• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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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.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.174-179
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• 2003

Through the simultaneous localization and map building (SLAM) technique, a robot can create maps about its unknown environment while it continuously localizes its position. Grid maps and feature maps have been widely used for SLAM together with application of probability methods and POMDP (partially observed Markov decision process). But this approach based on grid maps suffers from enormous computational burden. Topological maps, however, have drawn more attention these days because they are compact, provide natural interfaces, and are easily applicable to path planning in comparison with grid maps. Some topological SLAM techniques like GVG (generalized Voronoi diagram) were introduced, but it enables the robot to decide only whether the current position is part of GVG branch or not in the GVG algorithm. In this paper, therefore, to overcome these problems, we present a method for updating a global topological map from the local topological maps. These local topological maps are created through a labeled Voronoi diagram algorithm from the local grid map built based on the sensor information at the current robot position. And the nodes of a local topological map can be utilized as the features of the environment because it is robust in light of visibility problem. The geometric information of the feature is applied to the extended Kalman filter and the SLAM in the indoor environment is accomplished. A series of simulations have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can be applied relatively well.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1561-1597
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• 2019

In this paper we introduce the notions of topological entropy and topological pressure for non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets. NAIFSs differ from the usual (autonomous) iterated function systems, they are given [32] by a sequence of collections of continuous maps on a compact topological space, where maps are allowed to vary between iterations. Several basic properties of topological pressure and topological entropy of NAIFSs are provided. Especially, we generalize the classical Bowen's result to NAIFSs ensures that the topological entropy is concentrated on the set of nonwandering points. Then, we define the notion of specification property, under which, the NAIFSs have positive topological entropy and all points are entropy points. In particular, each NAIFS with the specification property is topologically chaotic. Additionally, the ${\ast}$-expansive property for NAIFSs is introduced. We will prove that the topological pressure of any continuous potential can be computed as a limit at a definite size scale whenever the NAIFS satisfies the ${\ast}$-expansive property. Finally, we study the NAIFSs induced by expanding maps. We prove that these NAIFSs having the specification and ${\ast}$-expansive properties.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.301-310
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• 2016

In this paper, we introduce and study the concept of a new class of sets called paraopen sets and paraclosed sets in topological spaces. During this process some of their properties are obtained. Also we introduce and investigate a new class of maps called paracontinuous, *-paracontinuous, parairresolute, minimal paracontinuous and maximal paracontinuous maps and study their basic properties in topological spaces.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.793-806
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• 2002

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 Maps (SOM) provides a mapping from high dimensional feature vectors onto a two-dimensional space. The mapping preserves the topology of the feature vectors. The map is called topological feature map. 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. In topological feature map, there are empty nodes in which no image is classified. We experiment on the performance of our algorithm using color feature vectors extracted from images. Promising results have been obtained in experiments.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.307-313
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• 2005

The Lefschetz fixed point theorem is extended to compact continuous maps defined on an admissible subset of a Hausdorff topological space.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1309-1318
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• 2020

In this paper we extend the concept of topological stability from continuous maps to the corresponding induced maps and prove that a continuous map is topologically stable if and only if its induced map also is topologically stable.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.77-89
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• 2002

In this paper, we define for a component $X_{0}$ of a nonsingular compact real algebraic surface X the complex genus of $X_{0}$, denoted by gc($X_{0}$), and use this to prove the nonexistence of nonzero degree entire rational maps f : $X_{0}$ Y provided that gc(Y) > gc($X_{0}$), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.73-85
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• 1998

This paper deals with the topological stability of continuous maps. First, the notion of local expansion is given and we show that local expansions of compact metric spaces have the shadowing property. Also, we prove that if a continuous surjective map f is a local homeomorphism and local expansion, then f is topologically stable in the class of continuous surjective maps. Finally, we find homeomorphisms which are not topologically stable.