Abstract: Credit risk, also known as default risk, is to evaluate the possibility of a debt suffering losses due to certain factors. Therefore, the credit evaluation system must be able to not only have the ability to identify defaults, but also be interpretable and provide reasons for defaults.
The construction of the listed companies' credit risk system involves at least three problems. The first problem is selecting a combination of features, as 2^m-1 feature combinations exist for m features. Further, different feature combinations from the same sample will have different evaluation results. Therefore, a scientific issue that this article aims to explore and answer is how to build a feature selection model and select a group of features with the greatest discriminative ability. The second problem is determining the feature weights, as the classification results obtained by assigning different weights for the same set of features will differ, or even oppose one another. In a classification model that includes feature weights, the weight setting directly affects the model's classification ability. Therefore, another issue that this article aims to address is how to reasonably weigh the system features. The third problem involves constructing an optimal classification model. Traditional classification models, such as the support vector machines and neural network models, among others, have a theoretical classification threshold of 0.5. As a sample's optimal classification threshold will differ, determining whether its selection is reasonable will directly affect the model's classification performance. Further, the previously mentioned models are "black box" models, and cannot explain the causes of defaults. Consequently, another issue that must be addressed is how to choose an interpretable, highly accurate classification model.
The following solutions for these three problems are proposed in this work. Firstly, the feature system with the largest discrimination ability is selected by the generalized F-Score with the largest discrimination and the smallest Pearson correlation coefficient among the features. Secondly, a set of optimal weights is obtained by constructing a combination weighting model, taking the maximum feature information content and the maximum consistency of weighting results as the objective function. Thirdly, through minimizing the generalized weighted distance between samples and categories, the relative membership degrees of the customer in different categories are obtained by solving the non-linear goal programming, and then the category of the customer is obtained.
An empirical analysis of the listed company samples shows that:(1) 31 features selected from 610 features have the ability to distinguish the defaults and non-defaults and conform to the principle of five Cs of credit, which is a scientific and reasonable feature system; (2) Weights of 31 features are obtained by combination weighting model, and financial factors within enterprises have the greatest impact on credit risk, and working capital turnover ratio having the greatest weight is a key feature affecting the credit risk. The number of supervisory committee meeting, dividend payout ratio, type of audit opinion are all important features affecting the credit rating; (3) Compared with eight models such as logistic regression and support vector machine, etc., it is found that the model proposed in this paper not only has good classification performance, but also is a model balancing classification accuracy and complexity.

Key words: credit risk, feature combination selection, combination weighting, optimal relative membership degree