According to the analysis of historical tourism data, it was found that tourism revenue is influenced by multiple factors, and there exists a linear relationship between these factors and tourism revenue. Therefore, this paper employs a linear regression model to investigate the factors influencing tourism revenue. However, research on tourism data has found that the disturbance term of the linear regression model is not frequency-stable. This indicates that the disturbance term should be an uncertain variable rather than a random variable. Therefore, this paper adopts an uncertain linear regression analysis model and employs the tourism data of Shandong Province in China from 2011 to 2020 as the sample to investigate the factors influencing tourism revenue. The study provides parameter estimation and residual analysis of the model, as well as predictions and confidence intervals of tourism revenue. Additionally, through an uncertain hypothesis test, it was verified that the adopted model fitted the relevant tourism data well. The results show that factors such as the number of travel agencies, railway length, domestic tourist numbers, and per capita disposable income of urban residents have a significant impact on tourism revenue. Based on the study, recommendations and measures for improving tourism revenue of Shandong Province are proposed.

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.

It is noted that some uncertain variables are independent while others are not. In general, there is a symmetrical relationship between independence and dependence among uncertain variables. The utilization of conditional uncertain measures as well as conditional uncertainty distributions proves highly efficacious in resolving uncertainties pertaining to an event subsequent to the acquisition of knowledge about other events. In this paper, the theorem about the conditional uncertainty distribution of two uncertain variables is proposed. It is demonstrated that the theorem holds regardless of whether the two variables are independent or not. In addition, it is also found that uncertainty distribution possesses an inherent inverse function when it is a regular uncertainty distribution within the framework of Uncertainty Theory; therefore, this paper delves into investigating the conditional inverse uncertainty distribution, including specific cases of the conditional inverse uncertainty distributions. Meanwhile, illustrative examples are applied to clarify the findings.