• The Mathematical Education
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• v.23 no.1
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• pp.7-11
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• 1984

Fuzzy 측도를 고전적인 방법에 병행해서 T-fuzzy $\sigma$-algebra의 개념을 얻어서 이로부터 Fuzzy 측도를 도입하고 다시 이와 관련된 예를 몇가지 들었다. 이 결과 고전적인 방법과 매우 가까운 Fuzzy 측도를 얻었음을 확인할 수 있었다.

• The Journal of the Korea Contents Association
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• v.2 no.4
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• pp.99-103
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• 2002

In this paper, we investigate for how to define a fuzzy measure by using the semi-normed fuzzy integral of a given measurable function with respect to another given fuzzy measure when t-seminorm is continuous. Let (X, F, g) be a fuzzy measure space, h$\in$L$^\circ$(X), and $\top$ be a continuous t-seminorm.. Then the set function $\nu$ defined by $\nu$(A)=$\int _A$h$\top$g for any $A\in$F is a fuzzy measure on (X, F).

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.5
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• pp.521-526
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• 2005

The fuzzy entropy is proposed for measuring of uncertainty with the help of relation between distance measure and similarity measure. The proposed fuzzy entropy is constructed through a distance measure. In this study, Hamming distance measure is employed for a distance measure. Also a similarity measure is constructed through a distance measure for the measure of similarity between fuzzy sets or crisp sets and the proposed fuzzy entropies and similarity measures are proved.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.4
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• pp.307-310
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• 2001

A measure of typicality associated with any fuzzy subset on a probability space is introduced. We will improve some results of Yager and consider limit of the measure of typicality of a fuzzy set with ,respect to a random sample.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.9C
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• pp.854-859
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• 2005

We construct the fuzzy entropy for measuring of uncertainty with the help of relation between distance measure and similarity measure. Proposed fuzzy entropy is constructed through distance measure. In this study, the distance measure is used Hamming distance measure. Also for the measure of similarity between fuzzy sets or crisp sets, we construct similarity measure through distance measure, and the proposed 려zzy entropies and similarity measures are proved.

• The KIPS Transactions:PartB
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• v.8B no.5
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• pp.463-468
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• 2001

We propose a new similarity measure based on relative membership function (RMF). In this paper, the RMF is suggested to represent the relativity between fuzzy subsets easily. Since the shape of the RMF is determined according to the values of its parameters, we can easily represent the relativity between fuzzy subsets by adjusting only the values of its parameters. Hence, we can easily reflect the relativity among individuals or cultural differences when we represent the subjectivity by using the fuzzy subsets. In this case, these parameters may be regarded as feature points for determining the structure of fuzzy subset. In the sequel, the degree of similarity between fuzzy subsets can be quickly computed by using the parameters of the RMF. We use Euclidean distance to compute the degree of similarity between fuzzy subsets represented by the RMF. In the meantime, we present a new linguistic approximation method as an application area of the proposed similarity measure and show its numerical example.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1077-1094
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• 2011

We accomplish clustering analyses for yeast cell cycle microarray expression data. To reflect the characteristics of a time-course data, we screen the genes using the test statistics with Fourier coefficients applying a FDR procedure. We compare the results done by model-based clustering, K-means, PAM, SOM, hierarchical Ward method and Fuzzy method with the yeast data. As the validity measure for clustering results, connectivity, Dunn index and silhouette values are computed and compared. A biological interpretation with GO analysis is also included.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.39-45
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• 2005

In this paper, we consider fuzzy measures and Choquet integrals. Also we discuss some results proved by us and new works.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.307-313
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• 1995

Using the representation theorem of fuzzy number, we give the Radon-Nikodym theorem for fuzzy-number-valued measures

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.53-60
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• 2008

Based on similarities between fuzzy set theory and mathematical morphology, Grabish proposed a fuzzy morphology based on the Sugeno fuzzy integral. This paper proposes a fuzzy mathematical morphology based on the defuzzification of the fuzzy measure which corresponds to fuzzy integral. Its process makes a fuzzy set used as a measure of the inclusion of each fuzzy measure for subsets. To calculate such an integral a $\lambda$-fuzzy measure is defined which gives every subsets associated with the universe of discourse, a definite non-negative weight. Fast implementable definitions for erosion and dilation based on the fuzzy measure was given. An application for robust skeletonization of two-dimensional objects was presented. Simulation examples showed that the object reconstruction from their skeletal subsets that can be achieved by using the proposed was better than by using the binary mathematical morphology in most cases.