• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.2
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• pp.187-191
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• 2002

In this paper, we introduce the notion of smooth neighborhoods in smooth topological spaces and investigate some of their properties. In particular, we can obtain some smooth topologies from a smooth neighborhood system.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.287-300
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• 2020

We introduce and study notions of expansivity, topological stability and persistence for Borel measures with respect to time varying bi-measurable maps on metric spaces. We prove that on Mandelkern locally compact metric spaces expansive persistent measures are topologically stable in the class of all time varying homeomorphisms.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.837-851
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• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.341-348
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• 2013

In this paper, the concept of supra $b$-irresolute maps is introduced and several properties of it is investigated. Furthermore, the notion of supra $b$-connectedness is defined and researched by means of supra $b$-separated sets.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.33-40
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• 1996

A convergence structure defined by Kent [4] is a correspondence between the filters on a given set X and the subsets of X which specifies which filters converge to points of X. This concept is defined to include types of convergence which are more general than that defined by specifying a topology on X. Thus, a convergence structure may be regarded as a generalization of a topology. With a given convergence structure q on a set X, Kent [4] introduced associated convergence structures which are called a topological modification and a pretopological modification. (omitted)

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.305-320
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• 2011

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of $\v{S}$ostak's I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.265-281
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• 2021

In the kneading theory developed by Milnor and Thurston, it is proved that the kneading matrix and the kneading determinant associated with a continuous piecewise monotone map are invariant under orientation-preserving conjugacy. This paper considers the problem for orientation-reversing conjugacy and proves that the former is not an invariant while the latter is. It also presents applications of the result towards the computational complexity of kneading matrices and the classification of maps up to topological conjugacy.

• The KIPS Transactions:PartB
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• v.8B no.5
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• pp.515-522
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• 2001

Feature-based similarity retrieval become an important research issue in image database systems. The features of image data are useful to discrimination of images. In this paper, we propose the highspeed k-Nearest Neighbor search algorithm based on Self-Organizing Maps. Self-Organizing Map(SOM) provides a mapping from high dimensional feature vectors onto a two-dimensional space. A topological feature map preserves the mutual relations (similarity) in feature spaces of input data, and clusters mutually similar feature vectors in a neighboring nodes. Each node of the topological feature map holds a node vector and similar images that is closest to each node vector. We implemented about k-NN search for similar image classification as to (1) access to topological feature map, and (2) apply to pruning strategy of high speed search. We experiment on the performance of our algorithm using color feature vectors extracted from images. Promising results have been obtained in experiments.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.