• Honam Mathematical Journal
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• v.31 no.2
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• pp.239-245
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• 2009

In this paper, we introduce the notions of m-semiopen sets and M-semicontinuous functions on spaces with minimal structures and study some properties of such notions. In particular, we investigate characterizations for the M-semicontinuous function and the relationship between M-continuity and M-semicontinuity.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.31-43
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• 2009

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF m-precontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.848-851
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• 2009

In [5], we introduced the concepts of IVF m-semiopen sets and IVF m-semicontinuous mappings on interval-valued fuzzy minimal spaces. In this paper, we investigate some properties of IVF m-semiopen sets and characterizations for the IVF m-semicontinuous mapping.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.589-596
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• 2013

This paper is an attempt to study and introduce the notion of ${\omega}$-dense set in weak structures and the notion of m-dense set in minimal structures. We have also investigate the relationships between ${\omega}$-dense sets, $m$-dense sets, ${\sigma}({\omega})$ sets, ${\pi}({\omega})$ sets, $r({\omega})$ sets, ${\beta}({\omega})$ sets, m-semiopen sets and $m$-preopen sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.216-221
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• 2014

In this paper, we introduce the concept of generalized double fuzzy semi-basically disconnected space and related notions such as (r, s)-generalized fuzzy semiopen-$F_{\sigma}$ sets, (r, s)-generalized fuzzy semiclosed-$G_{\delta}$ sets, generalized double fuzzy $semi^*$-open function, generalized double fuzzy $semi^*$-continuous function and generalized double fuzzy $semi^*$-irresolute function. Some interesting properties and characterizations of the concepts introduced are studied.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.341-345
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• 2012

In this paper, we introduce the notions of minimal semicon-tinuity, strongly $m$-semiclosed graph, $m$-semiclosed graph, $m$-semi-$T_2$, $m$-semicompact and investigate some properties for such notions.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.603-611
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\alpha}$-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy $r$-M ${\alpha}$-continuous and fuzzy $r$-M($M^*$) ${\alpha}$-open mappings, and investigate characterization for such mappings.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.2
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• pp.250-253
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• 2011

In this paper, we study characterizations of fuzzy weakly r-M continuous function on r-minimal structures in terms of generalized fuzzy r-minimal open sets.