Generalized information entropy and generalized information dimension

The concept of entropy has played a significant role in thermodynamics and information theory, and is also a current research hotspot. Information entropy, as a measure of information, has many different forms, such as Shannon entropy and Deng entropy, but there is no unified interpretation of infor...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 184; p. 114976
Main Authors: Zhan, Tianxiang, Zhou, Jiefeng, Li, Zhen, Deng, Yong
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.07.2024
Subjects:
Approximate calculation
Coding theory
Information entropy
Mass function
Probability
Probability
Coding theory
Mass function
Information entropy
Approximate calculation
ISSN:0960-0779
Online Access:Get full text
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Summary:The concept of entropy has played a significant role in thermodynamics and information theory, and is also a current research hotspot. Information entropy, as a measure of information, has many different forms, such as Shannon entropy and Deng entropy, but there is no unified interpretation of information from a measurement perspective. To address this issue, this article proposes Generalized Information Entropy (GIE) that unifies entropies based on mass function. Meanwhile, GIE establishes the relationship between entropy, fractal dimension, and number of events. Therefore, Generalized Information Dimension (GID) has been proposed, which extends the definition of information dimension from probability to mass fusion. GIE plays a role in approximation calculation and coding systems. In the application of coding, information from the perspective of GIE exhibits a certain degree of particle nature that the same event can have different representational states, similar to the number of microscopic states in Boltzmann entropy. •Generalized Information Entropy is compatible with Shannon entropy, Deng entropy, and RPS entropy.•Generalized Information Dimension achieves approximate calculation of large number entropy.•The form of Generalized Information Entropy is closer to Boltzmann entropy.•The linearity of Deng entropy is further explained (Zhao et al., 2024).
ISSN:0960-0779
DOI:10.1016/j.chaos.2024.114976