• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.8 no.2
• /
• pp.111-115
• /
• 2008

By generalizing the definition of fuzzy weakly semicontinuous mappings by B. S. Zhong, we introduce the concept of fuzzy weakly r-semicontinuous mappings in fuzzy topology of Chattopadhyay. Then the concept introduced by B. S. Zhong becomes a special case of our definition. Also, we show that fuzzy weakly r-semicontinuity and fuzzy weakly r-continuity are independent notions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.370-375
• /
• 1998

We introduce the concepts of fuzzy strongly ${\gamma}$-semiopen sets and fuzzy strongly ${\gamma}$-semicontinuous maps, and investigate some of their basic properties.

• Korean Journal of Mathematics
• /
• v.18 no.3
• /
• pp.261-269
• /
• 2010

We introduce the concept of fuzzy co-$r$-M-semicontinuous, and investigate the relationships between fuzzy co-$r$-M-semicontinuous mappings and several types of fuzzy $r$-minimal semicompactness.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2007.11a
• /
• pp.191-194
• /
• 2007

In this paper, we introduce the concepts of fuzzy (r,s)-pre-semiopen sets and fuzzy (r,s)-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in ${\v{S}}ostak's$ sense. The concepts of fuzzy (r,s)-pre-semiinterior, fuzzy (r,s)-pre-semiclosure, fuzzy (r,s)-pre-semineighborhood, and fuzzy (r,s)-quasi-pre-semineighborhood are given, and several properties of these concepts are discussed. Using these concepts, the characterizations for the fuzzy (r,s)-pre-semicontinuous mappings are obtained. Also, we introduce the notions of fuzzy (r,s)-presemiopen and fuzzy (r,s)-pre-semiclosed mappings on intuitionistic fuzzy topologica spaces in ${\v{S}}ostak's$ sense, and then we investigate some of their characteristic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.7 no.2
• /
• pp.120-126
• /
• 2007

In this paper, we investigate some of characteristic properties of fuzzy strongly (r, s)-semicontinuous, fuzzy strongly (r, s )-semiopen and fuzzy strongly (r, s )-semiclosed mappings on the intuitionistic fuzzy topological space in \check{S}ostak's$ sense.

• Journal of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.701-711
• /
• 2009

We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a nonrepresentable subset of the lexicographic plane and semicontinuous with respect to the metric topology.

• Korean Journal of Mathematics
• /
• v.6 no.1
• /
• pp.117-125
• /
• 1998

In this paper, we investigate some conditions which are equivalent to fuzzy $r$-homeomorphisms and give some characterizing theorems for fuzzy $r$-semicontinuous, $r$-semiopen and $r$-semiclosed maps.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.653-663
• /
• 2002

We introduce and investigate the concepts of ($(T_i,T_j)$-fuzzy $\alpha-(r.s)$-semiopen $\alpha-(r.s)$-semiclosed) sets and fuzzy pairwise $\alpha-(r.s)$-semicontinuous mappings in smooth bitopological spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.1 no.1
• /
• pp.62-68
• /
• 2001

In this paper, we introduce the concepts of fuzzy r-pre-semiopen and r-pre-semiclosed sets. With them we define fuzzy r-pre-semiinterior and r-pre-semiclosure. We also introduce and investigate the properties of a fuzzy r-pre-semicontinuous map, a fuzzy r-pre-semiopen map and a fuzzy r-pre-semiclosed map. These concepts are generalizations of the Bai Shi-Zhongs fuzzy pre-semicontinuity.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.12 no.3
• /
• pp.269-274
• /
• 2002

We introduce (${\tau}_i$, ${\tau}_j$) fuzzy (r,s)-semiclosures and (${\tau}_i$, ${\tau}_j$)-fuzzy (r,s)-semiinteriors. Using the notions, we investigate some of characteristic properties of fuzzy pairwise (r,s)-semicontinuous, fuzzy pairwise (r,s)-semiopen and fuzzy pairwise (r,s)-semiclosed mappings.