A new definition of cross entropy for uncertain random variables and its application

Article type: Research Article

Authors: Jia, Lifen^a | Yang, Xiangfeng^b | Gao, Xin^{c; *}

Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China | [b] School of Information Technology and Management, University of International Business and Economics, Beijing, China | [c] School of Mathematical Sciences and Physics, North China Electric Power University, Beijing, China.

Correspondence: [*] Corresponding author. Xin Gao, School of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, China. Tel: +86. 1061772871; E-mail: gaoxin@ncepu.edu.cn.

Abstract: This paper proposes a new definition of cross entropy for uncertain random variables, and derives a formula. Moreover, this paper introduces generalized cross entropy for uncertain random variables, and discusses its properties. Based on the definition of cross entropy, a cross entropy chance distribution model of degree-constrained minimum spanning tree (DCMST) problem is proposed. An algorithm is designed here to solve the model. Finally, a numerical example is provided to illustrate the effectiveness of the proposed model and algorithm.

Keywords: Cross entropy, uncertain random variable, minimum spanning tree, uncertain random network

DOI: 10.3233/JIFS-18268

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 1, pp. 1193-1204, 2018