup n-ary hypergroup Fuzzy set Belong to Quasicoincident with n-ary subhypergroup Fuzzy (∈, ∈ ∨q)-fuzzy n-ary subhypergroup 

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Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.Department of MathematicsYazd UniversityYazdIran
  2. 2.Department of MathematicsKaradeniz Technical UniversityTrabzonTurkey

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