Chaos, solitons and fractals, ISSN 0960-0779, 2016, Volume 91, pp. 549 - 553

.... However, how to measure uncertainty in evidence theory is still an open issue. The main contribution of this paper is that a new entropy, named as Deng entropy, is presented to measure the uncertainty of a basic probability assignment (BPA...

Shannon entropy | Uncertainty measure | Deng entropy | Entropy | Dempster-Shafer evidence theory | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPECIFICITY | PHYSICS, MULTIDISCIPLINARY | UNCERTAINTY | DEMPSTER-SHAFER THEORY | PHYSICS, MATHEMATICAL | BASIC PROBABILITY ASSIGNMENT

Shannon entropy | Uncertainty measure | Deng entropy | Entropy | Dempster-Shafer evidence theory | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPECIFICITY | PHYSICS, MULTIDISCIPLINARY | UNCERTAINTY | DEMPSTER-SHAFER THEORY | PHYSICS, MATHEMATICAL | BASIC PROBABILITY ASSIGNMENT

Journal Article

Entropy (Basel, Switzerland), ISSN 1099-4300, 2016, Volume 18, Issue 3, pp. 84 - 84

The entropies of Shannon, Renyi and Kolmogorov are analyzed and compared together with their main properties...

Iterated function system | Box-counting dimension | Fractal dimension | Rényi entropy | Generalized fractal dimension | Shannon entropy | Fractal antenna | Kolmogorov entropy | fractal antenna | iterated function system | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | COMPLEXITY | fractal dimension | generalized fractal dimension | box-counting dimension | Renyi entropy | SIERPINSKI | Fractals | Entropy | Entropy (Information) | Fractal analysis | Antennas

Iterated function system | Box-counting dimension | Fractal dimension | Rényi entropy | Generalized fractal dimension | Shannon entropy | Fractal antenna | Kolmogorov entropy | fractal antenna | iterated function system | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | COMPLEXITY | fractal dimension | generalized fractal dimension | box-counting dimension | Renyi entropy | SIERPINSKI | Fractals | Entropy | Entropy (Information) | Fractal analysis | Antennas

Journal Article

2019, ISBN 9783038972228

Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network...

hydrological risk analysis | modeling | water level | Poyang Lake basin | trend | composite multiscale sample entropy | flood frequency analysis | canopy flow | precipitation | water resources | complex systems | frequency analysis | optimization | combined forecast | neural network forecast | entropy spectral analysis time series analysis | environmental engineering | hydrometric network | sea surface temperature | kernel density estimation | robustness | turbulent flow | entropy production | connection entropy | flux concentration relation | turbulence | tropical rainfall | generalized gamma (GG) distribution | multi-events | El Niño | joint entropy | entropy weighting method | Anhui Province | changing environment | complexity | multiplicative cascades | Tsallis entropy | Hexi corridor | coherent structures | water resources vulnerability | uncertainty | variability | flow entropy | Hei River basin | fuzzy analytic hierarchy process | substitute | crop yield | conditional entropy production | entropy | flow duration curve | mean annual runoff | temperature | hydrometeorological extremes | resilience | Loess Plateau | information entropy | scaling | water distribution networks | cross entropy | randomness | forewarning model | entropy applications | quaternary catchment | spatio-temporal variability | probability distribution function | ant colony fuzzy clustering | radar | continuous probability distribution functions | Shannon entropy | informational entropy | information | confidence intervals | marginal entropy | rainfall forecast | entropy of information | streamflow | power laws | bootstrap aggregating | maximum entropy-copula method | spatial and dynamics characteristic | projection pursuit | set pair analysis | entropy theory | water resource carrying capacity | entropy parameter | precipitation frequency analysis | principle of maximum entropy | information theory | stochastic processes | network design | complement | cross elasticity | climacogram | methods of moments | hydrology | bagging | principle of maximum entropy (POME) | rainfall network | entropy ensemble filter | ensemble model simulation criterion | Lagrangian function | Beta-Lognormal model | cross-entropy minimization | ANN | configurational entropy | variation of information | statistical scaling | EEF method | water monitoring | maximum likelihood estimation | GB2 distribution | NDVI | four-parameter exponential gamma distribution | hydraulics | spatial optimization | Kolmogorov complexity | bootstrap neural networks | mutual information | accelerating genetic algorithm | groundwater depth | rainfall | tropical Pacific | water engineering | monthly streamflow forecasting | ENSO | nonlinear relation | Bayesian technique | non-point source pollution | Burg entropy | data-scarce | scaling laws | soil water content | arid region | land suitability evaluation | information transfer

