• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.263-271
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\beta}$-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy $r-M$ ${\beta}$-continuous mapping which is a generalization of fuzzy $r-M$ continuous mapping and fuzzy $r-M$ semicontinuous mapping, and investigate characterization for the continuity.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.569-573
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• 2010

We introduce the concept of fuzzy r-minimal preopen set on a fuzzy minimal space. We also introduce the concept of fuzzy r-M precontinuous mapping which is a generalization of fuzzy r-M continuous mapping, and investigate characterization of fuzzy r-M precontinuity.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.475-484
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• 2005

The main aim of this paper is to consider the fuzzy norm, define the fuzzy Banach spaces, its quotients and prove some theoremes and in particular Open mapping and Closed graph theoremes on these spaces.