Some Theorems for Inverse Uncertainty Distribution of Uncertain Processes

Xiumei Chen, Yufu Ning, Lihui Wang, Shuai Wang, Hong Huang
2021 Symmetry  
In real life, indeterminacy and determinacy are symmetric, while indeterminacy is absolute. We are devoted to studying indeterminacy through uncertainty theory. Within the framework of uncertainty theory, uncertain processes are used to model the evolution of uncertain phenomena. The uncertainty distribution and inverse uncertainty distribution of uncertain processes are important tools to describe uncertain processes. An independent increment process is a special uncertain process with
more » ... ent increments. An important conjecture about inverse uncertainty distribution of an independent increment process has not been solved yet. In this paper, the conjecture is proven, and therefore, a theorem is obtained. Based on this theorem, some other theorems for inverse uncertainty distribution of the monotone function of independent increment processes are investigated. Meanwhile, some examples are given to illustrate the results.
doi:10.3390/sym14010014 fatcat:rqaiponnybdtxipoech62neotq