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Marginalization in random permutation set theory: from the cooperative game perspective

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Abstract

Random permutation set theory (RPST), as an uncertainty modeling approach considering underlying ordered information, is proposed based on permutation set recently. Different from Dempster–Shafer Theory (DST), RPST extends the event space from power sets to permutation sets and thus can distinguish weights between ordered sets of the same cardinality. In this paper, we use an n-player cooperative game to interpret RPST and propose an OWA operator-based method to calculate the marginalizations of Permutation Mass Function (PerMF). In addition to reflecting the ordered information of the permutation events, the proposed method also relates the Probability Mass Function (ProbMF), the Basic Probability Assignment (BPA) and the PerMF from the perspective of random sets.

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All data and materials generated or analyzed during this study are included in this article.

Code availability

The code of the current study is available from the corresponding author on reasonable request.

Notes

  1. They can transform to each other by invertible matrices.

  2. The mass function is all positive, while the unique function may be negative. However, this does not affect the mathematical results.

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Acknowledgements

The authors are grateful for the guidance of master’s candidate, Jixiang Deng, and PhD candidate, Lipeng Pan, in the Information Fusion and Intelligent Systems Laboratory.

Funding

The work was partially supported by National Natural Science Foundation of China (Grant No. 61973332).

Author information

Authors and Affiliations

  1. Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Qianli Zhou & Yong Deng

  2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Ye Cui

  3. China Mobile Information Technology Center, Beijing, 100029, China

    Zhen Li

  4. School of Medicine, Vanderbilt University, Nashville, TN, 37240, USA

    Yong Deng

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  1. Qianli Zhou
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Contributions

Qianli Zhou took part in conceptualization, methodology, formal analysis, investigation, writing—original draft, writing—review & editing. Ye Cui involved in data experiment, formal analysis, writing—review & editing. Zhen Li took part in validation, writing—review & editing. Yong Deng involved in validation, resources, supervision, funding acquisition.

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Correspondence to Yong Deng.

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Zhou, Q., Cui, Y., Li, Z. et al. Marginalization in random permutation set theory: from the cooperative game perspective. Nonlinear Dyn 111, 13125–13141 (2023). https://doi.org/10.1007/s11071-023-08506-7

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