Soft Computing

, Volume 22, Issue 17, pp 5617–5623 | Cite as

A new definition of cross-entropy for uncertain variables

  • Xin Gao
  • Lifen Jia
  • Samarjit Kar


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.


Uncertainty theory Uncertain variable Cross-entropy 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical Sciences and PhysicsNorth China Electric Power UniversityBeijingChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Department of MathematicsNational Institute of Technology DurgapurDurgapurIndia

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