hydrological risk analysis | modeling | water level | Poyang Lake basin | trend | composite multiscale sample entropy | flood frequency analysis | canopy flow | precipitation | water resources | complex systems | frequency analysis | optimization | combined forecast | neural network forecast | entropy spectral analysis time series analysis | environmental engineering | hydrometric network | sea surface temperature | kernel density estimation | robustness | turbulent flow | entropy production | connection entropy | flux concentration relation | turbulence | tropical rainfall | generalized gamma (GG) distribution | multi-events | El Niño | joint entropy | entropy weighting method | Anhui Province | changing environment | complexity | multiplicative cascades | Tsallis entropy | Hexi corridor | coherent structures | water resources vulnerability | uncertainty | variability | flow entropy | Hei River basin | fuzzy analytic hierarchy process | substitute | crop yield | conditional entropy production | entropy | flow duration curve | mean annual runoff | temperature | hydrometeorological extremes | resilience | Loess Plateau | information entropy | scaling | water distribution networks | cross entropy | randomness | forewarning model | entropy applications | quaternary catchment | spatio-temporal variability | probability distribution function | ant colony fuzzy clustering | radar | continuous probability distribution functions | Shannon entropy | informational entropy | information | confidence intervals | marginal entropy | rainfall forecast | entropy of information | streamflow | power laws | bootstrap aggregating | maximum entropy-copula method | spatial and dynamics characteristic | projection pursuit | set pair analysis | entropy theory | water resource carrying capacity | entropy parameter | precipitation frequency analysis | principle of maximum entropy | information theory | stochastic processes | network design | complement | cross elasticity | climacogram | methods of moments | hydrology | bagging | principle of maximum entropy (POME) | rainfall network | entropy ensemble filter | ensemble model simulation criterion | Lagrangian function | Beta-Lognormal model | cross-entropy minimization | ANN | configurational entropy | variation of information | statistical scaling | EEF method | water monitoring | maximum likelihood estimation | GB2 distribution | NDVI | four-parameter exponential gamma distribution | hydraulics | spatial optimization | Kolmogorov complexity | bootstrap neural networks | mutual information | accelerating genetic algorithm | groundwater depth | rainfall | tropical Pacific | water engineering | monthly streamflow forecasting | ENSO | nonlinear relation | Bayesian technique | non-point source pollution | Burg entropy | data-scarce | scaling laws | soil water content | arid region | land suitability evaluation | information transfer

eBook

Annals of operations research, ISSN 1572-9338, 2019, pp. 1 - 24

... of Rényi entropy, an information-theoretic criterion that precisely quantifies the uncertainty embedded in a distribution, accounting for higher-order moments...

Parameter uncertainty | Entropy (Information theory) | Risk | Kurtosis | Entropy | Normality | Optimization | Information theory

Parameter uncertainty | Entropy (Information theory) | Risk | Kurtosis | Entropy | Normality | Optimization | Information theory

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 11/2016, Volume 62, Issue 11, pp. 6007 - 6018

The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors...

Ingleton score | Visualization | Shape | non-Shannon inequality | selfadhesivity | Ingleton inequality | Entropy | four-atom conjecture | Channel coding | Entropy region | entropy function | Convolution | information-theoretic inequality | Zhang-Yeung inequality | polymatroid | Network coding | Random variables | matroid | convolution | INFORMATION INEQUALITIES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Matrices | Research | Entropy (Information theory) | Approximation | Entropy (Information) | Decomposition | Closures | Information theory

Ingleton score | Visualization | Shape | non-Shannon inequality | selfadhesivity | Ingleton inequality | Entropy | four-atom conjecture | Channel coding | Entropy region | entropy function | Convolution | information-theoretic inequality | Zhang-Yeung inequality | polymatroid | Network coding | Random variables | matroid | convolution | INFORMATION INEQUALITIES | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Matrices | Research | Entropy (Information theory) | Approximation | Entropy (Information) | Decomposition | Closures | Information theory

Journal Article

2011, New Mathematical Monographs, ISBN 0521888859, Volume 18, xii, 391

"This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations...

