Some characterizations of fuzzy comultisets and quotient fuzzy multigroups

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The idea of fuzzy multisets has been applied to some group theoretic notions. Nonetheless, the notions of cosets and quotient groups have not been substantiated in fuzzy multigroup environment. The aim of this paper is to present the concepts of cosets and quotient groups in fuzzy multigroup context with some related results. To start with, the connection between fuzzy comultisets of fuzzy multigroups and the cosets of groups is established. Some characterizations of fuzzy comultisets are outlined with proofs. In addition, quotient fuzzy multigroup is proposed and some of its properties are explored. It is proven that a normal fuzzy multigroup of a fuzzy multigroup is commutative if and only if the quotient fuzzy multigroup is commutative. Finally, group theoretic isomorphism theorems are established in fuzzy multigroup setting.

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