Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups

  • Authors:

  • Sultan Yamak;Osman Kazancı;Bijan Davvaz

  • Affiliations:

  • Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey;Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey;Department of Mathematics, Yazd University, Yazd, Iran

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

In this paper, we study a generalization of group, hypergroup and n-ary group. Firstly, we define interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). We give a necessary and sufficient condition for, an interval-valued fuzzy subset to be an interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup with respect to a t-norm T (t-conorm S). Secondly, using the notion of image (anti image) and inverse image of a homomorphism, some new properties of interval-valued fuzzy (anti fuzzy) n-ary sub-hypergroup are obtained with respect to infinitely @?-distributive t-norms T (@?-distributive t-conorms S). Also, we obtain some results of T-product (S-product) of the interval-valued fuzzy subsets for infinitely @?-distributive t-norms T (@?-distributive t-conorms S). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n-ary group with infinitely @?-distributive t-norms T (@?-distributive t-conorms S).