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Fuzzy multisets
Open AccessArticle

On Generalized Direct Product of Fuzzy Multigroups

Annals of Communications in Mathematics 2020

, 3 (1)

, 35-45

DOI: https://doi.org/10.62072/acm.2020.030104

AbstractFuzzy multigroup is a structure that generalizes the idea of fuzzy group. In fact, the concept of fuzzy multigroups is the application of fuzzy multisets to group theory. The idea of direct product of fuzzy multigroups has been established. This paper extends the notion of direct product between two fuzzy multigroups to the case of finitely many fuzzy multigroups. Some properties of generalized direct product of fuzzy multigroups are elucidated. It is shown that generalized direct product of fuzzy multigroups is a fuzzy multigroup. Finally, a number of results are obtained and duly verified with respect to alph-cuts and level sets.
Open AccessArticle

Synopsis of the Notions of Multisets and Fuzzy Multisets

Annals of Communications in Mathematics 2019

, 2 (2)

, 101-120

DOI: https://doi.org/10.62072/acm.2019.020205

AbstractThis paper is an attempt to summarize the basic concepts of the theories of multiset and fuzzy multiset. We begin by describing multisets and the operations between them with some related results. In the same vein, the basic concepts of fuzzy multiset theory as well as the operations between fuzzy multisets are buttressed in relation to multiset theory. Finally, we present some properties of fuzzy multisets with some related results.