An Optimized Logistic Regression Model Based on the Maximum Entropy Estimation Under the Hesitant Fuzzy Environment

Abstract

The logistic regression model is one of the most widely used classification models. In some practical situations, few samples and massive uncertain information bring more challenges to the application of the traditional logistic regression. This paper takes advantages of the hesitant fuzzy set (HFS) in depicting uncertain information and develops the logistic regression model under hesitant fuzzy environment. Considering the complexity and uncertainty in the application of this logistic regression, the concept of hesitant fuzzy information flow (HFIF) and the correlation coefficient between HFSs are introduced to determine the main factors. In order to better manage situations with small samples, a new optimized method based on the maximum entropy estimation is also proposed to determine the parameters. Then the Levenberg–Marquardt Algorithm (LMA) under hesitant fuzzy environment is developed to solve the parameter estimation problem with fewer samples and uncertain information in the logistic regression model. A specific implementation process for the optimized logistic regression model based on the maximum entropy estimation under the hesitant fuzzy environment is also provided. Moreover, we apply the proposed model to the prediction problem of Emergency Extreme Air Pollution Event (EEAPE). A comparative analysis and a sensitivity analysis are further conducted to illustrate the advantages of the optimized logistic regression model under hesitant fuzzy environment.