• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2004.10a
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• pp.27-40
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• 2004

When we derive multi-scale databases from a source spatial database, thegeometries and topological relations in the source database are transformed according to a predefined set of constraints. This means that the derived databases should be checked to see if the constraints are respected during the construction or updates of databases and to maintain the consistency of multi-scale databases. In this paper, we focus on the topological consistency between the source and derived databases, which is one of the important constraints to respect. In particular, we deal with the method of assessment of topological consistency, when 2-dimensional objects are collapsed to 1-dimensional ones. We introduce eight types of topological relations between 2-dimensional objects and 19 topological ones between 1-dimensional objects and propose four different strategies to convert 2-dimensional topological relations in the source database to 1-dimensional ones objects in the target database. With these strategies, we guarantee the topological consistency between multi-scale databases.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.1-16
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• 2023

In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological complexity, with each other in digital images. For some certain digital images, we introduce κ-topological groups in the digital topological manner for having stronger ideas about the digital higher topological complexity. Our aim is to improve the understanding of the digital higher topological complexity. We present examples and counterexamples for κ-topological groups.

• East Asian mathematical journal
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• v.22 no.1
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• pp.79-91
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• 2006

In this paper, we will show some relations between decomposition series {$\pi^{\alpha}q\;:\;{\alpha}$ is an ordinal} and topological series {$\tau_{\alpha}q\;:\;{\alpha}$ is an ordinal} for a convergence structure q and the formular ${\pi}^{\beta}(\tau_{\alpha}q)={\pi}^{{\omega^{\alpha}\beta}}q$, where $\omega$ is the first limit ordinal and $\alpha$ and $\beta({\geq}1)$ are ordinals.

• The Journal of Korea Robotics Society
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• v.3 no.1
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• pp.42-51
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• 2008

Robots need to understand as much as possible about their environmental situation and react appropriately to any event that provokes changes in their behavior. In this paper, we pay attention to topological relations between spatial objects and propose a model of robotic cognition that represents and infers temporal relations. Specifically, the proposed model extracts specified features of the cooccurrence matrix represents from disparity images of the stereo vision system. More importantly, a habituation model is used to infer intrinsic spatial relations between objects. A preliminary experimental investigation is carried out to verify the validity of the proposed method under real test condition.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.361-370
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• 2002

We are to present some properties of binary relations on fuzzy topological spares by means of categorical method. The concept of fuzzy topological ordered spaces was introduced by Katsaras[8]. In this paper we study some special categories, i.e, FTQOS, FTPOS, LSCQ, USCQ, SCQ, CQ, NQO, CRQO, associated with fuzzy topological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.37-40
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• 2003

We introduce the category IRel (H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel (H) in the viewpoint of the topological universe introduced by L.D.Nel. Thus we show that IRel (H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel (H) is cartesian closed over Set.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.617-633
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• 2002

In this paper, we study some properties of fuzzy interior spaces. Also, we investigate the relations between fuzzy interior spaces and fuzzy topological spaces. In particular, we prove the existence of product fuzzy topological spaces and product fuzzy interior spaces. We investigate the relations between them.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.47-69
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• 2006

In this paper, an idea of graded fuzzy net is introduced; its convergence is studied; Relations between g-net and g-filter are established in L-fuzzy setting.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.59-62
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• 2002

We investigate some relations between the separation axioms in fuzzy topological spaces and one in fuzzy hyperspaces.

• Bulletin of the Korean Chemical Society
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• v.16 no.2
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• pp.169-180
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• 1995

A topological theory is introduced to extend Tsenoglou's theory to polymer blends having temporary and permanent networks composed of multicomponent polymers which have miscible and flexible chains. The topological theory may estimate the values of free elastic energy, the molecular weight between entanglements, and the equilibrium shear moduli, and it may establish more correctly the topological relations among these physical quantities. Through such introduction of the topological theory, there can be topologically analyzed the mixing law for the rubbery plateau modulus of a fluid polymer blend, and there can be considered the topological relationship to the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretically predictive values are compared and show good agreement with the experimental data for several miscible polymer blends.