• Journal of the Institute of Electronics Engineers of Korea CI
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• v.37 no.2
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• pp.11-20
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• 2000

Topological relationships play an important role in query optimization in spatial databases. If topological relationships are known a priori, then expensive query processing can be avoided. In this paper we address the problems of： ⅰ) identifying topological relationships among spatial objects, ⅱ) checking consistency of specified topological relationships, and ⅲ) exhaustively deriving new topological relationships from the ones specified. These activities lead to an efficient query processing when queries associated with topological relationships are invoked. Specifically, eight types of topological relationships (｛equal, disjoint, overlap, meets, contains, contained-in, properly-contains, and properly-contained-in｝) are considered. We present an algorithm to check the consistency of specified topological relationships and to derive all possible relationships from the given set of known relationships.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.128-132
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• 2002

One of the fundamental components important to the analysis of spatial objects is to represent topological relationships between spatial features. Users of geographic information systems retrieve a lot of objects from spatial database and analyze their condition by means of topological relationships. The existing methods that represent these relationships have the disadvantage that they have limited information in $R^2$. In this paper, we represent and define the topological relationships between 3-dimensional spatial objects using the several representing methods of 2-dimensional features. We use the diverse representing methods, which include the 4-, 9-intersection, dimension extended and calculus-based method. Furthermore, we discuss OGC's topological relationships and operators for 3-dimensional spatial data.

• Journal of the Korea Computer Graphics Society
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• v.4 no.1
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• pp.11-19
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• 1998

Non-manifold topological operations such as Euler and Boolean operations provide a versatile environment for modeling domains. The implementation of these operations raises geometrical issues that need to be addressed to ensure the topological validity of the underlying model, and they uses the glue operation which provides a basic method to modify the topology of non-manifold models when vertices, edges and faces are contacting each other. Topological information such as adjacency relationships should be inferred when gluing non-manifold models. Two methods of reasoning can be employed to find the topological information : topological reasoning and geometrical reasoning. The topological method can infer the adjacency relationships by using stored topological information. On the other hand, the geometrical method can find topological ambiguities by considering the geometrical shape at the local area of gluing when the topological relations were not stored. This paper describes the geometrical reasoning method.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.11-25
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• 1999

We will define a smooth fuzzy closure space and a subspace of it. We will investigate relationships between smooth fuzzy closure spaces and smooth fuzzy topological spaces. In particular, we will show that a subspace of a smooth fuzzy topological space can be obtained by the subspace of the smooth fuzzy closure space induced by it.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.487-500
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• 2003

We investigate categorical relationships between the category of smooth fuzzy topological spaces, the category of intuitionistic fuzzy topological spaces, and the category of intuitionistic fuzzy topological spaces, and the category of intuitioistic fuzzy topological spaces in Sostak's sense.

• Spatial Information Research
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• v.19 no.1
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• pp.93-105
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• 2011

In recent years, large and complex three-dimensional building has been constructed by the development of building technology and advanced IT skills, and people have lived there and spent a considerable time so far. Accordingly. in this sophisticatcd three-dimensional space, emergencies services or convenient information services have been in demand. In order to provide these services efficiently, understanding of topological relationships among the complex space should be supported naturally. Not on1y each method of understanding the topological relationships but also its efficiency can be different depending on different topological data models. B-rep based data model is the most widely used for storaging and representing of topological relationships. And from early 2000s, many researches on a network based topological data model have been conducted. The purpose of this study is to verify the efficiency of performance on spatial queries. As a result, Network-based topological data model is more efficient than B-rep based data model for determining the spatial relationship.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.4
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• pp.302-307
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• 2012

Real-time systems perform periodic tasks and real-time aperiodic tasks such as alarm processing. Especially the periodic tasks included in control systems such as robots have precedence relationships among them. This paper proposes a new scheduling algorithm based on topological sort and residual time. The precedence relationships among periodic tasks are translated to the priorities of the tasks using topological sort algorithm. During the execution of the system the proposed scheduling algorithm decides on whether or not a newly arrived real-time aperiodic task is accepted based on residual time whenever the aperiodic task such as alarm is arrived. The proposed algorithm is validated using examples.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.333-362
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• 2010

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.371-381
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• 2013

In this paper, we investigate some properties of ${\theta}$-($\mathcal{G}$, $\mathcal{H}$)-continuous functions in a grill topological spaces. Moreover, the relationships with other related functions are investigated.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.323-338
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• 2011

In this paper, we introduce ($$\tilde{g}$$, s)-continuous functions between topological spaces, study some of its basic properties and discuss its relationships with other topological functions.