A revision of sufficient and necessary condition of uncertainty distribution

Article type: Research Article

Authors: Liu, Yang | Lio, Waichon^{; *}

Affiliations: Department of Mathematical Sciences, Tsinghua University, Beijing, China

Correspondence: [*] Corresponding author. Waichon Lio, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China. E-mail: [email protected].

Abstract: Nowadays, uncertainty theory has become a branch of axiomatic mathematics and has been studied by many researchers. In particular, uncertainty distribution is one of the most important tools to deal with indeterminate quantity in uncertainty theory. Peng and Iwamura (2010) presented a sufficient and necessary condition of a function being an uncertainty distribution. This paper gives a counterexample to illustrate this condition is not appropriate. A revision of the sufficient and necessary condition is also provided in this paper.

Keywords: Uncertainty theory, uncertain variable, uncertainty distribution

DOI: 10.3233/JIFS-191535

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 4845-4854, 2020