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 ).
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