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On the axiomatic requirement of range to measure uncertainty

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  • Deng, Xinyang
  • Deng, Yong

Abstract

How to measure uncertainty is still an open issue. Probability theory is a primary tool to express the aleatoric uncertainty. The Shannon’s information entropy is an effective measure for the uncertainty in probability theory. Dempster–Shafer theory, an extension of probability theory, has the ability to express the aleatoric and epistemic uncertainty, simultaneously. With respect to such uncertainties in Dempster–Shafer theory, a justifiable uncertainty measure is required to satisfy five axiomatic requirements based on previous studies. In this paper, we show that one of the axiomatic requirements, the requirement of range, is questionable. The correct range of uncertainty should be [0,log22|X|] rather than [0,log2|X|] according to the concept of entropy.

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  • Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    • Handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:163-168
    DOI: 10.1016/j.physa.2014.03.060
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    References listed on IDEAS

    as
    1. Lucia, Umberto, 2013. "Thermodynamic paths and stochastic order in open systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3912-3919.
    2. Portesi, M & Plastino, A, 1996. "Generalized entropy as a measure of quantum uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 412-430.
    3. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    4. Sotolongo-Grau, O. & Rodriguez-Perez, D. & Sotolongo-Costa, O. & Antoranz, J.C., 2013. "Tsallis entropy approach to radiotherapy treatments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2007-2015.
    5. Gao, Cai & Wei, Daijun & Hu, Yong & Mahadevan, Sankaran & Deng, Yong, 2013. "A modified evidential methodology of identifying influential nodes in weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5490-5500.
    6. Wu, Liusan & Tan, Qingmei & Zhang, Yuehui, 2013. "Network connectivity entropy and its application on network connectivity reliability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5536-5541.
    7. Lucia, Umberto, 2009. "Irreversibility, entropy and incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4025-4033.
    8. Wei, Daijun & Deng, Xinyang & Zhang, Xiaoge & Deng, Yong & Mahadevan, Sankaran, 2013. "Identifying influential nodes in weighted networks based on evidence theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2564-2575.
    9. Lucia, U., 2012. "Maximum or minimum entropy generation for open systems?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3392-3398.
    10. Rosa, A.C.P. & de Jesus, J.C.O. & Moret, M.A., 2013. "Nonextensivity and entropy of astrophysical sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 6079-6083.
    11. Lucia, Umberto, 2008. "Statistical approach of the irreversible entropy variation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3454-3460.
    12. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    13. Lucia, Umberto, 2014. "Entropy generation and the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 256-260.
    14. Carrete, J. & Varela, L.M. & Gallego, L.J., 2008. "Microcanonical equations obtained from the Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6752-6758.
    15. Lucia, Umberto & Sciubba, Enrico, 2013. "From Lotka to the entropy generation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3634-3639.
    16. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    17. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
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    3. Deng, Yong, 2016. "Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 549-553.

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