Abstract
In this article, a novel interpretable classifier is proposed on the basis of axiomatic fuzzy set (AFS) theory and semantic entropy. AFS theory provides a unified and coherent way to deal with uncertainty of randomness and imprecision of fuzziness in data mining and knowledge discovery, which support many investigations in classification area. However, the existing AFS-based classifiers are weak in obtaining the optimal semantic description. To address this drawback, a new measure, named semantic entropy extended in Shannon's entropy, is developed to evaluate the discriminatory capabilities of semantic descriptions for each category. Moreover, the semantic entropy is utilized to design a classifier in the framework of AFS theory, called axiomatic fuzzy set and semantic entropy (AFSSE), which is capable of achieving sound classification performance and interpretability. Meanwhile, it provides a new framework of classifier design that can adapt more human-oriented recognition mechanisms. Furthermore, an evaluation index is used to prune descriptions to deliver a promising performance. Compared to the previous AFS-based classifiers, the proposed approach offers a semantic entropy to measure the information that is derived from semantic descriptions of data, so that the optimal semantic descriptions of each class can be obtained. For the purpose of illustrating the effectiveness of the classifier, several datasets are utilized to facilitate a comparative analysis of the proposed approach and other state-of-the-art classifiers. The experimental studies demonstrate that the proposed approach can achieve the semantic descriptions of each class and the performance of AFSSE is comparable with the performance of other approaches.