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

YAMAK S., KAZANCI O., Davvaz B.

INFORMATION SCIENCES, vol.178, no.20, pp.3957-3972, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 178 Issue: 20
  • Publication Date: 2008
  • Doi Number: 10.1016/j.ins.2008.06.007
  • Journal Name: INFORMATION SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3957-3972
  • Karadeniz Technical University Affiliated: Yes

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 J(t-conorm Y). 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 J (t-conorm Y). 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 v-distributive t-norrns J (Lambda-distributive t-conorms Y). Also, we obtain some results of J-product (Y-product) of the interval-valued fuzzy subsets for infinitely v-distributive t-norms J (Lambda-distributive t-conorms Y). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n-ary group with infinitely v-distributive t-norms J (Lambda-distributive t-conorms Y). (c) 2008 Elsevier Inc. All rights reserved.