• Korean Journal of Mathematics
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• 제4권2호
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• pp.135-140
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• 1996

We introduce the concepts of fuzzy $s$-open functions, and $s$-closed functions. And we investigate several properties of such functions. In particular, we study the relation between fuzzy $s$-continuous maps and fuzzy $s$-open maps( $s$-closed maps).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권1호
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• pp.49-57
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• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• Korean Journal of Mathematics
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• 제15권1호
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• pp.27-37
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• 2007

In this paper, we introduce the concepts of r-semi-generalized fuzzy closed sets, r-semi-generalized fuzzy open sets, r-semi-generalized fuzzy continuous maps in fuzzy topological spaces and investigate some of their properties.

• 대한수학회보
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• 제39권3호
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• pp.441-453
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• 2002

We introduce the concepts of fuzzy r-regular open sets and fuzzy almost r-continuous maps in the fuzzy topology of Chat-topadhyay. Also we investigate the equivalent conditions of the fuzzy almost r-continuity.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.364-369
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• 1998

In this paper, we introduce the notions of fuzzy ${\gamma}$-regular open sets and fuzzy almost ${\gamma}$-continuous maps, and investigate some of their basic properties.

• East Asian mathematical journal
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• 제33권5호
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• pp.483-494
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• 2017

In this paper we define new types of mappings known as $gpr^{\mu}$-closed mappings, $gpr^{\mu}$-open mappings and discuss its properties. Furthermore we introduce the concepts of supra $pre^*$-normal spaces and also investigate its properties.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.225-230
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• 1998

In this paper, we introduce the concepts of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topogical spaces.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.291-300
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• 2008

In this paper, we introduce several types of r-semi-generalized fuzzy compactness and fuzzy r-compactness in fuzzy topological spaces and investigate the relations between these compactness.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권1호
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• pp.59-63
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• 2005

In this paper, we introduce the concept of fuzzy m-sets induced by a given fuzzy supratopology and investigate general properties of the new class consisted of fuzzy m-sets. We also introduce notions of fuzzy m-continuity, fuzzy m-open(closed) maps and study some properties of them.

• 대한수학회지
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• 제60권2호
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.