Arithmetic operations for LR mixed fuzzy random variables via mean chance measure with applications

Article type: Research Article

Authors: Wang, Ke^a | Zhou, Jian^{a; *} | Ralescu, Dan A.^b

Affiliations: [a] School of Management, Shanghai University, Shanghai, China | [b] Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, USA

Correspondence: [*] Corresponding author. Jian Zhou, School of Management, Shanghai University, Shanghai 200444, China. Tel.: +86 21 66134414 805; Fax: +86 21 66134284; E-mail: zhou_jian@shu.edu.cn.

Abstract: This paper introduces arithmetic operations for LR mixed fuzzy random variables commonly used in practice for modeling fuzzy stochastic phenomena. The operations are proposed based on mean chance measure, which as a natural extension of both the probability of a random event and the credibility of a fuzzy event, measures the mean or expected (in the sense of probability) credibility that the fuzzy random event occurs. Following from the proposed operational laws, the mean chance distributions of LR mixed fuzzy random variables can be deduced explicitly rather than obtained by simulation, which will provide greater convenience for the decision making or optimization in mixed fuzzy and random environments. Furthermore, some important conclusions on the expected value operator defined via the mean chance measure as well as applications of the proposed arithmetic operations in system reliability analysis are also presented.

Keywords: Fuzzy random variable, mean chance, operational law, expected value, reliability analysis

DOI: 10.3233/JIFS-152173

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 451-466, 2017