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Journal articles on the topic 'Weighted Entropy'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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1

Stosic, Darko, Dusan Stosic, Tatijana Stosic, and Borko Stosic. "Generalized weighted permutation entropy." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 10 (2022): 103105. http://dx.doi.org/10.1063/5.0107427.

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A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods: Permutation entropy and Weighted permutation entropy. The method introduces a scaling parameter to discern the disorder and complexity of ordinal patterns with small and large fluctuations. Using this scaling parameter, the complexity-entropy causality plane is generalized to the complexity-entropy-scale causality box. Simulations conducted on synthetic series generat

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2

Guiaşu, Radu Cornel, and Silviu Guiaşu. "Conditional and Weighted Measures of Ecological Diversity." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 03 (2003): 283–300. http://dx.doi.org/10.1142/s0218488503002089.

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Shannon's entropy and Simpson's index are the most used measures of species diversity. As the Simpson index proves to be just an approximation of the Shannon entropy, conditional Simpson indices of diversity and a global measure of interdependence among species are introduced, similar to those used in the corresponding entropic formalism from information theory. Also, since both the Shannon entropy and the Simpson index depend only on the number and relative abundance of the respective species in a given ecosystem, the paper generalizes these indices of diversity to the case when a numerical w

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3

Kelbert, Mark, Izabella Stuhl, and Yuri Suhov. "Weighted entropy: basic inequalities." Modern Stochastics: Theory and Applications 4, no. 3 (2017): 233–52. http://dx.doi.org/10.15559/17-vmsta85.

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4

Das, Suchismita. "On weighted generalized entropy." Communications in Statistics - Theory and Methods 46, no. 12 (2016): 5707–27. http://dx.doi.org/10.1080/03610926.2014.960583.

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5

Misagh, F., and G. H. Yari. "On weighted interval entropy." Statistics & Probability Letters 81, no. 2 (2011): 188–94. http://dx.doi.org/10.1016/j.spl.2010.11.006.

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6

Chen, Yuan, and Aijing Lin. "Weighted link entropy and multiscale weighted link entropy for complex time series." Nonlinear Dynamics 105, no. 1 (2021): 541–54. http://dx.doi.org/10.1007/s11071-021-06599-6.

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7

Kvålseth, Tarald O. "On Weighted Exponential Entropies." Perceptual and Motor Skills 92, no. 1 (2001): 3–7. http://dx.doi.org/10.2466/pms.2001.92.1.3.

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As an alternative to Shannon's classical entropy measure of information, an exponential entropy function was proposed by Pal and Pal in 1989 and 1991. To generalize Pal's entropy further, this author introduced two different families of exponential entropies that are one-parameter generalizations of Pal's entropy. The purpose of the present paper is to define weighted entropies corresponding to those one-parameter generalizations. Some properties and examples of such weighted exponential entropies are discussed.

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8

Puneet, Kumar. "Weighted Average Charge for Hetergenous Questionnaires and Weighted Netropy." Business Research 1, no. 1 (2003): 131–42. https://doi.org/10.5281/zenodo.3888051.

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In the present paper we introduce the idea of Weighted Average Charge for Heterogeneous Questionnaires extending the Average Charge studied by Dancan G.T.(1974). Some Coding theorems and comparison results have been presented through weighted entropy. It is also shown that the weighted Average charge for Heterogeneous Questionnaires is bounded below by weighted entropy.

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9

Yu, Shiwei, and Ting-Zhu Huang. "Exponential weighted entropy and exponential weighted mutual information." Neurocomputing 249 (August 2017): 86–94. http://dx.doi.org/10.1016/j.neucom.2017.03.075.

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10

Verma, Rohit Kumar. "On Generating Measures of Fuzzy Cross-Entropy by Employing Measures of Fuzzy Weight Entropy." Asian Journal of Probability and Statistics 22, no. 3 (2023): 37–44. http://dx.doi.org/10.9734/ajpas/2023/v22i3486.

