• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.244-248
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• 2012

F-Measure is one of the external measures for evaluating the validity of clustering results. Though it has clear advantages over other widely used external measures such as Purity and Entropy, F-Measure has inherently been less sensitive than other validity measures. This insensitivity owes to the definition of F-Measure that counts only most influential portions. In this research, we present $F_n$-Measure, an external cluster evaluation measure based on F-Measure. $F_n$-Measure is so sensitive that it can detect their difference in the cases that F-Measure cannot detect the difference in clustering results. We compare $F_n$-Measure to F-Measure for a few clustering results and show which measure draws better result based upon homogeneity and completeness.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.367-371
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• 2005

The similarity measure is derived using fuzzy entropy and distance measure. By the elations of fuzzy entropy, distance measure, and similarity measure, we first obtain the fuzzy entropy. And with both fuzzy entropy and distance measure, similarity measure is obtained., We verify that the proposed measure become the similarity measure.

• Journal of the Korea Convergence Society
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• v.5 no.4
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• pp.155-161
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• 2014

We survey the relation of fuzzy entropy measure and similarity measure. Each measure represents features of data uncertainty and certainty between comparative data group. With the help of one-to-one correspondence characteristics, distance measure and similarity measure have been expressed by the complementary characteristics. We construct similarity measure using distance measure, and verification of usefulness is proved. Furthermore analysis of similarity measure from fuzzy entropy measure is also discussed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.366-369
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• 2007

In this paper we derived fuzzy entropy that is based on similarity measure. Similarity measure represents the degree of similarity between two informations, those informations characteristics are not important. First we construct similarity measure between two informations, and derived entropy functions with obtained similarity measure. Obtained entropy is verified with proof. With the help of one-to-one similarity is also obtained through distance measure, this similarity measure is also proved in our paper.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.455-459
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• 2007

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.295-308
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• 2016

Depending upon the nature of the problem, different divergence measures are suitable. So it is always desirable to develop a new divergence measure. In the present work, new information divergence measure, which is exponential in nature, is introduced and characterized. Bounds of this new measure are obtained in terms of various symmetric and non- symmetric measures together with numerical verification by using two discrete distributions: Binomial and Poisson. Fuzzy information measure and Useful information measure corresponding to new exponential divergence measure are also introduced.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.241-246
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• 2007

We investigate the relation between Hausdorff(packing) measure and lower(packing) Cantor measure on a deranged Cantor set. If the infimum of some distortion of contraction ratios is positive, then Hausdorff(packing) measure and lower(packing) Cantor measure of a deranged Cantor set are equivalent except for some singular behavior for packing measure case. It is a generalization of already known result on the perturbed Cantor set.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.2
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• pp.292-297
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• 2010

In this paper, we introduce the notions of inconsistency p-measure, consistency p-measure and fuzziness p-measure. We discuss various properties of them. We investigate the degree of inconsistency and roughness p-measure in a decision table.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1418-1421
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• 1993

The main purpose of this paper is to introduce and develop the notion of a fuzzy measure in separable Banach space. This definition of fuzzy measure is a natural generalization of the set-valued measure. Radon-Nikod m theorems for fuzzy measure are established.