• Korean Journal of Mathematics
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• 제27권2호
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• pp.475-485
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• 2019

In this paper, we introduced the notions of right and left closure systems on generalized residuated lattices. In particular, we study the relations between right (left) closure (interior) operators and right (left) closure (interior) systems. We give their examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권4호
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• pp.299-304
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• 2011

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권1호
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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.

• Korean Journal of Mathematics
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• 제14권1호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제15권1호
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• pp.39-41
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• 1976

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권3호
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• pp.221-227
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• 2008

We introduce and study the new concepts of interior and closure operators on strong generalized neighborhood spaces. Also we introduce and investigate the concept of sgn-continuity on SGNS.

• East Asian mathematical journal
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• 제21권1호
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• pp.27-39
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• 2005

We will define p-stack convergence spaces and show that each neighborhood structure is uniquely determined by p-stack convergence structure. Also, we will show that p-stack convergence spaces are a generalization of neighborhood spaces.

• 한국지능시스템학회논문지
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• 제23권1호
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• pp.80-86
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• 2013

We give a new definition of ordinary smooth closure and ordinary smooth interior of an ordinary subset in an ordinary smooth topological space which have almost all the properties of the corresponding operators in a classical topological space. As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.243-252
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• 2018

In this paper, we study the sequentially open and closed subsets of sequential topological groups determined by sequentially continuous group homomorphism. In particular, we investigate the sequentially openness (closedness) and sequentially compactness of subsets of sequential topological groups by the aid of sequentially continuity, sequentially interior or closure operators. Moreover, we explore subgroup and sequential quotient group of a sequential topological group.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권3호
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• pp.230-241
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• 2010

In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.