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By utilizing the ideas of fuzzy-weighted entropy and fuzzy-weighted directed divergence and appropriately selecting the weights, several new measures of fuzzy cross-entropy have been generated. Concurrently, some new measures of fuzzy weighted entropy have been suggested based on the new measures of fuzzy cross-entropy generated.

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11

Kayal, Suchandan, and Rajesh Moharana. "On weighted cumulative residual entropy." Journal of Statistics and Management Systems 20, no. 2 (2017): 153–73. http://dx.doi.org/10.1080/09720510.2016.1224471.

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12

Mirali, M., S. Baratpour, and V. Fakoor. "On weighted cumulative residual entropy." Communications in Statistics - Theory and Methods 46, no. 6 (2016): 2857–69. http://dx.doi.org/10.1080/03610926.2015.1053932.

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13

Khan, Jesmin F., and Sharif M. Bhuiyan. "Weighted entropy for segmentation evaluation." Optics & Laser Technology 57 (April 2014): 236–42. http://dx.doi.org/10.1016/j.optlastec.2013.07.012.

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14

Batty, Michael. "Cost, Accessibility, and Weighted Entropy." Geographical Analysis 15, no. 3 (2010): 256–67. http://dx.doi.org/10.1111/j.1538-4632.1983.tb00786.x.

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15

Mehanna, A. A. W. "Entropy Numbers of Weighted Shifts." Journal of Mathematical Analysis and Applications 262, no. 1 (2001): 62–69. http://dx.doi.org/10.1006/jmaa.2001.7529.

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16

Wu, Tiejun, Hafiz Mutee Ur Rehman, Yu-Ming Chu, Deeba Afzal, and Jianfeng Yu. "Some New Bounds of Weighted Graph Entropies with GA and Gaurava Indices Edge Weights." Mathematical Problems in Engineering 2020 (September 30, 2020): 1–9. http://dx.doi.org/10.1155/2020/5474501.

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Motivated by the concept of Shannon’s entropy, the degree-dependent weighted graph entropy was defined which is now become a tool for measurement of structural information of complex graph networks. The aim of this paper is to study weighted graph entropy. We used GA and Gaurava indices as edge weights to define weighted graph entropy and establish some bounds for different families of graphs. Moreover, we compute the defined weighted entropies for molecular graphs of some dendrimer structures.

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17

Koukoumis, C., and A. Karagrigoriou. "On Entropy-type Measures and Divergences with Applications in Engineering, Management and Applied Sciences." International Journal of Mathematical, Engineering and Management Sciences 6, no. 3 (2021): 688–707. http://dx.doi.org/10.33889/ijmems.2021.6.3.043.

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In this work we review Entropy-type measures and Divergences, discuss their properties and unfold their diverse applicability. In addition, we compare distances between populations and distributions via weighted Entropy-type measures relying mainly on Relative Entropy and Jeffrey’s Distance with weights. Finally, we introduce the Absolute Weighted Relative Entropy and the Absolute Weighted Jeffrey’s Distance. Two applications are presented for illustration, one from Geosciences and one from Financial Mathematics.

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18

Panait, Ioana. "Weighted Entropic Copula from Preliminary Knowledge of Dependence." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 1 (2018): 223–40. http://dx.doi.org/10.2478/auom-2018-0014.

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Abstract This paper introduces a weighted entropic copula from preliminary knowledge of dependence. Considering a copula with common distribution we formulate the weighted entropy dependence model (WMEC). We give an approximator for the copula function of this problem. Also, we discuss some asymptotical properties regarding the unknown parameters of the model.

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19

GUIASU, RADU CORNEL, and SILVIU GUIASU. "NEW MEASURES FOR COMPARING THE SPECIES DIVERSITY FOUND IN TWO OR MORE HABITATS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 18, no. 06 (2010): 691–720. http://dx.doi.org/10.1142/s0218488510006763.

