Pan-integral on credibility space and its properties

Article type: Research Article

Authors: Du, Wen Sheng^{; *}

Affiliations: School of Business, Zhengzhou University, Zhengzhou, P.R. China

Correspondence: [*] Corresponding author. Wen Sheng Du, School of Business, Zhengzhou University, No. 100 Science Avenue, High-Tech Zone, Zhengzhou 450001, P.R. China. E-mail: wsdu@zzu.edu.cn.

Abstract: Pan-integral is an important kind of nonlinear integral, and credibility measure is a monotone measure with self-duality. In this paper, we define the pan-integral on credibility space, a new type of integral construction, whose basic properties are discussed in detail. The relationship between the pan-integral and H-fuzzy integral on a special pan-credibility space is established as well. Moreover, some monotone convergence theorems for a sequence of nonnegative measurable functions are investigated.

Keywords: Pan-integral, credibility measure, pan-credibility space, monotone convergence theorem

DOI: 10.3233/JIFS-181588

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 6, pp. 5711-5719, 2019