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Partial divergence measure of uncertain random variables and its application

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Abstract

Cross-entropy (divergence measure) of two uncertain random variables characterizes the difference of two chance distributions. Sometimes, we occur with a complex system as a mixture of uncertain variables and controllable random variables; in order to characterize the difference in these situations, this paper introduces the concept of partial divergence measure of two uncertain random variables and investigates several properties of this concept. Furthermore, some formulas are derived to calculate the partial divergence measure. And how to use these formulas, several examples are provided. Finally, as an application of partial divergence measure, the concept is used to portfolio selection with uncertain random returns as a mixture of new markets and controllable historical markets.

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Acknowledgements

This work was supported by Social Science Foundation of Hebei Province (Grant No. HB18GL306).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Sistan and Baluchestan, Zahedan, Iran

    Hamed Ahmadzade & Habib Naderi

  2. School of Economics and Management, Hebei University of Technology, Tianjin, 300401, China

    Rong Gao

  3. Department of Statistics, Payame Noor University, 19395-4697, Tehran, Iran

    Mehran Farahikia

  4. Ayandeh bank, No. 1, Ahmad Ghasir (Bokharest) St, Argentina Sq, Tehran, Iran

    Mehran Farahikia

Authors
  1. Hamed Ahmadzade
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  2. Rong Gao
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  3. Habib Naderi
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  4. Mehran Farahikia
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Corresponding author

Correspondence to Hamed Ahmadzade.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

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Communicated by V. Loia.

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Ahmadzade, H., Gao, R., Naderi, H. et al. Partial divergence measure of uncertain random variables and its application. Soft Comput 24, 501–512 (2020). https://doi.org/10.1007/s00500-019-03929-0

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