Some concepts and properties of uncertain fields

Article type: Research Article

Authors: Gao, Rong^a | Chen, Xiaowei^{b; *}

Affiliations: [a] Department of Mathematical Sciences, Tsinghua University, Beijing, China | [b] School of Finance, Nankai University, Tianjin, China

Correspondence: [*] Corresponding author. Xiaowei Chen, School of Finance, Nankai University, Tianjin 300350, China. Tel.: +86 13920677544; E-mail: chenx@nankai.edu.cn.

Abstract: Uncertain field is virtually an extension of uncertain process with the index space changing from a totally ordered set into a partially ordered one such as time-space or a surface. For describing the uncertain field, this paper introduces several concepts of uncertainty distribution and inverse uncertainty distribution. In addition, a sufficient and necessary condition is proved for the uncertainty distribution of an uncertain field. Then a concept of independence of uncertain fields is introduced and the operational law is derived for a strictly monotone function of independent uncertain fields. Furthermore, another two concepts of uncertain stationary independent increment field and Liu field are proposed, and meanwhile some of their properties are investigated.

Keywords: Uncertainty theory, uncertain process, uncertain field, uncertainty distribution

DOI: 10.3233/JIFS-16314

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 6, pp. 4367-4378, 2017