• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• East Asian mathematical journal
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• 제23권1호
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• pp.45-58
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• 2007

The notions of IVF strongly semiopen (semiclosed) sets and IVF (strong) semi-interior (IVF (strong) semi-closure) are introduced, and several examples are provided. Related properties are investigated. In particular, characterizations of an IVF strongly semiopen set are discussed.

• 호남수학학술지
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• 제29권3호
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• pp.307-326
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• 2007

The aim of this paper is to introduce and study topological properties of semi-limit points, semi-derived, semi-interior, semi-closure, semi-border, and semi-frontier of a set using the concept of semi-open set.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권4호
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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.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.127-136
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• 2003

In this paper we obtain some properties of the weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and introduce the concepts of several types of $weak^*$ smooth compactness in smooth topological spaces and investigate some of their properties.

• 충청수학회지
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• 제35권2호
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• pp.103-113
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• 2022

The notions of soft rough pre open set, soft rough pre closed set, soft rough dense set, soft rough sub maximal, soft rough pre interior and soft rough pre closure are introduced and studied. We also investigate some related properties of these concepts.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.233-240
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• 2006

In this paper we introduce the concepts of several types of $weak^*$ quasi-smooth ${\alpha}$-compactness in terms of the concepts of weak smooth ${\alpha}$-closure and weak smooth ${\alpha}$-interior of a fuzzy set in smooth topological spaces and investigate some of their properties.

• 대한수학회논문집
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• 제25권2호
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• pp.273-282
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• 2010

The concept of intuitionistic fuzzy $\theta$-interior operator is introduced and discussed in intuitionistic fuzzy topological spaces. As applications of this concept, intuitionistic fuzzy strongly $\theta$-continuous, intuitionistic fuzzy $\theta$-continuous, and intuitionistic fuzzy weakly continuous functions are characterized in terms of intuitionistic fuzzy $\theta$-interior operator.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권3호
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• pp.217-229
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• 2004

In this paper, we introduce the concepts of interior of a fuzzy set and several types of fuzzy compactness and fuzzy RS-compactness in a redefined fuzzy topological space and investigate their properties.