• Journal of IKEEE
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• v.23 no.2
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• pp.419-424
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• 2019

The FCM algorithm finds the optimal solution through iterative optimization technique. In particular, there is a difference in execution time depending on the initial center of clustering, the location of noise, the location and number of crowded densities. However, this method gradually updates the center point, and the center of the initial cluster is shifted to one side. In this paper, we propose a TI-FCM(Triangular Inequality-Fuzzy C-Means) clustering algorithm that determines the cluster center density by maximizing the distance between clusters using triangular inequality. The proposed method is an effective method to converge to real clusters compared to FCM even in large data sets. Experiments show that execution time is reduced compared to existing FCM.

• International Journal of Computer Science & Network Security
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• v.22 no.11
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• pp.184-188
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• 2022

The article considers the improved method and model of automated air situation assessment using a decision support system based on fuzzy networks of target installations. The advanced method of automated assessment of the air situation using the decision support system is based on the methodology of reflexive control of the first rank. With this approach, the process of assessing the air situation in the framework of the formulated task can be reduced to determining the purpose, probabilistic nature of actions and capabilities of the air target. The use of a homogeneous functional network for the formal presentation of air situation assessment processes will formally describe the process of determining classes of events during air situation assessment and the process of determining quantitative and qualitative characteristics of recognized air situation situations. To formalize the patterns of manifestation of the values of quantitative and symbolic information, it is proposed to use the mathematical apparatus of fuzzy sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.44-48
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• 2000

퍼지 집합은 경계가 애매한 집단, 어떤 제약에 대한 만족정도가 애매한 개체들의 모임, 또는 애매한 개념을 소속정도를 이용하여 표현한다. 퍼지 집합에서는 자신의 나타내는 개념이나 제약에 대해서 무관한 개체나 상반되는 개체에 대해서도 소속정도 값으로 0을 부여한다. 응용에 따라서는 집합이 나타내는 개념이나 제약에 대해서 무관한 것과 상반되는 것을 구별하여 표현하는 것이 유용한 경우도 있다. 이 논문에서는 퍼지 집합에서 소속정도값 0을 갖는 무관한 원소들과 상반되는 원소들을 구별하여 표현하기 위해 소속 정도값의 영역을 구간 [-1, 1]로 확장한 바이폴라 퍼지집합이라는 확장된 퍼지 집합을 소개한다. 한편, 바이폴라 퍼지 집합에 대한 집합연산, 퍼지정도 척도, 관계, 추론 등의 연산에 대해서도 소개한다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.278-283
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• 1998

The interval approach to the linguistic expression coding nears us to the human idea. Thus, what seems "weak" for a person can appear very weak for another person or for the same person in others circumstances. However, the utilization of intervals is not restrained to the cases of linguistic expression coding. Indeed, the interval can facilitate the solution of several problems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.526-530
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• 1998

In this note by considering the notions of F-polygroups, the product of F-polygroups, F-subpolygroups and (weak) normal F-subpolygroups two questions are given. Then by an example it is shown that the answer of one of the questions (posed in the paper [12]) is in general negative. In other words, the product of two normal F-subpolygroups need not be normal.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.549-556
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• 2005

A hard-type centroids in the conventional clustering algorithm such as k-modes algorithm cannot keep the uncertainty inherently in data sets as long as possible before actual clustering(decision) are made. Therefore, we propose the k-populations algorithm to extend clustering ability and to heed the data characteristics. This k-population algorithm as found to give markedly better clustering results through various experiments.

• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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• pp.249-254
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• 2006

Category Fuz of fuzzy sets has a similar function to the topos Set. But Category Fuz forms a weak topos. We show that supports split weakly(SSW) and with some properties, implicity axiom of choice(IAC) holds in weak topos Fuz. So weak axiom of choice(WAC) holds in weak topos Fuz. Also we show that weak extensionality principle for arrow holds in weak topos Fuz.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.137-143
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• 2010

Category Fuz of fuzzy sets has a similar function to the Category Set. But it forms a weak topos. We study a natural number object and a weak natural number object in the weak topos Fuz. Also we study the weak natural number object in $Fuz^C$.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.75-87
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• 2020

Category F Rel of fuzzy sets and relations does not form a topos. J. Harding, C. Walker and E. Walker [3] showed that FRel has a tensor product and V. Durov [1] introduced basic definitions related to the notion of vectoid endowed with a tensor product. In this paper, we show that FRel forms a quasi topos. Also we show that there are quasi power objects in FRel. And by the use of the concepts of FRel and quasi topos, we get the logic operators of FRel. Moreover, we show that FRel forms a vectoid.

• Journal of the Korean Institute of Intelligent Systems
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• v.9 no.4
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• pp.375-383
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• 1999

사용자가 최소의 이해와 수정 노력으로 적합한 컴포넌트를 선택할수 있는 방안이 요구된다, 따라서 본 논문에서는 컴포넌트의 재사용도 측정을 위한 혼합적 척도를 제안한다. 현업에서의 연구와 경험을 통해서 증명된 객관성 있는 척도들을 측정인자로 설정한다. 러프집합을 이용하여 각측정인자들이 컴포넌트 재상요에 미치는 영향의 정도를 평가하고 각 측정인자들의 상대적 중요도를 구한다, Sugeno의 퍼지적분을 이용하여 측정인자들의 중요도와 측정값들을 종합함으로써 컴포넌트들의 재사용도를 측정한다. 마지막으로 제안된 ordinal scale과 ratio scale에 따름을 보여준다.