Some results of moments of uncertain set

Article type: Research Article

Authors: Yang, Xiangfeng^a | Gao, Jinwu^{b; *}

Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China | [b] School of Information, Renmin University of China, Beijing, China

Correspondence: [*] Corresponding author. Jinwu Gao, School of Information, Renmin University of China, Beijing 100872, China. Tel./Fax: +86 10 82500690; E-mail: jgao@ruc.edu.cn.

Abstract: Uncertain set theory is a generalization of uncertainty theory that has become a new branch of mathematics for modeling human belief degrees. Uncertain set is a fundamental concept to describe unsharp concepts in uncertain set theory. The moments are important characteristics of an uncertain set. This paper studies the moments and central moments of uncertain set and gives some formulas to calculate the moments and central moments by membership function. In addition, some examples are provided to calculate the moments and central moments of uncertain set.

Keywords: Uncertainty theory, uncertain set, membership function, moments

DOI: 10.3233/IFS-141523

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 6, pp. 2433-2442, 2015