On alpha-cuts homomorphism of fuzzy multigroups
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초록
The concept of fuzzy multigroup is an algebraic structure of fuzzy multiset that generalizes both the theories of classical group and fuzzy group. Fuzzy multigroup constitutes an application of fuzzy multiset to the elementary theory of classical group. In this paper, we give a concise note on $\alpha$-cuts of fuzzy multigroups and propose the notion of $\alpha$-cuts homomorphism of fuzzy multigroups. Some properties of $\alpha$-cuts homomorphism of fuzzy multigroups are explicated. The notions of quasi-surjective mapping, pre-surjective mapping, surjective $\alpha$-cuts homomorphic mapping and $\alpha$-cuts isomorphic mapping are established in $\alpha$-cuts homomorphism of fuzzy multigroups with some number of results.
Abstract
The concept of fuzzy multigroup is an algebraic structure of fuzzy multiset that generalizes both the theories of classical group and fuzzy group. Fuzzy multigroup constitutes an application of fuzzy multiset to the elementary theory of classical group. In this paper, we give a concise note on $\alpha$-cuts of fuzzy multigroups and propose the notion of $\alpha$-cuts homomorphism of fuzzy multigroups. Some properties of $\alpha$-cuts homomorphism of fuzzy multigroups are explicated. The notions of quasi-surjective mapping, pre-surjective mapping, surjective $\alpha$-cuts homomorphic mapping and $\alpha$-cuts isomorphic mapping are established in $\alpha$-cuts homomorphism of fuzzy multigroups with some number of results.
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