Topological entropy | Topological dynamics | Textbooks

Topological entropy | Topological dynamics | Textbooks

Book

Journal of cleaner production, ISSN 0959-6526, 2019, Volume 207, pp. 498 - 509

...; then, the study directs readers towards a successful implementation of GSCM practices. The proposed methodology uses a hybrid Entropy-TOPSIS-F framework to weight the criteria and select the supplier with the best environmental performance...

Shannon entropy | Green supply chain management | Supplier selection | Environmental performance | Entropy-TOPSIS-F | Fuzzy TOPSIS | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | SUSTAINABILITY | REVERSE LOGISTICS PARTNER | MODEL | CHAIN MANAGEMENT-PRACTICES | DECISION-MAKING METHOD | ENVIRONMENTAL SCIENCES | ENGINEERING, ENVIRONMENTAL | MULTI CRITERIA APPROACH | FRAMEWORK | ENVIRONMENTAL CRITERIA | SELECTION | MCDM APPROACH | Decision-making | Furniture industry | Employee motivation | Environmental management systems | Analysis | Rankings | Furniture | Environmental auditing | Logistics | Environmental protection

Shannon entropy | Green supply chain management | Supplier selection | Environmental performance | Entropy-TOPSIS-F | Fuzzy TOPSIS | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | SUSTAINABILITY | REVERSE LOGISTICS PARTNER | MODEL | CHAIN MANAGEMENT-PRACTICES | DECISION-MAKING METHOD | ENVIRONMENTAL SCIENCES | ENGINEERING, ENVIRONMENTAL | MULTI CRITERIA APPROACH | FRAMEWORK | ENVIRONMENTAL CRITERIA | SELECTION | MCDM APPROACH | Decision-making | Furniture industry | Employee motivation | Environmental management systems | Analysis | Rankings | Furniture | Environmental auditing | Logistics | Environmental protection

Journal Article

IEEE transactions on information theory, ISSN 1557-9654, 2018, Volume 64, Issue 5, pp. 3579 - 3589

This paper addresses the correspondence between linear inequalities for Shannon entropy and differential entropy for sums of independent group-valued random variables...

Additives | differential entropy | additive-combinatorial entropy inequality | Tools | Probability density function | Shannon entropy | Data processing | Entropy | Random variables | Electronic mail | quantization | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | SUMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Asymptotic properties | Entropy (Information theory) | Independent variables | Inequalities | Quantum theory | Combinatorial analysis | Linear functions

Additives | differential entropy | additive-combinatorial entropy inequality | Tools | Probability density function | Shannon entropy | Data processing | Entropy | Random variables | Electronic mail | quantization | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | SUMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Asymptotic properties | Entropy (Information theory) | Independent variables | Inequalities | Quantum theory | Combinatorial analysis | Linear functions

Journal Article

Journal of cleaner production, ISSN 0959-6526, 09/2018, Volume 195, pp. 593 - 604

...) in China during 1980–2015 was established and Comprehensively Evaluated (CE) using the entropy method...

Petroleum flow | Entropy | CO2 emissions | China | Material flow indicators | emissions | PATHWAYS | ANALYTIC HIERARCHY PROCESS | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | SPATIOTEMPORAL VARIATIONS | DECOMPOSITION | ALUMINUM STOCKS | ZINC CYCLE | DYNAMIC-ANALYSIS | ENVIRONMENTAL SCIENCES | SHANNON ENTROPY | ENGINEERING, ENVIRONMENTAL | FOSSIL ENERGY-CONSUMPTION | Petroleum mining | Analysis

