A new definition of cross-entropy for uncertain variables
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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.
KeywordsUncertainty 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.
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Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants performed by any of the authors.
- Dai W (2017) Quadratic entropy of uncertain variables. Inf Int Interdiscip J (to be published)Google Scholar
- Dai W, Bi R, Cui B (2012) Quadratic cross entropy of uncertain variables. http://orsc.edu.cn/online/120706
- Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10Google Scholar
- Tang W, Gao W (2013) Triangular entropy of uncertain variables. Inf Int Interdiscip J 16(2(A)):1279–1282Google Scholar
- Yao K, Ji X (2014) Uncertain decision making and its application to portfolio selection problem. Int J Uncertain Fuzziness Knowl Based Syst 22(1):113–123Google Scholar
- Zhang X, Meng G (2013) Expected-variance-entropy model for uncertain parallel machine scheduling. Inf Int Interdiscip J 16(2(A)):903–908Google Scholar