Abstract
Recently, a new type of set, called random permutation set (RPS), is proposed by considering all the permutations of elements in a certain set. For measuring the uncertainty of RPS, the entropy of RPS is presented. However, the maximum entropy principle of RPS entropy has not been discussed. To address this issue, this paper presents the maximum entropy of RPS. The analytical solution of maximum RPS entropy and its PMF condition are proven and discussed. Besides, numerical examples are used to illustrate the maximum RPS entropy. The results show that the maximum RPS entropy is compatible with the maximum Deng entropy and the maximum Shannon entropy. Moreover, in order to further apply RPS entropy and maximum RPS entropy in practical fields, a comparative analysis of the choice of using Shannon entropy, Deng entropy, and RPS entropy is also carried out.
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Acknowledgements
The authors greatly appreciate the editor’s encouragement and the reviews’ suggestions. The work was 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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The work was 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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All authors contributed to the study conception and design. All authors performed material preparation, data collection, and analysis. Jixiang Deng wrote the first draft of the paper. All authors contributed to the revisions of the paper. All authors read and approved the final manuscript.
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Deng, J., Deng, Y. Maximum entropy of random permutation set. Soft Comput 26, 11265–11275 (2022). https://doi.org/10.1007/s00500-022-07351-x
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DOI: https://doi.org/10.1007/s00500-022-07351-x