• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.525-540
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• 2023

In this paper, we introduce the concept of fuzzy nano M open and fuzzy nano M closed mappings in fuzzy nano topological spaces. Also, we study about fuzzy nano M Homeomorphism, almost fuzzy nano M totally mappings, almost fuzzy nano M totally continuous mappings and super fuzzy nano M clopen continuous functions and their properties in fuzzy nano topological spaces. By using these mappings, we can able to extended the relation between normal spaces and regular spaces in fuzzy nano topological spaces.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.250-255
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• 2005

For navigation of a service robot, mapping and localization are very important. To estimate the robot pose, the map of the environment is required and it can be built by exploration or SLAM. Exploration is the fundamental task of guiding a robot autonomously during mapping such that it covers the entire environment with its sensors. In this paper, an efficient exploration scheme based on the position probability of the end nodes of a topological map is proposed. In this scheme, a topological map is constructed in real time using the thinning-based approach. The robot then updates the position probability of each end node maintaining its position at the current location based on the Bayesian update rule using the range data. From this probability, the robot can determine whether or not it needs to visit the specific end node to examine the environment around this node. Various experiments show that the proposed exploration scheme can perform exploration more efficiently than other schemes in that, in most cases, exploration for the entire environment can be completed without directly visiting everywhere in the environment.

• 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.

• The Journal of Korea Robotics Society
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• v.9 no.2
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• pp.104-110
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• 2014

Mapping is a fundamental element for robotic services. There are available many types of map data representation such as grid map, metric map, topology map, etc. As more robots are deployed for services, more chances of exchanging map data among the robots emerge and standardization of map data representation (MDR) becomes more valuable. Currently, activities in developing MDR standard are underway in IEEE Robotics and Automation Society. The MDR standard is for a common representation and encoding of the two-dimensional map data used for navigation by mobile robots. The standard focuses on interchange of map data among components and systems, particularly those that may be supplied by different vendors. This paper aims to introduce MDR standard and its application to map merging. We have applied the basic structure of the MDR standard to a grid map and Voronoi graph as a kind of topology map and performed map merging between two different maps. Simulation results show that the proposed MDR is suitable for map data exchange among robots.

• Proceedings of the KAIS Fall Conference
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• 2003.11a
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• pp.223-230
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• 2003

Feature-based similarity retrieval has become an important research issue in multimedia database systems. The features of multimedia data are useful for discriminating between multimedia objects (e 'g', documents, images, video, music score, etc.). For example, images are represented by their color histograms, texture vectors, and shape descriptors, and are usually high-dimensional data. The performance of conventional multidimensional data structures(e'g', R- Tree family, K-D-B tree, grid file, TV-tree) tends to deteriorate as the number of dimensions of feature vectors increases. The R＊-tree is the most successful variant of the R-tree. In this paper, we propose a SOM-based R＊-tree as a new indexing method for high-dimensional feature vectors.The SOM-based R＊-tree combines SOM and R＊-tree to achieve search performance more scalable to high dimensionalities. Self-Organizing Maps (SOMs) provide mapping from high-dimensional feature vectors onto a two dimensional space. The mapping preserves the topology of the feature vectors. The map is called a topological of the feature map, and preserves the mutual relationship (similarity) in the feature spaces of input data, clustering mutually similar feature vectors in neighboring nodes. Each node of the topological feature map holds a codebook vector. A best-matching-image-list. (BMIL) holds similar images that are closest to each codebook vector. In a topological feature map, there are empty nodes in which no image is classified. When we build an R＊-tree, we use codebook vectors of topological feature map which eliminates the empty nodes that cause unnecessary disk access and degrade retrieval performance. We experimentally compare the retrieval time cost of a SOM-based R＊-tree with that of an SOM and an R＊-tree using color feature vectors extracted from 40, 000 images. The result show that the SOM-based R＊-tree outperforms both the SOM and R＊-tree due to the reduction of the number of nodes required to build R＊-tree and retrieval time cost.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.8
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• pp.1605-1614
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• 2009

The technique of simultaneous localization and mapping is the most important research topic in mobile robotics. In the process of building a map in its available memory, the robot memorizes environmental information on the plane of grid or topology. Several approaches about this technique have been presented so far, but most of them use mapping technique as either grid-based map or topology-based map. In this paper we propose a frame of solving the SLAM problem of linking map covering, map building, localizing, path finding and obstacle avoiding in an automatic way. Some algorithms integrating grid and topology map are considered and this make the SLAM performance faster and more stable. The proposed scheme uses an occupancy grid map in representing the environment and then formulate topological information in path finding by A${\ast}$ algorithm. The mapping process is shown and the shortest path is decided on grid based map. Then topological information such as direction, distance is calculated on simulator program then transmitted to robot hardware devices. The localization process and the dynamic obstacle avoidance can be accomplished by topological information on grid map. While mapping and moving, pose of the robot is adjusted for correct localization by implementing additional pixel based image layer and tracking some features. A laser range finer and electronic compass systems are implemented on the mobile robot and DC geared motor wheels are individually controlled by the adaptive PD control method. Simulations and experimental results show its performance and efficiency of the proposed scheme are increased.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.575-589
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• 2011

In order to examine the possibility of some topological structures into the fields of network science, telecommunications related to the future internet and a digitization, the paper studies the Marcus Wyse topological structure. Further, this paper develops the notions of lattice based Marcus Wyse continuity and lattice based Marcus Wyse homeomorphism which can be used for studying spaces $X{\subset}R^2$ in the Marcus Wyse topological approach. By using these two notions, we can study and classify lattice based simple closed Marcus Wyse curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.305-320
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• 2013

Topological semilattices with path-connected intervals are special abstract convex spaces. In this paper, we obtain generalized KKM type theorems and their analytic formulations, maximal element theorems and collectively fixed point theorems on abstract convex spaces. We also apply them to topological semilattices with path-connected intervals, and obtain generalized forms of the results of Horvath and Ciscar, Luo, and Al-Homidan et al..

• Honam Mathematical Journal
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• v.42 no.4
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• pp.681-699
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• 2020

In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.477-483
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• 2014

In this paper, we introduce a new class of regular generalized b-continuous map and study some of their properties as well as inter relationship with other continuous maps.