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Both the weighted entropy, which generalizes the Shannon entropy, and the weighted quadratic index, which generalizes the Gini-Simpson index, are used for getting a unified treatment of some diversity measures proposed recently in ecology. The weights may reflect the ecological importance, rarity, or economic value of the species from a given habitat. The weighted measures, being concave functions, may be used in the additive partition of diversity. The weighted quadratic index has a special advantage over the weighted entropy because its maximum value has a simple analytical formula which all

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20

Kattumannil, Sudheesh Kumar, E. P. Sreedevi, and Narayanaswamy Balakrishnan. "A Generalized Measure of Cumulative Residual Entropy." Entropy 24, no. 4 (2022): 444. http://dx.doi.org/10.3390/e24040444.

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In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy m

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21

Wang, Tao, and Yu Huang. "Weighted topological and measure-theoretic entropy." Discrete & Continuous Dynamical Systems - A 39, no. 7 (2019): 3941–67. http://dx.doi.org/10.3934/dcds.2019159.

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22

Afzal, Farkhanda, Mehmona Abdul Razaq, Deeba Afzal, and Saira Hameed. "Weighted entropy of penta chains graph." Eurasian Chemical Communications 2, no. 6 (2020): 652–62. http://dx.doi.org/10.33945/sami/ecc.2020.6.2.

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23

Stuhl, I., M. Kelbert, Y. Suhov, and S. Yasaei Sekeh. "Weighted Gaussian entropy and determinant inequalities." Aequationes mathematicae 96, no. 1 (2022): 85–114. http://dx.doi.org/10.1007/s00010-021-00861-3.

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24

mieja, M. "Weighted approach to general entropy function." IMA Journal of Mathematical Control and Information 32, no. 2 (2014): 329–41. http://dx.doi.org/10.1093/imamci/dnt044.

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25

Nourbakhsh, Mohammadreza, and Gholamhoseein Yari. "Weighted Renyi's entropy for lifetime distributions." Communications in Statistics - Theory and Methods 46, no. 14 (2017): 7085–98. http://dx.doi.org/10.1080/03610926.2016.1148729.

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26

Jiang, Wanchang, and Ning Dai. "Identifying Key Classes Algorithm in Directed Weighted Class Interaction Network Based on the Structure Entropy Weighted LeaderRank." Mathematical Problems in Engineering 2020 (December 10, 2020): 1–12. http://dx.doi.org/10.1155/2020/9234042.

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Identifying key classes can help software maintainers quickly understand software systems. The existing key class recognition algorithms consider the weight of class interaction, but the weight mechanism is single or arbitrary. In this paper, the multitype weighting mechanism is considered, and the key classes are accurately identified by using four kinds of interaction. By abstracting the software system into the directed weighted class interaction network, a novel Structure Entropy Weighted LeaderRank of identifying key classes algorithm is proposed. First, considering multiple types and dir

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27

Di Crescenzo, Antonio, and Abdolsaeed Toomaj. "Weighted Mean Inactivity Time Function with Applications." Mathematics 10, no. 16 (2022): 2828. http://dx.doi.org/10.3390/math10162828.

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We consider an extension of the mean inactivity time based on a non-negative weight function. We show various properties of the new notion, and relate it to various functions of interest in reliability theory and information measures, such as the dynamic cumulative entropy, the past entropy, the varentropy, and the weighted cumulative entropy. Moreover, based on the comparison of weighted mean inactivity times, we introduce and study a new stochastic order and compare it with other suitable orders. We also discuss some results about the variance of transformed random variables and the weighted

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28

Savita, Savita, and Rajeev Kumar. "Dynamic Weighted Cumulative Residual Entropy Estimators for Laplace Distribution: Bayesian Approach." Indian Journal Of Science And Technology 17, no. 6 (2024): 556–65. http://dx.doi.org/10.17485/ijst/v17i6.1661.

