• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.167-189
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• 2007

In this paper we define a topology (analogous to Chang-type fuzzy topology) and a fuzzy topology (analogous to $H\"{o}hle-type$ fuzzy topology) associated with a lattice and study some of their properties.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.99-107
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• 2010

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.323-331
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• 2004

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.113-126
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• 1997

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen's fuzzy topology and show that the category of Lowen's fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.848-851
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• 2010

In this paper, we introduce the concept of fuzzy quasi topologies which are generalizations of smooth topologies and Chang's fuzzy topologies, and obtain some basic properties of their structures.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.1
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• pp.79-86
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• 2015

This paper is devoted to finding relationship between intuitionistic fuzzy preorders and intuitionistic fuzzy topologies. For any intuitionistic fuzzy preordered space, an intuitionistic fuzzy topology will be constructed. Conversely, for any intuitionistic fuzzy topological space, we obtain an intuitionistic fuzzy preorder on the set. Moreover, we will show that the family of all intuitionistic fuzzy preorders on an underlying set has a very close link to the family of all intuitionistic fuzzy topologies on the set satisfying some extra condition.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.29-34
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• 2005

The aim of this paper is to introduce fuzzy γ-continuity and fuzzy γ-retracts in a fuzzy topology on fuzzy sets and establish some of their properties. Also, the relations between these new concepts are discussed.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.325-340
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• 2003

We introduce a fuzzy g-closure operator induced by a fuzzy topological space in view of the definition of Sostak [13]. We show that it is a fuzzy closure operator. Furthermore, it induces a fuzzy topology which is finer than a given fuzzy topology. We investigate some properties of fuzzy g-closure operators.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.357-368
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• 2012

We introduce the concepts of fuzzy ${\delta}$-interior and show that the set of all fuzzy ${\delta}$-open sets is also a fuzzy topology, which is called the fuzzy ${\delta}$-topology. We obtain equivalent forms of fuzzy ${\delta}$-continuity. More-over, the notions of fuzzy ${\delta}$-compactness and fuzzy locally ${\delta}$-compactness are defined and their basic properties under fuzzy ${\delta}$-continuous mappings are investigated.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.404-407
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• 2009

In this paper, we introduce the concept of fuzzy generalized topologies which are generalizations of smooth topologies and Chang's fuzzy topologies and obtain some basic properties of their structure. Also we introduce and study the concepts of fuzzy generalized continuity and weakly fuzzy generalized continuity.