An extended characterization of fuzzy bags

Abstract

The algebraic structures known as bags were introduced by R. Yager as set-like algebraic structures where elements are allowed to be repeated. Since the original papers by Yager, different definitions of the concept of fuzzy bag, and the corresponding operators, are available in the literature, as well as some extensions of the union, intersection and difference operators of sets, and new algebraic operators.In general, the current definitions of bag pose very interesting issues related to the ontological aspects and practical use of bags. In this paper, we introduce a characterization of bags viewing them as the result of a count operation on the basis of a mathematical correspondence. We also discuss on the extension of our alternative characterization of bags to the fuzzy case. On these basis, we introduce some operators on bags and fuzzy bags, and we compare them to existing approaches. Finally, we deal with the case where no information about the correspondence is available, and only bounds can be provided for the count of elements of the result of algebraic operators. For this purpose, the notion of IC-bag (Chakrabarty, in: Proc.

On Algebraic Structure of L-Fuzzy Bags

“…However, we prefer to keep the notation for bags as proposed in Refs. and due to the higher transparency and link to the original notion of bags given in Ref. .…”

“…In this subsection, some basic concepts of bags, which are needed in the rest of the paper, are given; for more details, see Refs. and . Definition Let P and O be two universes (sets) called “properties” and “objects,” respectively.…”

“…Example Let John, Ana, Bill, Tom, Sue, Stan, Ben} and be the set of objects and the set of properties, respectively. Let be the functions in Table with .…”

A study on firerings

“…Firesets and fuzzy firesets have been applied in many areas such as in multicriteria decision making, statistics, data based system, biological system etc [19,21,24,25,27,29]. More works on fireset can be found in [3,[5][6][7][8][9][10][11][12][13]17]. Group theory plays a vital role in algebraic theory.…”

The notion of intuitionistic fuzzy IC-bags

“…2 Bags, Fuzzy Bags, and IC-Bags: An Overview This section presents an overview of the notions of Bags, Fuzzy Bags, and IC-Bags as presented in [16,14,15,13,5,4,6,9,12,17].…”