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Objectives: To develop Bayesian estimators of dynamic weighted cumulative residual entropy (DWCRE) for Laplace distribution and to investigate posterior risks using various priors and loss functions. Methods: Weighted entropy measure of information is provided by a probabilistic experiment whose basic events are described by their objective probabilities and some qualitative (objective or subjective) weights. In this paper, we have used priors (Jeffrey’s, Hartigan, Uniform and Gumble Type II) and several loss functions. Findings: Bayesian estimators and associated posterior risks for Laplace d

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29

Tunnicliffe, Martin, and Gordon Hunter. "Dimensionality, Granularity, and Differential Residual Weighted Entropy." Entropy 21, no. 9 (2019): 825. http://dx.doi.org/10.3390/e21090825.

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While Shannon’s differential entropy adequately quantifies a dimensioned random variable’s information deficit under a given measurement system, the same cannot be said of differential weighted entropy in its existing formulation. We develop weighted and residual weighted entropies of a dimensioned quantity from their discrete summation origins, exploring the relationship between their absolute and differential forms, and thus derive a “differentialized” absolute entropy based on a chosen “working granularity” consistent with Buckingham’s Π -theorem. We apply this formulation to three common c

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30

Edmunds, D. E., and Jiong Sun. "Approximation and entropy numbers of embeddings in weighted Orlicz spaces." Mathematica Bohemica 116, no. 3 (1991): 281–95. http://dx.doi.org/10.21136/mb.1991.126169.

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31

Lu, Jing, Hafiz Mutee-ur-Rehman, Saima Nazeer, and Xuemei An. "The Edge-Weighted Graph Entropy Using Redefined Zagreb Indices." Mathematical Problems in Engineering 2022 (March 28, 2022): 1–12. http://dx.doi.org/10.1155/2022/5958913.

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Measurements of graphs and retrieving structural information of complex networks using degree-based network entropy have become an informational theoretical concept. This terminology is extended by the concept of Shannon entropy. In this paper, we introduce entropy with graphs having edge weights which are basically redefined Zagreb indices. Some bounds are calculated to idealize the performance in limiting different kinds of graph entropy. In addition, we discuss the structural complexity of connected graphs representing chemical structures. In this article, we have discussed the edge-weighte

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32

Misagh, Farsam. "On Shift-Dependent Cumulative Entropy Measures." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/7213285.

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Measures of cumulative residual entropy (CRE) and cumulative entropy (CE) about predictability of failure time of a system have been introduced in the studies of reliability and life testing. In this paper, cumulative distribution and survival function are used to develop weighted forms of CRE and CE. These new measures are denominated as weighted cumulative residual entropy (WCRE) and weighted cumulative entropy (WCE) and the connections of these new measures with hazard and reversed hazard rates are assessed. These information-theoretic uncertainty measures are shift-dependent and various pr

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33

Su, Yuze, Xiangru Meng, Qiaoyan Kang, and Xiaoyang Han. "Dynamic Virtual Network Reconfiguration Method for Hybrid Multiple Failures Based on Weighted Relative Entropy." Entropy 20, no. 9 (2018): 711. http://dx.doi.org/10.3390/e20090711.

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Network virtualization can offer more flexibility and better manageability for next generation Internet. With the increasing deployments of virtual networks in military and commercial networks, a major challenge is to ensure virtual network survivability against hybrid multiple failures. In this paper, we study the problem of recovering virtual networks affected by hybrid multiple failures in substrate networks and provide an integer linear programming formulation to solve it. We propose a heuristic algorithm to tackle the complexity of the integer linear programming formulation, which include

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34

Hirica, Iulia-Elena, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae, and Vasile Preda. "Lie Symmetries of the Nonlinear Fokker–Planck Equation Based on Weighted Kaniadakis Entropy." Mathematics 10, no. 15 (2022): 2776. http://dx.doi.org/10.3390/math10152776.

