Wang–Mendel (WM) fuzzy system is an effective and interpretable model for solving tabular data classification problem. However, original WM fuzzy system is weak in handling dataset with high dimensionality or large volume. Meanwhile, its capability of characterizing data is narrow, which results from lacking hierarchical transformation of features like deep learning-based models. In this article, we propose a deep fuzzy rule-based classification system (DFRBCS) based on improved WM method, in which fuzzy technique and deep learning strategy are combined to make a desirable tradeoff between model’s interpretability and prediction accuracy. We first redefine the consequent part of fuzzy rule in WM fuzzy system with class probability vector, which endows the improved WM fuzzy system with capacity for serving as building block of deep model. The model structure of DFRBCS is designed in layer-by-layer manner, where raw features can be transformed hierarchically. For every layer in DFRBCS, it contains many improved WM fuzzy systems whose input spaces are generated by shuffling and sliding window operation on concatenated outputs of fuzzy systems in previous layer. Comparative experiments are conducted on 45 real-world datasets with various sizes and dimensionality between our method, five baseline models, and the other deep fuzzy classifiers (D-TSK-FC, HID-TSK-FC, FCCI-TSK, DSA-FC, and MEEFIS). The experimental results show that DFRBCS is competitive in classification performance and promising in model’s interpretability.

In this paper, 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 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 data sets 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.

In this article, we present a semantic semisupervised learning (Semantic SSL) approach targeted at unifying two machine-learning paradigms in a mutually beneficial way, where the classical support vector machine (SVM) learns to reveal primitive logic facts from data, while axiomatic fuzzy set (AFS) theory is utilized to exploit semantic knowledge and correct the wrongly perceived facts for improving the machine-learning model. This novel semisupervised method can easily produce interpretable semantic descriptions to outline different categories by forming a fuzzy set with semantic explanations realized on the basis of the AFS theory. Besides, it is known that disagreement-based semisupervised learning (SSL) can be viewed as an excellent schema so that a co-training approach with SVM and the AFS theory can be utilized to improve the resulting learning performance. Furthermore, an evaluation index is used to prune descriptions to deliver promising performance. Compared with other semisupervised approaches, the proposed approach can build a structure to reflect data-distributed information with unlabeled data and labeled data, so that the hidden information embedded in both labeled and unlabeled data can be sufficiently utilized and can potentially be applied to achieve good descriptions of each category. Experimental results demonstrate that this approach can offer a concise, comprehensible, and precise SSL frame, which strikes a balance between the interpretability and the accuracy.

Open-domain question answering (QA) tasks require a model to retrieve inference chains associated with the answer from massive documents. The core of a QA model is the information filtering ability and reasoning ability. This article proposes a semantic knowledge reasoning graph model based on the multidimensional axiomatic fuzzy set (AFS), which can generate the knowledge graph (KG) and build reasoning paths for reading comprehension tasks through unsupervised learning. Moreover, taking advantage of the interpretable AFS framework enables the proposed model to have the ability to learn and analyze the semantic relationships between candidate documents. Meanwhile, the utilization of the multidimensional AFS acquires semantic descriptions of candidate documents more concise and flexible. The similarity degree between paragraphs is calculated according to the AFS description to generate the graph. Interpretable chains of reasoning provided by the AFS knowledge graph (AFS Graph) will serve as the basis for the answer prediction. Compared with the previous methods, the AFS Graph model presented in this article improves interpretability and reasoning ability. Experimental results show that the proposed model can achieve the state-of-the-art performance on datasets of HotpotQA, SQuAD, and Natural Questions Open.

In exploratory data mining, most classifiers pay more attention on the accuracy and speed of learned models, but they are lacking of the interpretability. In this paper, an interpretable and comprehensible classifier is proposed based on Linear Discriminant Analysis (LDA) and Axiomatic Fuzzy Sets (AFS). The algorithm utilizes LDA to extract features with the largest inter-class variance. Besides, the proposed approach aims to explore a transformation from the selected feature space to a semantic space where the samples in the same class are made as close as possible to one another, whereas the samples in the different class are as far as possible from one another. Moreover, the descriptions of each class can be obtained by the proposed approach. When compared with well-known classifiers such as LogisticR, C4.5Tree, SVM and KNN, the proposed method not only can achieve better performance in terms of accuracy but also has the capability of interpretability and comprehension.