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

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.249-254
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• 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
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• v.14 no.2 s.36
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• pp.63-70
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• 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
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• v.14 no.3
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• pp.231-239
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• 2014

It presents the concepts of ordinary smooth interior and ordinary smooth closure of an ordinary subset and their structural properties. It also introduces the notion of ordinary smooth (open) preserving mapping and addresses some their properties. In addition, it develops the notions of ordinary smooth compactness, ordinary smooth almost compactness, and ordinary near compactness and discusses them in the general framework of ordinary smooth topological spaces.

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

• East Asian mathematical journal
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• v.23 no.2
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• pp.213-227
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• 2007

In this paper the concept of fuzzy nearly C-compactness is introduced in Generalized fuzzy topological spaces. Several characterizations and some interesting properties of these spaces in Generalized fuzzy topological spaces are discussed. The properties of fuzzy almost continuous and fuzzy almost open functions in Generalized fuzzy topological spaces are also studied.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.125-133
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• 2013

In this paper, we introduce the notion of near pairwise compactness which generalizes the notion of pairwise compactness.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.557-566
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• 2008

In this paper, we introduce the concept of IVF weakly continuity and investigate some characterizations for IVF weakly continuous mappings on the interval-valued fuzzy topological spaces. We introduce and study the concepts of almost IVF compactness and nearly IVF compactness.

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

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.661-690
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• 2019

The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-$Lindel{\ddot{o}}fness$, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi-$Lindel{\ddot{o}}fness$. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-$Lindel{\ddot{o}}f$ spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.