Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups |
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Authors: | Sultan Yamak Osman Kazanc? |
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Affiliation: | a Department of Mathematics, Karadeniz Technical University, Trabzon, Turkey b Department of Mathematics, Yazd University, Yazd, Iran |
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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). |
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Keywords: | n-Ary group Hypergroup n-Ary hypergroup Fuzzy set n-Ary sub-hypergroup Fuzzy n-Ary sub-hypergroup t-Norm t-Conorm Interval-valued fuzzy subset |
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