• Korean Journal of Mathematics
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• v.24 no.1
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• pp.27-40
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• 2016

In this paper, we introduce the concepts of interval-valued intuitionistic gradation of openness of fuzzy sets which is a generalization of intuitionistic gradation of openness of fuzzy sets and interval-valued intuitionistic gradation preserving mapping and then investigate their properties.

• The Pure and Applied Mathematics
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• v.13 no.2 s.32
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• pp.71-94
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• 2006

In this paper we study lattice valued fuzzy gradation of openness so that fuzzy gradation of openness [13] could be obtained as a particular case. Some of its properties are studied. We also give definitions of lattice valued graded fuzzy filters, graded, fuzzy grills, graded fuzzy preproximities and proximities.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.725-729
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• 2009

In this paper, we introduce the concepts of intuitionistic fuzzy generalized topological spaces and intuitionistic gradation of generalized openness. We also introduce the concepts of IFG-mapping, weak IFG-mapping and IFG-open mapping, and obtain some characterizations for such mappings.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.75-91
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• 2005

The main objective of this paper is to introduce the gradation of neigh-bourhoodness in L-fuzzy topology and to introduce the fuzziness in the concept of convergence of L-fuzzy nets.

• 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.

• 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.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.47-69
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• 2006

In this paper, an idea of graded fuzzy net is introduced; its convergence is studied; Relations between g-net and g-filter are established in L-fuzzy setting.

• 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.

• 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.