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The paper studies the Lie symmetries of the nonlinear Fokker–Planck equation in one dimension, which are associated to the weighted Kaniadakis entropy. In particular, the Lie symmetries of the nonlinear diffusive equation, associated to the weighted Kaniadakis entropy, are found. The MaxEnt problem associated to the weighted Kaniadakis entropy is given a complete solution, together with the thermodynamic relations which extend the known ones from the non-weighted case. Several different, but related, arguments point out a subtle dichotomous behavior of the Kaniadakis constant k, distinguishing

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35

Kayal, Suchandan. "Generalized Residual Entropy and Upper Record Values." Journal of Probability and Statistics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/640426.

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In this communication, we deal with a generalized residual entropy of record values and weighted distributions. Some results on monotone behaviour of generalized residual entropy in record values are obtained. Upper and lower bounds are presented. Further, based on this measure, we study some comparison results between a random variable and its weighted version. Finally, we describe some estimation techniques to estimate the generalized residual entropy of a lifetime distribution.

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36

Qin, Guyue, and Pengjian Shang. "Analysis of Time Series Based on a New Entropy Plane by Using Weighted Dispersion Pattern." International Journal of Bifurcation and Chaos 31, no. 09 (2021): 2150128. http://dx.doi.org/10.1142/s0218127421501285.

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Complexity is an important feature of complex time series. In this paper, we construct a weighted dispersion pattern and propose a new entropy plane using past Tsallis entropy and past Rényi entropy by using weighted dispersion pattern (PTEWD and PREWD, respectively), to quantify the complexity of time series. Through analyzing simulated data and actual data, we have verified the reliability of the entropy plane method. This entropy plane successfully distinguishes American and Chinese stock indexes, as well as developed and emergent stock markets. We introduce PTEWD and PREWD into multiscale

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37

Huang, Yujie, Hafiz Mutee-ur-Rehman, Saima Nazeer, Deeba Afzal, and Xiaoli Qiang. "Some Bounds of Weighted Entropies with Augmented Zagreb Index Edge Weights." Discrete Dynamics in Nature and Society 2020 (August 17, 2020): 1–12. http://dx.doi.org/10.1155/2020/3562382.

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The graph entropy was proposed by Körner in the year 1973 when he was studying the problem of coding in information theory. The foundation of graph entropy is in information theory, but it was demonstrated to be firmly identified with some established and often examined graph-theoretic ideas. For instance, it gives an equal definition to a graph to be flawless, and it can likewise be connected to acquire lower bounds in graph covering problems. The objective of this study is to solve the open problem suggested by Kwun et al. in 2018. In this paper, we study the weighted graph entropy by taking

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38

Li, Xiaohu, and Shuhong Zhang. "SOME NEW RESULTS ON RÉNYI ENTROPY OF RESIDUAL LIFE AND INACTIVITY TIME." Probability in the Engineering and Informational Sciences 25, no. 2 (2011): 237–50. http://dx.doi.org/10.1017/s0269964810000379.

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This article deals with Rényi entropies for the residual life and the inactivity time. Monotonic properties of the entropy in order statistics, record values, and weighted distributions are investigated, and the comparison on weighted random variables is studied in terms of residual Rényi entropy as well.

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39

Kannappan, Pl, and P. K. Sahoo. "On the general solution of a functional equation connected to sum form information measures on open domain—III." International Journal of Mathematics and Mathematical Sciences 9, no. 3 (1986): 545–50. http://dx.doi.org/10.1155/s0161171286000686.

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In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degreeβ. Here, we find the general solution of the functional equation (2) on an open domain, without using0-probability and1-probability.

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40

Sánchez, Joan Andreu, Martha Alicia Rocha, Verónica Romero, and Mauricio Villegas. "On the Derivational Entropy of Left-to-Right Probabilistic Finite-State Automata and Hidden Markov Models." Computational Linguistics 44, no. 1 (2018): 17–37. http://dx.doi.org/10.1162/coli_a_00306.

