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 TT (t  -conorm SS). 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 TT (t  -conorm SS). 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 TT (∧∧-distributive t  -conorms SS). Also, we obtain some results of TT-product (SS-product) of the interval-valued fuzzy subsets for infinitely ∨∨-distributive t  -norms TT (∧∧-distributive t  -conorms SS). Lastly, we investigate some properties of interval-valued fuzzy subsets of the fundamental n  -ary group with infinitely ∨∨-distributive t  -norms TT (∧∧-distributive t  -conorms SS).