Some Theorems for Inverse Uncertainty Distribution of Uncertain Processes

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 independent 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.

Uncertain Independent Increment Processes are Contour Processes

Uncertain processes are used to model dynamic indeterminate systems associated with human uncertainty, and uncertain independent increment processes are a type of uncertain processes with independent uncertain increments. This paper mainly verifies a basic property about the sample paths of uncertain independent increment processes, which states that uncertain independent increment processes defined on a continuous uncertainty space are contour processes, a type of uncertain processes with a spectrum of sample paths as the skeletons. Based on this property, the extreme values and the time integral of an uncertain independent increment process are investigated, and their inverse uncertainty distributions are obtained.

Different Random Distributions Research on Logistic-Based Sample Assumption

Logistic-based sample assumption is proposed in this paper, with a research on different random distributions through this system. It provides an assumption system of logistic-based sample, including its sample space structure. Moreover, the influence of different random distributions for inputs has been studied through this logistic-based sample assumption system. In this paper, three different random distributions (normal distribution, uniform distribution, and beta distribution) are used for test. The experimental simulations illustrate the relationship between inputs and outputs under different random distributions. Thereafter, numerical analysis infers that the distribution of outputs depends on that of inputs to some extent, and this assumption system is not independent increment process, but it is quasistationary.