• 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.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.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.219-232
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• 2011

We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.4
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• pp.290-295
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• 2012

Due to importance of the concepts of ${\theta}$-closure and ${\delta}$-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy ${\delta}$-closure by using the concept of quasi-coincidence in fuzzy topological spaces. In this paper, we will introduce the concept of ${\delta}$-closure in intuitionistic fuzzy topological spaces, which is a generalization of the ${\delta}$-closure by Ganguly and Saha.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.231-239
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• 2014

It presents the concepts of ordinary smooth interior and ordinary smooth closure of an ordinary subset and their structural properties. It also introduces the notion of ordinary smooth (open) preserving mapping and addresses some their properties. In addition, it develops the notions of ordinary smooth compactness, ordinary smooth almost compactness, and ordinary near compactness and discusses them in the general framework of ordinary smooth topological spaces.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.336-344
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• 2013

In this paper, we characterize the intuitionistic fuzzy ${\delta}$-continuous, intuitionistic fuzzy weakly ${\delta}$-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly ${\theta}$-continuous functions in terms of intuitionistic fuzzy ${\delta}$-closure and interior or ${\theta}$-closure and interior.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.1
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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].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.4
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• pp.262-266
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• 2007

We characterize a fuzzy pairwise $\gamma$-irresolute continuous mapping on a fuzzy bitopological space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.188-192
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• 2007

We characterize a fuzzy pairwise ${\gamma}-irresolute$ continuous mapping on a fuzzy bitopological space.