Notion of Fuzzy Ic-Bags

Abstract

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

The notion of intuitionistic fuzzy IC-bags

“…In this section, we briefly present the notion of Fuzzy IC Bags as presented in [8]. Thus for any ω ∈ R, ξ φ (ω) is an IC-Bag drawn from I.…”

“…This generalization was based on Atanassov's notion of intuitionistic fuzzy sets [1,2]. Chakrabarty proposed the notion of Fuzzy Bags with Interval Counts (Fuzzy IC-Bags) in [8] which generalizes the notion of IC-Bags [4].…”

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.…”

On B-groups

“…On the contrary, a bag is a type of collection in which redundancy of objects is not only allowed, but it also plays a key role in determining the behaviour of the objects [9], [7], [15], [12], [2], [8], [4]. Some algebraic structures like the group, semigroup, abelian group, etc.…”