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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| Veröffentlicht in: | Chaos, solitons and fractals Jg. 184; S. 114976 |
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| Abstract | 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). |
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| AbstractList | 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). |
| ArticleNumber | 114976 |
| Author | Zhou, Jiefeng Li, Zhen Zhan, Tianxiang Deng, Yong |
| Author_xml | – sequence: 1 givenname: Tianxiang orcidid: 0000-0002-5188-0381 surname: Zhan fullname: Zhan, Tianxiang organization: Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, Sichuan, China – sequence: 2 givenname: Jiefeng orcidid: 0009-0003-0424-2381 surname: Zhou fullname: Zhou, Jiefeng organization: Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, Sichuan, China – sequence: 3 givenname: Zhen orcidid: 0000-0002-5156-3730 surname: Li fullname: Li, Zhen email: zhen.li@pku.edu.cn organization: China Mobile Information Technology Center, China Mobile, 100029, Beijing, China – sequence: 4 givenname: Yong orcidid: 0000-0001-9286-2123 surname: Deng fullname: Deng, Yong email: dengentropy@uestc.edu.cn organization: Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, Sichuan, China |
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