Sheng, Yuhong; Shi, Gang; Ralescu, Dan A. Entropy of uncertain random variables with application to minimum spanning tree problem. (English) Zbl 1377.60013 Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 25, No. 4, 497-514 (2017). Summary: Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain random variables via chance distributions, this paper proposes also the relative entropy for uncertain random variables, as well as it investigates some mathematical properties of this concept. As an application, a model is presented to formulate a minimum spanning tree problem with uncertain random edge weights involving a relative entropy chance distribution. Finally, a numerical example of an uncertain random network is put forward to illustrate the effectiveness of the proposed model. Cited in 4 Documents MSC: 60A86 Fuzzy probability 62B10 Statistical aspects of information-theoretic topics Keywords:uncertain random variable; entropy; relative entropy; chance distribution; minimum spanning tree PDFBibTeX XMLCite \textit{Y. Sheng} et al., Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 25, No. 4, 497--514 (2017; Zbl 1377.60013) Full Text: DOI