Uncertain Process And Uncertain Integral

There are a lot of uncertain phenomena existing in nature. In order to research these uncertain phenomena, uncertainty theory has been proposed. Probability theory, credibility theory and trust theory are known collectively as uncertainty theory, which is used to deal with human reliability. In the framework of uncertainty theory, the concept of uncertain process is initiated as a series of uncertain variables changing over time, and it is used to describe uncertain phenomena changing over time.Based on uncertainty theory, complex uncertain process was defined, then the properties of complex uncertain process were obtained. At the same time, infinite uncertain calculus was defined. In order to study uncertain vector, the concept of joint uncertainty distribution and the entropy uncertain vector were presented. These results extend the contents of uncertainty theory.The contents in this paper are as follows:1.Some properties of complex uncertain process are studied, include the expected value and independence of uncertain process, properties of complex uncertain calculus.2.Infinit uncertain integral is defined, and the integral interval of uncertain process with respect to canonical process was extended to infinite interval.3.The regular joint uncertainty distribution and entropy of uncertain vector are defined,which provides measurement tool for the uncertainty of uncertain vector.