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A new definition of cross-entropy for uncertain variables

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Abstract

Cross-entropy for uncertain variables is used to measure the divergence between two uncertainty distributions. Logarithm cross-entropy and quadratic cross-entropy for uncertain variables fail to measure the degree of divergence associated with some uncertain variables; thus, this paper proposes a new definition of cross-entropy for uncertain variables as a supplement and discusses its properties. A formula of cross-entropy is derived via inverse uncertainty distributions. Moreover, this paper also defines the generalized cross-entropy of uncertain variables and investigates its properties.

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Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities No. 2016MS65 and National Natural Science Foundation of China Grant No. 71671064.

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Authors and Affiliations

  1. School of Mathematical Sciences and Physics, North China Electric Power University, Beijing, 102206, China

    Xin Gao

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Lifen Jia

  3. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, 713209, India

    Samarjit Kar

Authors
  1. Xin Gao
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  2. Lifen Jia
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  3. Samarjit Kar
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Correspondence to Lifen Jia.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants performed by any of the authors.

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Communicated by Y. Ni.

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Gao, X., Jia, L. & Kar, S. A new definition of cross-entropy for uncertain variables. Soft Comput 22, 5617–5623 (2018). https://doi.org/10.1007/s00500-017-2534-6

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  • DOI: https://doi.org/10.1007/s00500-017-2534-6

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