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Probabilistic finite-state automata are a formalism that is widely used in many problems of automatic speech recognition and natural language processing. Probabilistic finite-state automata are closely related to other finite-state models as weighted finite-state automata, word lattices, and hidden Markov models. Therefore, they share many similar properties and problems. Entropy measures of finite-state models have been investigated in the past in order to study the information capacity of these models. The derivational entropy quantifies the uncertainty that the model has about the probabili

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41

Bhad, Bilal Ahmad, and Mirza Abdul Khaliq Baig. "A New Two Parametric Weighted Generalized Entropy for Lifetime Distributions." Journal of Modern Applied Statistical Methods 18, no. 2 (2020): 2–21. http://dx.doi.org/10.22237/jmasm/1604189340.

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The concept of weighted generalized entropy and its dynamic residual (version) is developed. The general expressions of these two uncertainty measures corresponding to some well-known lifetime distributions are derived. It is shown that the proposed dynamic entropy determines the survival function uniquely. Some significant properties and inequalities of this dynamic entropy are also discussed.

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42

Heinig, H. P., and M. Smith. "Extensions of the Heisenberg-Weyl inequality." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 185–92. http://dx.doi.org/10.1155/s0161171286000212.

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In this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove then-dimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2). From a general weighted form of the Hausdorff-Young theorem, a one-dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg-Weyl inequalities are given.

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43

Xu, Zhongqi, Cunlai Pu, Rajput Ramiz Sharafat, Lunbo Li, and Jian Yang. "Entropy-based link prediction in weighted networks." Chinese Physics B 26, no. 1 (2017): 018902. http://dx.doi.org/10.1088/1674-1056/26/1/018902.

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44

Bierkens, Joris, and Hilbert J. Kappen. "Explicit solution of relative entropy weighted control." Systems & Control Letters 72 (October 2014): 36–43. http://dx.doi.org/10.1016/j.sysconle.2014.08.001.

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45

Guiasu, Silviu. "Grouping data by using the weighted entropy." Journal of Statistical Planning and Inference 15 (January 1986): 63–69. http://dx.doi.org/10.1016/0378-3758(86)90085-6.

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Lai, Weng Kin, Imran M. Khan, and Geong Sen Poh. "Weighted Entropy-based Measure for Image Segmentation." Procedia Engineering 41 (2012): 1261–67. http://dx.doi.org/10.1016/j.proeng.2012.07.309.

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47

CHEN, XIANG-HUI, ARTHUR P. DEMPSTER, and JUN S. LIU. "Weighted finite population sampling to maximize entropy." Biometrika 81, no. 3 (1994): 457–69. http://dx.doi.org/10.1093/biomet/81.3.457.

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48

Mirali, M., and S. Baratpour. "Dynamic version of weighted cumulative residual entropy." Communications in Statistics - Theory and Methods 46, no. 22 (2016): 11047–59. http://dx.doi.org/10.1080/03610926.2016.1257711.

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49

PARKASH, O., P. SHARMA, and R. MAHAJAN. "New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle." Information Sciences 178, no. 11 (2008): 2389–95. http://dx.doi.org/10.1016/j.ins.2007.12.003.

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50

Gao, Jing, and Pengjian Shang. "Multiscale weighted Rényi entropy causality plane for financial time series." International Journal of Modern Physics C 30, no. 05 (2019): 1950037. http://dx.doi.org/10.1142/s0129183119500372.

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The permutation entropy (PE) is a statistical measure which can describe complexity of time series. In recent years, the research on PE is increasing gradually. As part of its application, the complexity–entropy causality plane (CECP) and weighted CECP (WCECP) have been recently used to distinguish the stage of stock market development. In this paper, we focus on weighted Rényi entropy causality plane (WRECP), and then extend WCECP and WRECP into multiscale WCECP (MWCECP) and multiscale WRECP (MWRECP) by introducing a new parameter scale. By data simulating and analyzing, we show the power of

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