关键词: 水平Choquet积分, 鲁棒多元回归, 分数阶累加, 灰狼优化算法

Abstract: In the face of complex data, the existing data outlier method has been difficult to meet the demand. Especially the modeling data suffers from various interference, leading to the deviation of modeling results from the model. The consistency plays an important role in the complex fluctuating data modeling, where the hidden inconsistencies pose a significant threat to the model performance. Therefore, it is urgent to find suitable methods for correcting data. In the field of decision-making, robust ordinal regression is achieved by repeatedly communicating with decision-makers to obtain more robust parameter results. In this paper, this idea is introduced into the prediction model to identify inconsistencies in the data to improve the robustness of the model. Besides, limited data limits the performance of models in forecasting process. However, fully mining the hidden information contained in data under existing conditions and utilizing the information of existing data is a concerned issue in current prediction models. Level dependent Choquet integral is an interval division based on traditional Choquet integral, which obtains more data information through more precise division. It can effectively solve the problem of insufficient data information mining in existing data. Multiple regression is widely used in many fields, but there are still two shortcomings in dealing with multivariate prediction problems. The relationship between dependent and independent variables should be considered simultaneously for outlier detection, that is, whether there is an exception in the whole rather than just a single sequence. Traditional decomposition techniques do not consider the interaction between variables when enriching data, and it is necessary to enrich sample data and fully mine information based on the consideration of interaction. Therefore, effectively solving the above two problems is of great significance for improving the performance of multiple regression models, and providing new ideas for the development of predictive model.
This article proposes a robust multiple regression model based on horizontal Choquet integration. Firstly, the model first checks the relationship between dependent and independent variables through 0-1 planning. If the results are all 0, there will be no outliers, that is, the data is consistent. If not all 0, there will be outliers that make the data inconsistent, and then the outliers will be eliminated to ensure that the data used are not disturbed. Secondly, level dependent Choquet integration processing is carried out on the data to obtain more precise data through interval division. The purpose is to obtain more abundant data samples on the basis of considering the interaction between indicators to deeply mine the information in the original data. Finally, the refined sample data obtained is subject to fractional order accumulation. The multiple regression model is established using the least squares principle to obtain model parameter estimates. The grey wolf optimization algorithm is used to optimize the fractional order accumulation coefficients to improve the performance of the model. The significance of fractional order accumulation aims to improve the predictive performance of multiple regression models. The multiple regression model established based on the sequence obtained by the r-order accumulation operator has more selectivity than the traditional multiple regression. When r equals 0, it is the traditional multiple regression. Therefore, adding the r-order accumulation operator is an extension of the traditional multiple regression. On this basis, the new model is applied to the prediction of carbon dioxide emissions of the Chinese fleet. The research results show that the prediction effect of the robust multiple regression model based on level dependent Choquet integration is better than other classic models. At the same time, the data mining system designed in this paper can also be applied to many other prediction models.

Key words: level dependent Choquet integral, robust multiple regression, fractional order accumulation, grey wolf optimization