• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.325-340
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• 2003

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.35-51
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• 2004

We introduce fuzzy closure systems and fuzzy closure operators as extensions of closure systems and closure operators. We study relationships between fuzzy closure systems and fuzzy closure spaces. In particular, two families F(S) and F(C) of fuzzy closure systems and fuzzy closure operators on X are complete lattice isomorphic.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.57-64
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• 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
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• v.15 no.1
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• pp.72-78
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• 2015

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.791-801
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• 2005

In this paper, we introduce the concepts of closure and interior defined by an intuitionistic gradation of openness. We also introduce the concepts of weakly gp-maps, gp-open maps and several types of compactness, and obtain some characterizations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.1
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• pp.37-41
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• 2008

In this paper, we investigate the properties of implicative closure operators on the stsc-quantale L. We find implicative closure operators induced by a function.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.177-183
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• 2004

In this paper, we introduce the concepts of half-interior, half-closure, half-gp-maps and half-gp-open maps defined by intuitionistic gradations of openness.