Since the original paper by Yager, different definitions of the concept of fuzzy multisets (bags), and the corresponding operations are available in the literature, as well as some extensions of the union, intersection and difference operators of sets, and new algebraic operators. In this paper, a study of some algebraic properties of these operations including idempotency, identity, absorption, associativity, distributivity, demorgan's laws and the principle of Inclusion/Exclusion is presented in the context of membership sequence of fuzzy multisets. Also, the compatibility of the union and intersection on these structures and sets via their root sets is established.

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A multiset is a collection of objects in which repetition of elements is significant. In this paper an attempt to define a symmetric group under multiset context is presented and the analogous to Cayley's theorem is derived.

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