• 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.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.695-702
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• 2005

We study the transformed measures with respect to the real parameters of a self-similar measure on a self-similar Can­tor set to give a simple proof for some result of its multifractal spectrum. A transformed measure with respect to a real parameter of a self-similar measure on a self-similar Cantor set is also a self­similar measure on the self-similar Cantor set and it gives a better information for multifractals than the original self-similar measure. A transformed measure with respect to an optimal parameter deter­mines Hausdorff and packing dimensions of a set of the points which has same local dimension for a self-similar measure. We compute the values of the transformed measures with respect to the real parameters for a set of the points which has same local dimension for a self-similar measure. Finally we investigate the magnitude of the local dimensions of a self-similar measure and give some correlation between the local dimensions.

• 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 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.

• 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.

• 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 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.

• 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.

• International Journal of Quality Innovation
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• v.3 no.2
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• pp.84-92
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• 2002

In this Paper, We propose new performance measure model in Logistic Industry. New model has been learned by key points of PZB model and advanced structure of MBNQA which has cause measure points and effect measure points. The Structure of new performance measure model is Cubic Model which is reflected with time. We try to verify this model apply advance logistic company.

• 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.