Wada index based on the weighted and truncated Shannon entropy

Saunorienė, Loreta; Ragulskis, Minvydas; Cao, Jinde; Sanjuán, Miguel A. F.

doi:10.1007/s11071-021-06261-1

Cited by 19 publications

(11 citation statements)

References 24 publications

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“…Shannon introduced entropy theory into the field of information, which broadened the research of uncertainty measurement [27]. Since Shannon entropy was proposed, entropy theory has been widely developed and improved [45], [46], [47], [48], [49]. However, in Dempster-Shafer evidence theory, how to calculate the uncertainty of BPA is still a developmental problem.…”

Section: A New Methods For Measuring Uncertainty a Measure Uncertainty Based On Renyi Entropymentioning

confidence: 99%

Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Chen

Luo

2021

IEEE Access

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Since the Dempster-Shafer evidence theory was developed, it has been extensively concerned by researchers. Compared with Bayesian probability theory, Dempster-Shafer evidence theory satisfies weaker constraints and has the advantage to indicate uncertainty, so it is widely used in the information system. However, how to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory is still a problem worthy of attention. Therefore, based on Renyi entropy, this paper proposes a novel method to measure the uncertainty of basic probability assignment in Dempster-Shafer evidence theory. In addition, after proving that this method is compatible with Shannon entropy, a large number of comparative experiments are carried out to illustrate its effectiveness. Finally, through the application in decision-making, it is proved that the combination rule considering uncertainty can produce more reasonable results.

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Section: A New Methods For Measuring Uncertainty a Measure Uncertainty Based On Renyi Entropymentioning

confidence: 99%

Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Chen

Luo

2021

IEEE Access

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“…DistE 2D is used to analyse the irregularity of smallsized textures. In [40], the Wada index used the geometrical For the analysis, we choose the directed graph − → G because: 1) the directed adjacency matrix has more entries equal to zero than the undirected version and hence the algorithm is faster, 2) the algorithm PE 2D presented in [13] (and almost every 2D algorithm) implicitly uses this orientation in the vectorisation, 3) the orientation preserves more information of the geometry of the graphs and hence gives us better results, 4) if…”

Section: B Permutation Entropy For Images (2d)mentioning

confidence: 99%

Permutation Entropy for Graph Signals

Fabila-Carrasco

Tan

Escudero

2022

IEEE Trans. on Signal and Inf. Process. over Networks

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Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (onedimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice pattern (two-dimensional data) using its symmetry, thus enabling their application to images. However, these metrics have not been developed for signals sampled on irregular domains, defined by a graph. Here, we define for the first time an entropy metric to analyse signals measured over irregular graphs by generalising permutation entropy, a well-established nonlinear metric based on the comparison of neighbouring values within patterns in a time series. Our algorithm is based on comparing signal values on neighbouring nodes, using the adjacency matrix. We show that this generalisation preserves the properties of classical permutation for time series and the recent permutation entropy for images, and it can be applied to any graph structure with synthetic and real signals. We expect the present work to enable the extension of other nonlinear dynamic approaches to graph signals.

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“…1, the basin entropy of the Newton fractal can be estimated as S b = (n b /n)ε α log m. This result is in agreement with Eq. 5 of [13], so that the unpredictability of the system increases more when it changes from 2 to 3 attractors than when it changes from 9 to 10.…”

Section: Number Of Attractors and Wada Propertymentioning

confidence: 99%

“…Thus, the number of basins separated by the boundaries plays an important role in the basin entropy, but so does another important parameter: the Wada index [13]. This number accounts for the distribution of the colors inside the boundary boxes, so that it is maximal for equiprobable situations.…”

Section: Number Of Attractors and Wada Propertymentioning

confidence: 99%

“…Along the last decades, a plethora of different kinds of basins with special characteristics has been reported: locally connected and disconnected [3], Wada [5], riddled [6,7], intermingled [8], etc. At the same time, a variety of different tools has arisen to describe and characterize them: the uncertainty exponent [9], the lacunarity [10], the basin stability [11], the Wada parameter [12], the Wada index [13], etc. Among them, the basin entropy [14] integrates some previous measures in a natural way.…”

Section: Introductionmentioning

confidence: 99%

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Classifying basins of attraction using the basin entropy

Daza,

Wagemakers,

Sanjuán

2022

Preprint

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A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property.

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Wada index based on the weighted and truncated Shannon entropy

Cited by 19 publications

References 24 publications

Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Uncertainty Measure of Basic Probability Assignment Based on Renyi Entropy and Its Application in Decision-Making

Permutation Entropy for Graph Signals

Classifying basins of attraction using the basin entropy

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