• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.258-261
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• 2003

The aim of this paper is to introduce the concept $\gamma$-connectedness in fuzzy topological spaces. We also investigate some interre lations between this types of fuzzy connectedness together with the preservation properties under some types of fuzzy continuity. A comparison between some types of connectedness in fuzzy topological spaces is of interest.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.63-76
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• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the 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 topological spaces.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.237-248
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• 2023

The aim of this paper is to study the concept of s-topological d-algebras which is a d-algebra supplied with a certain type of topology that makes the binary operation defined on it d-topologically continuous. This concept is a generalization of the concept of topological d-algebra. We obtain several properties of s-topological d-algebras.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.79-84
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• 2022

We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T₁-connected fuzzy topological spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.1
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• pp.80-86
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• 2013

We give a new definition of ordinary smooth closure and ordinary smooth interior of an ordinary subset in an ordinary smooth topological space which have almost all the properties of the corresponding operators in a classical topological space. As a consequence of these definitions we reduce the additional hypotheses in the results of [1] and also generalize several properties of the types of compactness in [1].

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.6
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• pp.799-805
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• 2012

We introduce the notions of ordinary smooth, quasi-ordinary smooth and weak ordinary smooth structure, showing that various properties of an ordinary smooth topological space can be expressed in terms of these structures. In particular, the definitions and results of [2, 4, 5] may be expressed in terms of the ordinary smooth and quasi-ordinary smooth structures. Furthermore, we present the basic concepts relating to the weak ordinary smooth structure of an ordinary smooth topological space and the fundamental properties of the objects in these structures.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.5
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• pp.1-4
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• 1998

The main goal of this paper is to investigate some properties of the locally convex fuzzy topological vector space.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.825-838
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• 2021

In this paper the concept of ordered fuzzy filters is introduced in Heyting almost distributive lattices and the properties of these ordered fuzzy filters are studied. We characterized and proved a set of theorems of ordered fuzzy filters. Some topological properties of prime ordered fuzzy filters are also studied.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.1
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• pp.66-76
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• 2012

In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.