Petroleum flow | Entropy | CO2 emissions | China | Material flow indicators | emissions | PATHWAYS | ANALYTIC HIERARCHY PROCESS | GREEN & SUSTAINABLE SCIENCE & TECHNOLOGY | SPATIOTEMPORAL VARIATIONS | DECOMPOSITION | ALUMINUM STOCKS | ZINC CYCLE | DYNAMIC-ANALYSIS | ENVIRONMENTAL SCIENCES | SHANNON ENTROPY | ENGINEERING, ENVIRONMENTAL | FOSSIL ENERGY-CONSUMPTION | Petroleum mining | Analysis

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2010, Volume 56, Issue 8, pp. 3712 - 3720

... . This paper shows that the integral over all signal-to-noise ratios (SNRs) of the excess mean-square estimation error incurred by the mismatched estimator is twice the relative entropy D(P ||Q) (in nats...

minimum mean- square error (MMSE) estimation | Estimation error | Divergence | Estimation theory | Probability | Entropy | Shannon theory | free probability | Gaussian noise | relative entropy | Random variables | Mutual information | Network address translation | Signal to noise ratio | Information theory | statistics | mutual information | GAUSSIAN CHANNELS | MEAN-SQUARE ERROR | ANALOGS | PERTURBATION | FREE PROBABILITY-THEORY | COMPUTER SCIENCE, INFORMATION SYSTEMS | minimum mean-square error (MMSE) estimation | POWER INEQUALITY | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | FISHER INFORMATION MEASURE | Measurement | Entropy (Information theory) | Integrals | Noise | Gaussian | Representations | Estimators

minimum mean- square error (MMSE) estimation | Estimation error | Divergence | Estimation theory | Probability | Entropy | Shannon theory | free probability | Gaussian noise | relative entropy | Random variables | Mutual information | Network address translation | Signal to noise ratio | Information theory | statistics | mutual information | GAUSSIAN CHANNELS | MEAN-SQUARE ERROR | ANALOGS | PERTURBATION | FREE PROBABILITY-THEORY | COMPUTER SCIENCE, INFORMATION SYSTEMS | minimum mean-square error (MMSE) estimation | POWER INEQUALITY | SIMPLE PROOF | ENGINEERING, ELECTRICAL & ELECTRONIC | FISHER INFORMATION MEASURE | Measurement | Entropy (Information theory) | Integrals | Noise | Gaussian | Representations | Estimators

Journal Article

Oikos, ISSN 1600-0706, 2006, Volume 113, Issue 2, pp. 363 - 375

Entropies such as the Shannon-Wiener and Gini-Simpson indices are not themselves diversities...

Species diversity | Opinion | Diversity indices | Communities | Shannon entropy | Entropy | Gini index | Mathematical functions | Biodiversity | Species | Butterflies | SPECIES-DIVERSITY | STATISTICS | EVENNESS | FRAMEWORK | MULTIPLE COMMUNITIES | ECOLOGY | SIMILARITY | Environmental aspects | Usage | Entropy (Physics) | Biological diversity | Indexes | Mathematical analysis | Measurement techniques

Species diversity | Opinion | Diversity indices | Communities | Shannon entropy | Entropy | Gini index | Mathematical functions | Biodiversity | Species | Butterflies | SPECIES-DIVERSITY | STATISTICS | EVENNESS | FRAMEWORK | MULTIPLE COMMUNITIES | ECOLOGY | SIMILARITY | Environmental aspects | Usage | Entropy (Physics) | Biological diversity | Indexes | Mathematical analysis | Measurement techniques

Journal Article

12.
Full Text
The maximum entropy production and maximum Shannon information entropy in enzyme kinetics

Physica A, ISSN 0378-4371, 2018, Volume 496, pp. 220 - 232

We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions...

Stability analysis | Maximum entropy production | Enzyme kinetics | Glucose isomerase | Shannon information entropy | CATALYSIS | CALCIUM OSCILLATIONS | PHYSICS, MULTIDISCIPLINARY | FLEXIBILITY | THERMODYNAMICS | ISOMERASE | PRODUCTION PRINCIPLE | FLUCTUATION THEOREM | SYSTEMS | STEADY-STATE

Stability analysis | Maximum entropy production | Enzyme kinetics | Glucose isomerase | Shannon information entropy | CATALYSIS | CALCIUM OSCILLATIONS | PHYSICS, MULTIDISCIPLINARY | FLEXIBILITY | THERMODYNAMICS | ISOMERASE | PRODUCTION PRINCIPLE | FLUCTUATION THEOREM | SYSTEMS | STEADY-STATE

Journal Article

Mathematical Programming, ISSN 0025-5610, 1/2017, Volume 161, Issue 1, pp. 1 - 32

In this expository article, we study optimization problems specified via linear and relative entropy inequalities...

