In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the given data are not random, or when the data are imprecise, and only the range of the data is available, the traditional linear regression method cannot be used. This paper presents an uncertain total least squares estimation method and an uncertain robust total least squares linear regression method based on uncertainty theory and total least squares method. The uncertain total least squares estimation can fully consider errors in the given data and the uncertain robust total least squares linear regression method can effectively eliminate outliers in the data. It is possible to obtain a more reasonable fitting effect with both of these methods, as well as to solve the predicted value and the confidence interval with these two methods. In terms of robust total least squares linear regression estimation, both uncertain total least squares regression estimation and uncertain robust total least squares regression estimation are feasible based on numerical examples. There are more accurate fitting equations and more reliable results with uncertain robust least squares linear regression estimation.

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.

Volatile markets and uncertain deterioration rate make it extremely difficult for manufacturers to make the quantity of saleable vegetables just meet the fluctuating demands, which will lead to inevitable out of stock or over production. Aggregate production planning (APP) is to find the optimal yield of vegetables, shortage and overstock symmetry, are not conducive to the final benefit.The essence of aggregate production planning is to deal with the symmetrical relation between shortage and overproduction. In order to reduce the adverse effects caused by shortage, we regard the service level as an important constraint to meet the customer demand and ensure the market share. So an uncertain aggregate production planning model for vegetables under condition of allowed stockout and considering service level constraint is constructed, whose objective is to find the optimal output while minimizing the expected total cost. Moreover, two methods are proposed in different cases to solve the model. A crisp equivalent form can be transformed when uncertain variables obey linear uncertain distributions and for general case, a hybrid intelligent algorithm integrating the 99-method and genetic algorithm is employed. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed model.