Some Properties of Complex Uncertain Process

Abstract

Uncertainty appears not only in real quantities but also in complex quantities. Complex uncertain process is essentially a sequence of complex uncertain variables indexed by time. In order to describe complex uncertain process, a formal definition of complex uncertain distribution is given in this paper, as well as the concepts of independence and variance. In addition, some properties of complex uncertain integral are presented.

A systematic review of uncertainty theory with the use of scientometrical method

“…Liu not only initialized the independent increment process (Liu, 2008 ), but also introduced an extreme value theorem (Liu, 2013b ), and put forward the concepts of uncertainty distributions, inverse uncertainty distributions and independence to describe the uncertain process (Liu, 2014 ). Over the years, more and more uncertain processes have been discovered, that is, the half a standard process (Gao, 2011b ), stable independent increment process (Chen, 2012 ), enlightenment process (Di Caprio et al, 2014 ), outline of the process (Yao, 2015c ), strongly monotonic uncertain process (You & Xiang, 2018 ), insurance risk process (Yao & Qin, 2015 ; Yao & Zhou, 2018b ), complex Liu process (Qin & Wen, 2015 ), finite variation process (Chen, 2015 ), renewal incentive process (Yao & Qin, 2015 ), uncertain stochastic process (Gao & Yao, 2015 ), uncertain renewal process, and so on. Moreover, authors have delved into the concepts, properties, variances, analytical functions, changes, sample paths, uncertain integrals, independence, and continuity of these uncertain processes.…”