• 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.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.377-384
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• 2015

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.4-9
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• 2009

Fuzzy entropy is designed for non convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.21-22
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• 2008

Fuzzy entropy is designed for non-convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non-convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.351-363
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• 2016

In this paper, we consider the entropy-based goodness of fit test (Vasicek's test) for a composite hypothesis. The test measures the discrepancy between the nonparametric entropy estimate and the parametric entropy estimate obtained from an assumed parametric family of distributions. It is shown that the proposed test is asymptotically normal under regularity conditions, but is affected by parameter estimates. As a remedy, a bootstrap version of Vasicek's test is proposed. Simulation results are provided for illustration.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.681-699
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• 2020

In this paper, topological entropy of iterated function systems (IFS) on one dimensional spaces is considered. Estimation of an upper bound of topological entropy of piecewise monotone IFS is obtained by open covers. Then, we provide a way to calculate topological entropy of piecewise monotone IFS. In the following, some examples are given to illustrate our theoretical results. Finally, we have a discussion about the possible applications of these examples in various sciences.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.77-84
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• 2021

Let f : [0, 1] → [0, 1] be a multimodal map with positive topological entropy. The dynamics of the renormalization operator for multimodal maps have been investigated by Daniel Smania. It is proved that the measure of maximal entropy for a specific category of Cr interval maps is unique.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.123-132
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• 2023

We define an operator version of the relative Rényi entropy as the generalization of relative von Neumann entropy, and provide its fundamental properties and the bounds for its trace value. Moreover, we see an effect of the relative Rényi entropy under tensor product, and show the sub-additivity for density matrices.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.125-135
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• 1998

In this paper we define the entropy rate and stationary Markov chain and we show the monotonicity of entropy per element and prove that the random tree $T_n$ grows linearly with n.