• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.219-232
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• 2004

We study relationships between closure operators and BL-algebras. We investigate the properties of closure operators and BL-homomorphisms on BL-algebras. We show that the image of a closure operator on a BL-algebra is isomorphic to a quotient BL-algebra.

• Korean Journal of Mathematics
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• v.27 no.2
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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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• 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.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.621-627
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• 2012

Star operations are defined by R. E. Hodel in 1994. In this paper some relations among star operators, sequential closure operators and closure operators are discussed. Moreover, we introduce an induced topology by a family of subsets of a space, and some interesting results about star operators are established by the induced topology.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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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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• 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.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.205-210
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• 2001

We give a characterization of regular operators that allows us to prove that a bounded operator acting between Banach spaces is almost regular if and only if it is regular, solving an open problem in [5]. As an application, we show that some operators in the closure of the set of all regular operators are regular.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.4
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• pp.404-410
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• 1999

We will prove the existence of initial fuzzy closure structures. From this fact we can define subspaces and products of fuzzy closure spaces. Furthermore the family $\Delta$(X) of all fuzzy closure operators on X is a complete lattice. In particular an initial structure of fuzzy topological spaces can be obtained by the initial structure of fuzzy closure spaces induced by those. We suggest some examples of it.