• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.187-190
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• 2007

In this paper, we introduce concepts of entropy and similarity measure of interval-valued intuitionistic fuzzy sets (IVIFSs), discuss their relationship between similarity measure and entropy of IVIFSs, show that similarity measure and entropy of IVIFSs can be transformed by each other based on their axiomatic definitions and give some formulas to calculate entropy and similarity measure of IVIFSs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.7C
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• pp.931-936
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• 2004

GBFCM(DM), Gradient-based Fuzzy c-means with Divergence Measure, for efficient clustering of GPDF(Gaussian Probability Density Function) in MPEG VBR video data modeling is proposed in this paper. The proposed GBFCM(DM) is based on GBFCM( Gradient-based Fuzzy c-means) with the Divergence for its distance measure. In this paper, sets of real-time MPEG VBR Video traffic data are considered. Each of 12 frames MPEG VBR Video data are first transformed to 12-dimensional data for modeling and the transformed 12-dimensional data are Pass through the proposed GBFCM(DM) for classification. The GBFCM(DM) is compared with conventional FCM and GBFCM algorithms. The results show that the GBFCM(DM) gives 5∼15% improvement in False Alarm Rate over conventional algorithms such as FCM and GBFCM.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.497-503
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• 2007

We consider a non-empty subset having same local dimension of a self-similar measure on a most generalized Cantor set. We study trans-formed lower(upper) local dimensions of an element of the subset which are local dimensions of all the self-similar measures on the most generalized Cantor set. They give better information of Hausdorff(packing) dimension of the afore-mentioned subset than those only from local dimension of a given self-similar measure.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.657-667
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• 2006

The concept of entropy, introduced in communication theory by Shannon (1948) as a measure of uncertainty, is of prime interest in information-theoretic statistics. This paper considers the minimum variance unbiased estimation for the maximum entropy of the transformed inverse Gaussian random variable by $Y=X^{-1/2}$. The properties of the derived UMVU estimator is investigated.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.453-465
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• 2000

In this paper, a new method for finding the approximate solution of a second order nonlinear partial differential equation is introduced. In this method the problem is transformed to an equivalent optimization problem. them , by considering it as a distributed parameter control system the theory of measure is used for obtaining the approximate solution of the original problem.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.151-164
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• 2001

In this paper, a new approach for finding the approximate solution of the Stokes problem is introduced. In this method the problem is transformed to an equivalent optimization problem. Then, by considering it as a distributed parameter control system, the theory of measure is used to approximate values of pressure are obtained by a finite difference scheme.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.76-81
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• 2016

In this paper, we present the entropy and similarity measure for generalized hesitant fuzzy information, and discuss their desirable properties. Some measure formulas are developed, and the relationships among them are investigated. We show that the similarity measure and entropy for generalized hesitant fuzzy information can be transformed by each other based on their axiomatic definitions. Furthermore, an approach of multiple attribute decision making problems where attribute weights are unknown and the evaluation values of attributes for each alternative are given in the form of GHFEs is investigated.

• Journal of the Korean Society of Visualization
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• v.7 no.2
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• pp.42-46
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• 2010

In this paper we report the method of visualizing and measuring the fluid flow within a small droplet of millimeter size. We use a vertical laser sheet in visualization of the micrometer size and special attention is given to the arrangement of microscope to obtain clear images. Then we use a PIV technique to measure the velocity of the internal flow from the images taken. Since the droplet is of spherical shape, the images represent highly deteriorated picture of the real objects due to the refraction phenomenon. In order to compensate the refraction, we in this study developed two kinds of methods for the real velocity. In the first method, the refracted images are directly used to obtain the velocity in the image space, and then the velocity is transformed to the real space. In the second method the images are first transformed to the real-space objects, and then the PIV is used to measure the velocity field. We compared the two results to prove the usefulness of the compensation technique.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.