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Exponential negation of a probability distribution

  • Fuzzy systems and their mathematics
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Abstract

Negation operation is important in intelligent information processing. Different existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation are investigated, and we find that the fix point is the uniform probability distribution, which reaches the maximum entropy. The proposed exponential negation is an entropy increase operation, and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The convergence speed of the proposed negation is also faster than the existed negation. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.

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Acknowledgements

The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant No. 61973332) and JSPS Invitational Fellowships for Research in Japan (short-term).

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Authors and Affiliations

  1. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Qinyuan Wu & Yong Deng

  2. Yingcai Honors College, University of Electronic Science and Technology of China, Chengdu, China

    Qinyuan Wu

  3. School of Education, Shaanxi Normal University, Xi’an, 710062, China

    Yong Deng

  4. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, 923-1211, Japan

    Yong Deng

  5. Department of Mathematics and Computer Science, Northeastern State University, 611 N. Grand Ave, #323, Webb center, Tahlequah, OK, 74464, USA

    Neal Xiong

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  1. Qinyuan Wu
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Contributions

QW and YD contributed to the work concept or design.

QW drafted the paper.

QW, YD and NX made important revisions to the paper.

QW, YD and NX approved the final version of the paper for publication.

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Correspondence to Yong Deng.

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The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors.

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Wu, Q., Deng, Y. & Xiong, N. Exponential negation of a probability distribution. Soft Comput 26, 2147–2156 (2022). https://doi.org/10.1007/s00500-021-06658-5

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