• Korean Journal of Mathematics
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• v.13 no.2
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• pp.249-254
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• 2005

In this paper, we introduce the concepts of intuitionistic fuzzy half-compactness, nearly intuitionistic fuzzy half-compactness and almost intuitionistic fuzzy half-compactness defined by intuitionistic gradations of openness, and obtain some characterizations.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.57-64
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• 2006

In this paper, we introduce the concepts of $r$-closure and $r$-interior defined by intuitionistic gradation of openness. We also introduce the concepts of $r$-gp-maps, weakly $r$-gp-maps, and obtain some characterizations in terms of $r$-closure and $r$-interior operators.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.49-54
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• 1997

In this paper we study the generalized Reidemeister number $R({\varphi},{\psi})$ for a self-map $({\varphi},{\psi}):(X,G){\rightarrow}(X,G)$ of a transformation group (X, G), as an extension of the Reidemeister number $R(f)$ for a self-map $f:X{\rightarrow}X$ of a topological space X.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.67-75
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• 1984

Let X be a topological space. We consider a groupoid G over X and the quotient groupoid G/N for any normal subgroupoid N of G. The concept of groupoid (topological groupoid) is a natural generalization of the group(topological group). An useful example of a groupoid over X is the foundamental groupoid .pi.X whose object group at x.mem.X is the fundamental group .pi.(X, x). It is known [5] that if X is locally simply connected, then the topology of X determines a topology on .pi.X so that is becomes a topological groupoid over X, and a covering space of the product space X*X. In this paper the concept of the locally simple connectivity of a topological space X is applied to the groupoid G over X. That concept is defined as a term '1-connected local subgroupoid' of G. Using this concept we topologize the groupoid G so that it becomes a topological groupoid over X. With this topology the connected groupoid G is a covering space of the product space X*X. Further-more, if ob(.overbar.G)=.overbar.X is a covering space of X, then the groupoid .overbar.G is also a covering space of the groupoid G. Since the fundamental groupoid .pi.X of X satisfying a certain condition has an 1-connected local subgroupoid, .pi.X can always be topologized. In this case the topology on .pi.X is the same as that of [5]. In section 4 the results on the groupoid G are generalized to the quotient groupoid G/N. For any topological groupoid G over X and normal subgroupoid N of G, the abstract quotient groupoid G/N can be given the identification topology, but with this topology G/N need not be a topological groupoid over X [4]. However the induced topology (H) on G makes G/N (with the identification topology) a topological groupoid over X. A final section is related to the covering morphism. Let G$_{1}$ and G$_{2}$ be groupoids over the sets X$_{1}$ and X$_{2}$, respectively, and .phi.:G$_{1}$.rarw.G$_{2}$ be a covering spimorphism. If X$_{2}$ is a topological space and G$_{2}$ has an 1-connected local subgroupoid, then we can topologize X$_{1}$ so that ob(.phi.):X$_{1}$.rarw.X$_{2}$ is a covering map and .phi.: G$_{1}$.rarw.G$_{2}$ is a topological covering morphism.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.115-123
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• 2001

In this paper we consider the topological properties of $\textit{\Theta}_\textit{\kappa}$and show that the induced map $\tilde{\textit{\Theta}_\textit{\kappa}}$ is well defined and renders the diagram commutative.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.507-517
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• 2003

Self-organizing map (SOM) has been developed mainly by T. Kohonen and his colleagues as a unsupervised learning neural network. Because of its topological ordering property, SOM is known to be very useful in pattern recognition and text information retrieval areas. Recently, data miners use Kohonen´s mapping method frequently in exploratory analyses of large data sets. One problem facing SOM builder is that there exists no sensible criterion for evaluating goodness-of-fit of the map at hand. In this short communication, we propose valid evaluation procedures for the Kohonen SOM of any size. The methods can be used in selecting the best map among several candidates.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.1-27
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• 2008

We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.

• The Journal of Korea Robotics Society
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• v.3 no.1
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• pp.33-41
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• 2008

Based on object recognition technology, we present a new global localization method for robot navigation. For doing this, we model any indoor environment using the following visual cues with a stereo camera; view-based image features for object recognition and those 3D positions for object pose estimation. Also, we use the depth information at the horizontal centerline in image where optical axis passes through, which is similar to the data of the 2D laser range finder. Therefore, we can build a hybrid local node for a topological map that is composed of an indoor environment metric map and an object location map. Based on such modeling, we suggest a coarse-to-fine strategy for estimating the global localization of a mobile robot. The coarse pose is obtained by means of object recognition and SVD based least-squares fitting, and then its refined pose is estimated with a particle filtering algorithm. With real experiments, we show that the proposed method can be an effective vision- based global localization algorithm.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1415-1417
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• 2003

In this study, as the passing of a year, the changes of tidal flat area in Seohan Bay, North Korea was monitored through using Landsat ETM Data and the ancient topological map. The map to present tidal flat distribution characteristic based on the ancient topographical map (1918) was constructed as GIS DB. In addition, a tidal flat distribution map was estimated by using the satellite images with unsupervised classification method. Even though it is difficult to approach to study area, it was possible to gain the data and to monitor the change of the coast tidal flat by comparing to area change yielded.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.967-979
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• 2019

Chaotic dynamical systems, preferably on a Cantor-like space with some arithmetic operations are considered as good pseudo-random number generators. There are many definitions of chaos, of which Devaney-chaos and pos itive topological entropy seem to be the strongest. Let $A=\{0,1,{\dots},p-1\}$. We define a continuous map on $A^{\mathbb{Z}}$ using addition with a carry, in combination with the shift map. We show that this map gives rise to a dynamical system with positive entropy, which is also Devaney-chaotic: i.e., it is transitive, sensitive and has a dense set of periodic points.