Extended Classification Methods And Their Interpretability Based On Axiomatic Fuzzy Sets

Interpretability is a hot topic in the field of data mining.When the results of data processing are interpretable,they can provide transparent guidance for decision-makers.Axiomatic fuzzy sets(AFS)theory is a novel method for dealing with fuzzy and random uncertainties.Its membership function is directly transformed from the inherent logic and information of the original data.Classification methods based on axiomatic fuzzy sets can produce results with better semantics and are widely used in different fields.However,the accuracy of AFS-based classification methods often comes at the cost of reducing the interpretability of the results.By combining the traditional AFS classification method with other tools,this paper constructs extended classification methods to achieve a balance between accuracy and interpretability.The main topics of this paper include the following aspects:(1)The traditional AFS classification method acquires knowledge through the generated fuzzy rules.When there are a large number of training samples,the obtained class description is too complicated,and its membership function is easily influenced by the noise data.To solve this problem,a sample selection algorithm of unstable cut points is introduced,and a type-2 AFS classification method based on sample selection is proposed.This classification method uses a sample selection algorithm of unstable cut points to set an appropriate threshold to retain samples near the unstable cut-point,which forms a subset of samples to reduce the number of training samples.At the same time,the use of interval type-2 membership functions has the advantage of strong processing ability of uncertain information.On the premise of ensuring that the classification performance of the model is unchanged,the class description is simplified to make the semantic description relatively simple.(2)The traditional AFS classification method uses the principle of maximum membership to determine the class labels of test samples,which ignores the neighborhood information of the test samples.To solve this problem,this paper designs an interpretable classification method AFS-KNN based on AFS theory and k-nearest neighbors.Firstly,the training data are transformed into semantic descriptions,and then k neighbors of the test samples are selected by using the membership degree of the samples.The test sample is classified into the category with the largest sum of the same class memberships in the k neighbors to avoid the influence of outliers.By comparing the 11 data sets in the UCI database,the results show that the AFS-KNN method has a certain improvement over the k-nearest neighbor method and the traditional AFS classification method in terms of interpretability and accuracy.(3)When using traditional supervised learning methods for classification,more samples are often needed to train the classification model to make the classification results more accurate.However,in practical problems,it is difficult and expensive to mark the class labels of the samples.To solve this problem,this paper combines cost-sensitive learning and the mutual neighbor method to construct a new active learning method CS-AFS-KNN-MUL in the framework of AFS theory.This method aims to train as few labeled samples as possible,using cost-sensitive methods to select key samples and adding them to the known training sample set.This process continues iteratively until all the test samples obtain class labels.An experimental analysis of 13 data sets of the UCI database shows that the CS-AFS-KNN-MUL method is superior to other methods in accuracy and the average cost is low.