• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.129-130
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• 2008

In this paper, we introduce the concept of generalized fuzzy (r,s)-closed sets on intuitionistic fuzzy topological spaces in ${\v{S}ostak's$ sense. Using this concept, we introduce the notions of generalized fuzzy (r,s)-continuous mappings, and then we investigate some of their properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.95-100
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• 1996

In this paper, we first introduce fuzzy less strongly irresolute, fuzzy preless strongly semiopen and fuzzy pre-less strongly semiclosed mappings on fuzzy topological space, and establish their various characteristic properties. Finally, we introduce and study fuzzy less strongly semi-connectedness with the help of fuzzy less strongly semiopen sets and fuzzy less strongly semi-q-neighborhoods.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.299-303
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• 2006

In this paper, we introduce the concepts of fuzzy strongly (r, s)-semiopen sets and fuzzy strongly (r, s)-semicontinuous mappings on the intuitionistic fuzzy topological space in Sostak's sense and then we investigate some of their characteristic properties.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.685-691
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• 2012

We define and characterize a somewhat fuzzy precontinuous mapping and a somewhat fuzzy preopen mapping on a fuzzy topological space. Besides, some interesting properties of those mappings are given.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1077-1084
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• 2012

We define and characterize a somewhat fuzzy pre-irresolute continuous mapping and a somewhat fuzzy irresolute preopen mapping on a fuzzy topological space. Besides, some interesting properties of those mappings are given.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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• pp.406-411
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• 2008

In this paper, we introduce the concept of fuzzy (r, s)-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense. The concepts of fuzzy (r, s)-pre-semineighborhood and fuzzy (r, s)-quasi-pre-semineighborhood are given. The characterizations for the fuzzy (r, s)-pre-semicontinuous mappings are obtained. Also, we introduce the notions of fuzzy (r, s)-pre-semiopen and fuzzy (r, s)-pre-semiclosed mappings, and then we investigate some of their characteristic properties.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.711-738
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• 2010

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.277-285
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• 2001

The purpose of this paper is to give a proof of a generalized convex-valued selection theorem which is given by weakening a Banach space to a completely metrizable locally convex topological vector space, i.e., a Frechet space. We also develop the properties of upper semi-continuous singlevalued mapping to those of upper semi-continuous multivalued mappings. These properties wil be applied in our further consideraations of selection theorems.

• East Asian mathematical journal
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• v.22 no.2
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• pp.131-149
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• 2006

In this paper we introduce the concept of $\gamma$-preopen sets in a topological space together with its corresponding $\gamma$-preclosure and $\gamma$-preinterior operators and a new class of topology $\tau_{{\gamma}p}$ which is generated by the class of $\gamma$-preopen sets. Also we introduce $\gamma$-pre $T_i$ spaces(i=0, $\frac{1}{2}$, 1, 2) and study some of its properties and we proved that if $\gamma$ is a regular operation, then$(X,\;{\tau}_{{\gamma}p})$ is a $\gamma$-pre $T\frac{1}{2}$ space. Finally we introduce $(\gamma,\;\beta)$-precontinuous mappings and study some of its properties.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.723-736
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• 1999

The paper is devoted to generalizations of continuity of set-valued mappings and some properties of hypertopologies on the collection of some subsets of a topological space. It is also dedicated to continuous selection theorems without relatively higher separation axioms. More precisely, we give characterizations of $\lambda$-collectionwise normality using continuous functions as in Michael's papers.