Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups ?
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 (t -conorm S 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 (t -conorm S 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 T (? ? -distributive t -conorms S S ). Also, we obtain some results of T T -product (S S -product) of the interval-valued fuzzy subsets for infinitely ? ? -distributive t -norms T T (? ? -distributive t -conorms S S ). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n -ary group with infinitely ? ? -distributive t -norms T T (? ? -distributive t -conorms S S ).
t-norm t-conorm fuzzy n-ary sub-hypergroup n-ary sub-hypergroup hypergroup n-ary group interval-valued fuzzy subset n-ary hypergroup fuzzy set