Intuitionistic Fuzzy Ideals on Approximation Systems

Information Sciences, 2016

In this paper we deal with the theory of rough ideals started in [4]. We show that the approximation spaces built from an equivalence relation compatible with the ring structure, i.e. associated to a two-sided ideal, are too naive in order to develop practical applications. We propose the use of certain crisp equivalence relations obtained from fuzzy ideals. These relations make available more flexible approximation spaces since they are enriched with a wider class of rough ideals. Furthermore, these are fully compatible with the notion of primeness (semiprimeness). The theory is illustrated by several examples of interest in Engineering and Mathematics.

Journal of the Egyptian Mathematical Society

In this paper, we defined the fuzzy upper, fuzzy lower, and fuzzy boundary sets of a rough fuzzy set λ in a fuzzy approximation space (X, R). Based on λ and R, we introduced the fuzzy ideal approximation interior operator intlambda R and the fuzzy ideal approximation closure operator cl R λ. We joined the fuzzy ideal notion with the fuzzy approximation spaces, and then introduced the fuzzy ideal approximation closure and interior operators associated to a rough fuzzy set λ. Fuzzy ideal approximation connectedness and the fuzzy ideal approximation continuity between fuzzy ideal approximation spaces are introduced.

Journal of Intelligent & Fuzzy Systems

In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator int Φ λ and the fuzzy ideal approximation closure operator cl Φ λ , and moreover, we define the fuzzy ideal approximation preinterior operator p int Φ λ and the fuzzy ideal approximation preclosure operator p cl Φ λ with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set λ ∈ IX. Also, we define fuzzy separation axioms, fuzzy connectedness and fuzzy compactness in fuzzy approximation spaces and in fuzzy ideal approximation spaces as well, and prove the implications in between.

2006 3rd International IEEE Conference Intelligent Systems, 2006

The notion of intuitionistic fuzzy approximation space is introduced. Rough sets on such spaces are defined and some of their properties are studied.

Transstellar Journal , 2019

In this paper, we introduce the concept of-intuitionistic fuzzy ideal and-intuitionistic fuzzy ideal and study their properties.

In this paper we define rough intuitionistic fuzzy sets (analogous to the definition of rough fuzzy sets introduced by Dubois and Prade [8] ) and study their properties. Some propositions in this notion are proved.

Iranian Journal of Fuzzy Systems, 2022

Since Pawlak defined the notion of rough sets in 1982, many authors made wide research studying rough sets in the ordinary case and the fuzzy case. This paper introduced a new style of rough fuzzy sets based on a fuzzy ideal ℓ on a universal finite set X. New lower and new upper fuzzy sets are introduced, and consequently, fuzzy interior and fuzzy closure operators of a rough fuzzy set are discussed. These definitions, if ℓ is restricted to ℓ • = {0}, imply the fuzzification of previous definitions given in the ordinary case, and moreover in the crisp case, we get exactly these previous definitions. The new style gives us a better accuracy value of roughness than the previous styles. Rough fuzzy connectedness is introduced as a sample of applications on the recent style of roughness.

Journal of Intelligent & Fuzzy Systems, 2019

In this paper, an in depth study is done on topological properties of intuitionistic fuzzy rough sets in light of different conditions like serial, strongly serial, left continuity, transitivity on intuitionistic fuzzy relations, t-norms, implicators by adopting a axiomatic approach with the ingredients of intuitionistic fuzzy logic. Numerous intuitionistic fuzzy topologies based on many different kinds of intuitionistic fuzzy relations are explored. Also, a special class of intuitionistic fuzzy relations known as T-similarity class has been studied algebraically and found interesting lattices to model real life problems for better applications of intuitionistic fuzzy rough sets.

INTERNATIONAL CONFERENCE ON RECENT TRENDS IN PURE AND APPLIED MATHEMATICS (ICRTPAM-2021)

Rough set theory offers a new mathematical method for inadequate understanding. In this way, ambiguity is conveyed by a boundary area which can be defined using algebraic operator union and intersection which are known as approximations. In this paper, we study some properties of rough fuzzy ideals of-ring and prove some results on these.

The concept of fuzzy approximation space that depends on a fuzzy proximity relation is a generalization of the concept of the knowledge base. But intuitionistic fuzzy approximation space that depends on an intuitionistic fuzzy proximity relation is a better generalization of the concept of knowledge base than fuzzy approximation space. Therefore, rough sets defined on intuitionistic fuzzy approximation spaces extend the concept of rough sets on fuzzy approximation spaces. This paper presents how rough sets on intuitionistic fuzzy approximation spaces provides better result over rough sets on fuzzy approximation spaces on knowledge representation. Index Terms: Fuzzy relation, fuzzy proximity relation, fuzzy approximation space, intuitionistic fuzzy approximation space and rough set.