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Research Article

A generalized Rényi entropy to measure the uncertainty of a random permutation set

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Received 02 Mar 2022, Accepted 01 Dec 2023, Published online: 20 Dec 2023

References

  • Alam, M., Y. Wang, J. Chen, G. Lou, H. Yang, Yin. Zhou, S. Luitel, G. Jiang, and Y. He. 2023. QTL detection for rice grain storage protein content and genetic effect verifications. Molecular Breeding: New Strategies in Plant Improvement 43 (12):89. doi:10.1007/s11032-023-01436-7. PMC: 38059164
  • Balakrishnan, N., F. Buono, and M. Longobardi. 2022. A unified formulation of entropy and its application. Physica A: Statistical Mechanics and Its Applications 596:127214. doi:10.1016/j.physa.2022.127214.
  • Beck, C. 2009. Generalised information and entropy measures in physics. Contemporary Physics 50 (4):495–510. doi:10.1080/00107510902823517.
  • Chen, L., and Y. Deng. 2023. Entropy of random permutation set. Communications in Statistics-Theory and Methods, 1–19.
  • Clausius, R. 1850. The mechanical theory of heat: With its applications to the steam engine. Poggendorff’s Annalen 79:368–97.
  • Dempster, A. P. 1967. Upper and lower probabilities induced by a multivalued mapping. The Annals of Mathematical Statistics 38 (2):325–39. doi:10.1214/aoms/1177698950.
  • Deng, J., and Y. Deng. 2022. Maximum entropy of random permutation set. Soft Computing 26 (21):11265–75. doi:10.1007/s00500-022-07351-x.
  • Deng, Y. 2020. Uncertainty measure in evidence theory. Science China Information Sciences 63 (11): 1–19.
  • Deng, Y. 2022. Random permutation set. International Journal of Computers Communications & Control 17 (1):4542.
  • Hiai, F., and M. Mosonyi. 2017. Different quantum f-divergences and the reversibility of quantum operations. Reviews in Mathematical Physics 29 (07):1750023. doi:10.1142/S0129055X17500234.
  • Hiai, F., M. Mosonyi, D. Petz, and C. Bény. 2011. Quantum f-divergences and error correction. Reviews in Mathematical Physics 23 (07):691–747. doi:10.1142/S0129055X11004412.
  • Liu, Fan., X. Gao, Jie. Zhao, and Y. Deng. Generalized belief entropy and its application in identifying conflict evidence. IEEE Access. 7:126625–33. doi:10.1109/ACCESS.2019.2939332.
  • Rényi, A. 1961. On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Contributions to the Theory of Statistics 1 (4):547–62. University of California Press.
  • Shafer, G. 1976. A mathematical theory of evidence, Vol. 42. Princeton University Press.
  • Shannon, C. E. 1948. A mathematical theory of communication. Bell System Technical Journal 27 (3):379–423. doi:10.1002/j.1538-7305.1948.tb01338.x.
  • Song, Y., and Y. Deng. 2021. Entropic explanation of power set. International Journal of Computers Communications & Control 16 (4):4413.
  • Xiao, F., Z. Cao, and C.-T. Lin. 2022. A complex weighted discounting multisource information fusion with its application in pattern classification. IEEE Transactions on Knowledge and Data Engineering 35 (8):7609–23. doi:10.1109/TKDE.2022.3206871.
  • Xiao, F., and W. Pedrycz. 2022. Negation of the quantum mass function for multisource quantum information fusion with its application to pattern classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2):2054–70. doi:10.1109/TPAMI.2022.3167045.
  • Zheng, Z., and Yi. Yang. 2021. Rectifying pseudo label learning via uncertainty estimation for domain adaptive semantic segmentation. International Journal of Computer Vision 129 (4): 1106–20. doi:10.1007/s11263-020-01395-y.

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