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Open AccessArticle

On Dynamic Multisets and their Operations

Annals of Communications in Mathematics 2021

, 4 (3)

, 284-292

DOI: https://doi.org/10.62072/acm.2021.040308

AbstractThe concept of multisets emerged by violating a principle of distinct collection of object in crisp sets. In some practical situations, multisets with multiplicity of their objects varying overtime are frequently encountered, such multisets are called dynamic multisets. However, there has been no formal mathematical study on dynamic multisets. Dynamic multiset is a special kind of multiset with time varying multiplicity of elements. The importance of dynamic multisets stems from their potential usefulness in resolving a task of finding duplicate records within large databases. In this paper, we vividly explore the concept of dynamic multisets and present some of its properties. We observe that, the operations on dynamic multisets are the same as that of static multisets, with the time parameter as the only distinction. Finally, some application-driven examples of dynamic multisets are presented.
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.