• Korean Journal of Mathematics
• /
• v.16 no.3
• /
• pp.291-300
• /
• 2008

In this paper, we introduce several types of r-semi-generalized fuzzy compactness and fuzzy r-compactness in fuzzy topological spaces and investigate the relations between these compactness.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.5
• /
• pp.614-620
• /
• 2003

The aim of this paper is to introduce good definitions of compactness, almost compactness, near compactness, weak compactness, and S-closedness in fuzzy topological spaces in Sostak s sense. These compactness related concepts are defined for arbitrary fuzzy sets and some of their properties studied.

• The Pure and Applied Mathematics
• /
• v.11 no.3
• /
• pp.217-229
• /
• 2004

In this paper, we introduce the concepts of interior of a fuzzy set and several types of fuzzy compactness and fuzzy RS-compactness in a redefined fuzzy topological space and investigate their properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.41-44
• /
• 2003

First, we investigate some properties of fuzzy compactness. Second, we introduce the concept of fuzzy local compactness in fuzzy topological space and study some of its properties. Finally, we investigate some relations between F-compactness in fuzzy topological spaces and one in fuzzy hyperspaces.

• Korean Journal of Mathematics
• /
• v.13 no.2
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.14 no.2 s.36
• /
• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.13 no.3
• /
• pp.224-230
• /
• 2013

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy ${\theta}$-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy ${\theta}$-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy ${\theta}$-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy ${\theta}$-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.4
• /
• pp.281-284
• /
• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• Korean Journal of Mathematics
• /
• v.24 no.4
• /
• pp.663-679
• /
• 2016

In this paper, we introduce the concepts of several types of interval-valued intuitionistic fuzzy mappings and several types of interval-valued intuitionistic fuzzy compactness in interval-valued intuitionistic smooth topological spaces and then investigate their properties.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.359-370
• /
• 2002

The purpose of this paper is to introduce and discuss the concept of $\beta$-compactness for L-fuzzy topological spaces.