Fuzzy Multisets and Fuzzy Computing

Abstract

Multisets and Multirelations are extensions of ordinary sets and relations while fuzzy multisets and fuzzy multirelations are fuzzy extensions of these concept. Although many generalizations tend to be meaningless, these are quite useful as one can model things we see every day. In addition, these structures have found uses in the theory of computation. In particular, fuzzy multisets are used in fuzzy models of computation, that is, models of computation where vagueness is manifested by fuzzy sets play central role. These fuzzy models of computation include fuzzy P systems, the fuzzy chemical abstract machine, and fuzzy Petri nets.

Synopsis of the Notions of Multisets and Fuzzy Multisets

“…This section discusses some basic definitions in fuzzy multiset theory, its representations and operations. We review fuzzy multiset theory [2,24,23,12,33,35] and thereby deduce some relevant results.…”

“…Some fundamentals of fuzzy multiset theory. The ideas in this subsection are taken from [2,24,23,12,33,35] with lucid explanations. Definition 3.1.…”

“…An outline on the development of the concept of fuzzy multisets can be found in [27]. More studies on the theory of fuzzy multisets have been carried out in literature as seen in [6,13,14,19,33]. The idea of fuzzy mutisets is very applicable in real-life problems, like in data analysis, decision making, clustering, information retrieval, flexible querying, etc [1,2,15,16,17,24,23,25,26].…”

On Some Algebraic Structures of Type 2 Fuzzy Multisets

“…In the 20th century, mathematicians formalized multisets and began to study them as a precise mathematical structure. The development of multiset theory can be seen in (Blizard, 1989;Bedregal, Beliakor, Bustince, Calvo, Mesiar & Paternain, 2012;Girish & John, 2012;Syropoulos, 2016). Compared to other traditional structures the hybrid structure of type 2 fuzzy multiset is an effective method which provide additional degrees of freedom to present the vagueness and uncertainty of the real world and sustain a realistic evaluation (Paul & John, 2015).…”