• 충청수학회지
• /
• 제36권2호
• /
• pp.135-148
• /
• 2023

We prove that for any preordered intuitionistic fuzzy approximation space, an intuitionistic fuzzy topology can be created, and conversely, for any intuitionistic fuzzy topology, a reflexive intuitionistic fuzzy relation can be constructed. We also show that there is a relationship, called Galois correspondence, between the functors of these categories. Additionally, by applying certain limitations on the category of intuitionistic fuzzy topological spaces, we obtain an isomorphism between these categories.

• Korean Journal of Mathematics
• /
• 제13권2호
• /
• pp.249-254
• /
• 2005

In this paper, we introduce the concepts of intuitionistic fuzzy half-compactness, nearly intuitionistic fuzzy half-compactness and almost intuitionistic fuzzy half-compactness defined by intuitionistic gradations of openness, and obtain some characterizations.

• 한국지능시스템학회논문지
• /
• 제19권1호
• /
• pp.128-132
• /
• 2009

Sostak개념의 intuitionistic fuzzy topological space에서 fuzzy S-weakly (r,s)-continuous mapping의 개념과 연산을 소개하며 기본적인 성질을 조사한다.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제14권2호
• /
• pp.63-70
• /
• 2007

In this paper, we introduce the concepts of r-gp-open map, weakly r-gp-open map, intuitionistic fuzzy r-compactness, nearly intuitionistic fuzzy r-compactness and almost intuitionistic fuzzy r-compactness defined by intuitionixtic gradations of openness, and obtain some characterizations.

• 한국지능시스템학회논문지
• /
• 제16권1호
• /
• pp.108-112
• /
• 2006

In this paper, we investigate some characterizing theorems for fuzzy (r,s)-semicontinuous, (r,s)-semiopen and (r,s)-semiclosed mappings on the intuitionistic fuzzy topological space in $\eseck{S}ostak's$ sense.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제8권4호
• /
• pp.312-315
• /
• 2008

In this paper, we investigate some characterizations for fuzzy weakly (r, s)-continuous mapping on an intuitionistic fuzzy topological space in ${\check{S}}ostak's$ sense.

• Journal of applied mathematics & informatics
• /
• 제40권1_2호
• /
• pp.85-98
• /
• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• 한국지능시스템학회논문지
• /
• 제20권6호
• /
• pp.875-883
• /
• 2010

We introduce the concept of intuitionistic smooth topology in Lowen's sense and we prove that the family IST(X) of all intuitionistic smooth topologies on a set is a meet complete lattice with least element and the greatest element [Proposition 3.6]. Also we introduce the notion of level fuzzy topology on a set X with respect to an intuitionistic smooth topology and we obtain the relation between the intuitionistic smooth topology $\tau$ and the intuitionistic smooth topology $\eta$ generated by level fuzzy topologies with respect to $\tau$ [Theorem 3.10].

• Korean Journal of Mathematics
• /
• 제14권1호
• /
• pp.57-64
• /
• 2006

In this paper, we introduce the concepts of $r$-closure and $r$-interior defined by intuitionistic gradation of openness. We also introduce the concepts of $r$-gp-maps, weakly $r$-gp-maps, and obtain some characterizations in terms of $r$-closure and $r$-interior operators.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제11권4호
• /
• pp.254-258
• /
• 2011

In this paper, we introduce the notion of fuzzy (r, s)-S1-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense, which is a generalization of $S_1$-pre-semicontinuous mappings by Shi-Zhong Bai. The relationship between fuzzy (r, s)-pre-semicontinuous mapping and fuzzy (r, s)-$S_1$-pre-semicontinuous mapping is discussed. The characterizations for the fuzzy (r, s)-$S_1$-pre-semicontinuous mappings are obtained.