Entropy measure for orderable sets

Zhang, Hui; Deng, Yong

doi:10.1016/j.ins.2021.01.073

Cited by 47 publications

(17 citation statements)

References 39 publications

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“…The world is full of unknowns, and the unknown world will have many unknown problems Zhang and Deng 2021). Unknown information needs to be represented by tools that represent information (Turhan and Demirekler 2017;).…”

Section: Preliminariesmentioning

confidence: 99%

Interval-valued belief entropies for Dempster–Shafer structures

Xue

Deng

2021

Soft Comput

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In practical application problems, the uncertainty of an unknown object is often very difficult to accurately determine, so Yager proposed the interval-valued entropies for Dempster-Shafer structures, which is based on Dempster-Shafer structures and classic Shannon entropy and is an interval entropy model. Based on Dempster-Shafer structures and classic Shannon entropy, the interval uncertainty of an unknown object is determined, which provides reference for theoretical research and provides help for industrial applications. Although the interval-valued entropies for Dempster-Shafer structures can solve the uncertainty interval of an object very efficiently, its application scope is only a traditional probability space. How to extend it to the evidential environment is still an open issue. This paper proposes interval-valued belief entropies for Dempster-Shafer structures, which is an extension of the interval-valued entropies for Dempster-Shafer structures. When the belief entropy degenerates to the classic Shannon entropy, the interval-valued belief entropies for Dempster-Shafer structures will degenerate into the interval-valued entropies for Dempster-Shafer structures. Numerical examples are applied to verify the validity of the interval-valued belief entropies for Dempster-Shafer structures. The experimental results demonstrate that the proposed entropy can obtain the interval uncertainty value of a given uncertain object successfully and make decision effectively.

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Section: Preliminariesmentioning

confidence: 99%

Interval-valued belief entropies for Dempster–Shafer structures

Xue

Deng

2021

Soft Comput

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“…Assuming that Θ is a set of mutually exclusive and exhaustive elements F i ( i = 1 , 2 , 3 , 4 , … , N ) , and it can be defined as 31…”

Section: Preliminariesmentioning

confidence: 99%

A novel divergence measure in Dempster–Shafer evidence theory based on pignistic probability transform and its application in multi-sensor data fusion

Hou

Deng

et al. 2021

International Journal of Distributed Sensor Networks

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Dempster–Shafer (D–S) evidence theory is more and more extensively applied in multi-sensor data fusion. However, it is still an open issue that how to effectively combine highly conflicting evidence in D–S evidence theory. In this article, a novel divergence measure, called pignistic probability transformation divergence, is proposed to measure the difference between evidences. The proposed pignistic probability transformation divergence can reflect the interaction between single-element and multi-element subsets by introducing the pignistic probability transformation, and satisfies the properties of boundedness, non-degeneracy, and symmetry. Moreover, the pignistic probability transformation divergence can degenerate as Jensen–Shannon divergence when mass function and the probability distribution are consistent. Based on the pignistic probability transformation divergence, a new multi-sensor data fusion method is presented. The proposed method takes advantage of pignistic probability transformation divergence to measure the discrepancy between evidences in order to obtain the credibility weights, and belief entropy to measure the uncertainty of the evidences in order to obtain the information volume weights, which can fully mine the potential information between evidences. Then, the credibility weights and the information volume weights are integrated to generate an appropriate weighted average evidence before using Dempster’s combination rule. The results of two application cases illustrate that the proposed method outperforms other related methods for combining highly conflicting evidences.

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“…This measure can effectively assess the amount of “surprise” (new information) contained in any given instance of the result of a random variable with a known distribution function. Originally formulated in the context of telecommunications, researchers have extended the applications of this technique in a wide array of research fields, such as econometry [ 2 ], computer theory [ 3 ], set theory [ 4 ], and medicine [ 5 ].…”

Section: Introductionmentioning

confidence: 99%

The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

Dávalos

Jabloun

Ravier

et al. 2021

Entropy

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Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener–Khinchin theorem, we theoretically characterize the linear filter’s intrinsic PE and separated its contribution from the signal’s ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.

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Entropy measure for orderable sets

Cited by 47 publications

References 39 publications

Interval-valued belief entropies for Dempster–Shafer structures

Interval-valued belief entropies for Dempster–Shafer structures

A novel divergence measure in Dempster–Shafer evidence theory based on pignistic probability transform and its application in multi-sensor data fusion

The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

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