Golden–Thompson inequality | Theoretical, Mathematical and Computational Physics | Mathematics | Dynamical systems | Optimization over non-commuting variables | Von-Neumann entropy | 94A15 | Mathematical Methods in Physics | Araki–Umegaki relative entropy | Robust optimization | 81P45 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Quantum channel capacity | 94A17 | Shannon entropy | Quantum information | Combinatorics | Matrix permanent | Araki-Umegaki relative entropy | Golden-Thompson inequality | STATISTICAL-MECHANICS | MATRIX | MATHEMATICS, APPLIED | INFORMATION | ALGORITHM | CONVEX-OPTIMIZATION | MAXIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUANTUM CHANNELS | PERMANENTS | 2ND-ORDER CONE | MIXED VOLUMES | Electrical engineering | Atoms | Studies | Entropy | Quantum physics | Analysis | Optimization | Mathematical programming | Functions (mathematics) | Maximization | Mathematical analysis | Inequalities | Convexity

Golden–Thompson inequality | Theoretical, Mathematical and Computational Physics | Mathematics | Dynamical systems | Optimization over non-commuting variables | Von-Neumann entropy | 94A15 | Mathematical Methods in Physics | Araki–Umegaki relative entropy | Robust optimization | 81P45 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Quantum channel capacity | 94A17 | Shannon entropy | Quantum information | Combinatorics | Matrix permanent | Araki-Umegaki relative entropy | Golden-Thompson inequality | STATISTICAL-MECHANICS | MATRIX | MATHEMATICS, APPLIED | INFORMATION | ALGORITHM | CONVEX-OPTIMIZATION | MAXIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | QUANTUM CHANNELS | PERMANENTS | 2ND-ORDER CONE | MIXED VOLUMES | Electrical engineering | Atoms | Studies | Entropy | Quantum physics | Analysis | Optimization | Mathematical programming | Functions (mathematics) | Maximization | Mathematical analysis | Inequalities | Convexity

Journal Article

The Annals of statistics, ISSN 0090-5364, 10/2008, Volume 36, Issue 5, pp. 2153 - 2182

A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in ${\Bbb R}^{m}$ is presented...

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | DISTANCES | STATISTICS & PROBABILITY | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ASYMPTOTICS | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | ENTROPY | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | DISTANCES | STATISTICS & PROBABILITY | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ASYMPTOTICS | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | ENTROPY | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Journal Article

The Astrophysical journal, ISSN 1538-4357, 2019, Volume 870, Issue 2, p. 128

...) discreteness effects. We integrate orbit ensembles in fixed potentials, estimating the entropy to analyze the time evolution of the distribution function...

galaxies: formation | galaxies: halos | galaxies: kinematics and dynamics | STATISTICAL-MECHANICS | VLASOV | INSTABILITY | DENSITY | LAWS | VIOLENT RELAXATION | SYMMETRY | ASTRONOMY & ASTROPHYSICS | DYNAMICS | GALAXIES | BODY | Thermodynamics | Time dependence | Shannon theorem | Evolution | Orbits | Entropy | Open clusters | Time | Vlasov equations | Entropy production | Relaxation time | Distribution functions

galaxies: formation | galaxies: halos | galaxies: kinematics and dynamics | STATISTICAL-MECHANICS | VLASOV | INSTABILITY | DENSITY | LAWS | VIOLENT RELAXATION | SYMMETRY | ASTRONOMY & ASTROPHYSICS | DYNAMICS | GALAXIES | BODY | Thermodynamics | Time dependence | Shannon theorem | Evolution | Orbits | Entropy | Open clusters | Time | Vlasov equations | Entropy production | Relaxation time | Distribution functions

Journal Article