Deep learning models, despite their popularity, face challenges such as long training times and a lack of interpretability. In contrast, fuzzy inference systems offer a balance of accuracy and transparency. This paper addresses the limitations of traditional Takagi-Sugeno-Kang fuzzy models by extending the recently proposed New Takagi-Sugeno-Kang model to a new Mamdani-based regressor. These models are data-driven, allowing users to define the number of rules to balance accuracy and interpretability. To handle the complexity of large datasets, this research integrates wrapper and ensemble techniques. A Genetic Algorithm is used as a wrapper for feature selection, creating genetic versions of the models. Furthermore, ensemble models, including the Random New Mamdani Regressor, Random New Takagi-Sugeno-Kang, and Random Forest New Takagi-Sugeno-Kang, are introduced to improve robustness. The proposed models are validated on photovoltaic energy forecasting datasets, a critical application due to the intermittent nature of solar power. Results demonstrate that the genetic and ensemble fuzzy models, particularly the Genetic New Takagi-Sugeno-Kang and Random Forest New Takagi-Sugeno-Kang, achieve superior performance. They often outperform both traditional machine learning and deep learning models while providing a simpler and more interpretable rule-based structure. The models are available online in a library called nfisis (https://pypi.org/project/nfisis/).

High-order Takagi-Sugeno-Kang (TSK) fuzzy classifiers possess powerful classification performance yet have fewer fuzzy rules, but always be impaired by its exponential growth training time and poorer interpretability owing to High-order polynomial used in consequent part of fuzzy rule, while Low-order TSK fuzzy classifiers run quickly with high interpretability, however they usually require more fuzzy rules and perform relatively not very well. Address this issue, a novel TSK fuzzy classifier embeded with knowledge distillation in deep learning called HTSK-LLM-DKD is proposed in this study. HTSK-LLM-DKD achieves the following distinctive characteristics: 1) It takes High-order TSK classifier as teacher model and Low-order TSK fuzzy classifier as student model, and leverages the proposed LLM-DKD (Least Learning Machine based Decoupling Knowledge Distillation) to distill the fuzzy dark knowledge from High-order TSK fuzzy classifier to Low-order TSK fuzzy classifier, which resulting in Low-order TSK fuzzy classifier endowed with enhanced performance surpassing or at least comparable to High-order TSK classifier, as well as high interpretability; specifically 2) The Negative Euclidean distance between the output of teacher model and each class is employed to obtain the teacher logits, and then it compute teacher/student soft labels by the softmax function with distillating temperature parameter; 3) By reformulating the Kullback-Leibler divergence, it decouples fuzzy dark knowledge into target class knowledge and non-target class knowledge, and transfers them to student model. The advantages of HTSK-LLM-DKD are verified on the benchmarking UCI datasets and a real dataset Cleveland heart disease, in terms of classification performance and model interpretability.

Abstract: One major drawback of deep convolutional neural networks (CNNs) for use in safety critical applications is their black-box nature. This makes it hard to verify or monitor complex, symbolic requirements on already trained computer vision CNNs. In this work, we present a simple, yet effective, approach to verify that a CNN complies with symbolic predicate logic rules which relate visual concepts. It is the first that (1) does not modify the CNN, (2) may use visual concepts that are no CNN in- or output feature, and (3) can leverage continuous CNN confidence outputs. To achieve this, we newly combine methods from explainable artificial intelligence and logic: First, using supervised concept embedding analysis, the output of a CNN is post-hoc enriched by concept outputs.

A method of a fusion of fuzzy inference and policy gradient reinforcement learning has been proposed that directly learns, as maximizes the expected value of the reward per episode, parameters in a policy function represented by fuzzy rules with weights. A study has applied this method to a task of speed control of an automobile and has obtained correct policies, some of which control speed of the automobile appropriately but many others generate inappropriate vibration of speed. In general, the policy is not desirable that causes sudden time change or vibration in the output value, and there would be many cases where the policy giving smooth time change in the output value is desirable. In this paper, we propose a fusion method using the objective function, that introduces defuzzification with the center of gravity model weighted stochastically and a constraint term for smoothness of time change, as an improvement measure in order to suppress sudden change of the output value of the fuzzy controller. Then we show the learning rule in the fusion, and also consider the effect by reward functions on the fluctuation of the output value. As experimental results of an application of our method on speed control of an automobile, it was confirmed that the proposed method has the effect of suppressing the undesirable fluctuation in time-series of the output value. Moreover, it was also showed that the difference between reward functions might adversely affect the results of learning.

In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules, but they cannot effectively describe the behavior within local regions defined by the antecedent parts. In this article, a theoretical and practical design methodology is developed to address this problem. First, the information granulation (Fuzzy C-Means) method is applied to capture the structure in the data and split the input space into subspaces, as well as form the antecedent parts. Second, the quadratic polynomials (QPs) are employed as the consequent parts. Compared with constant and linear functions, QPs can describe the input-output behavior within the local regions (subspaces) by refining the relationship between input and output variables. However, although QP can improve the approximation ability of the model, it could lead to the deterioration of the prediction ability of the model (e.g., overfitting). To handle this issue, we introduce an exponential weight approach inspired by the weight function theory encountered in harmonic analysis. More specifically, we adopt the exponential functions as the targeted penalty terms, which are equipped with l2 regularization (l2) (i.e., exponential weighted l2, ewl_2) to match the proposed reinforced second-order fuzzy rule-based model (RSFRM) properly. The advantage of el 2 compared to ordinary l2 lies in separately identifying and penalizing different types of polynomial terms in the coefficient estimation, and its results not only alleviate the overfitting and prevent the deterioration of generalization ability but also effectively release the prediction potential of the model.

This paper proposes a new architecture of incremen-tal fuzzy inference system (also called Evolving Fuzzy System-EFS). In the context of classifying data stream in non stationary environment, concept drifts problems must be addressed. Several studies have shown that EFS can deal with such environment thanks to their high structural flexibility. These EFS perform well with smooth drift (or incremental drift). The new architecture we propose is focused on improving the processing of brutal changes in the data distribution (often called brutal concept drift). More precisely, a generalized EFS is paired with a module of anticipation to improve the adaptation of new rules after a brutal drift. The proposed architecture is evaluated on three datasets from UCI repository where artificial brutal drifts have been applied. A fit model is also proposed to get a "reactivity time" needed to converge to the steady-state and the score at end. Both characteristics are compared between the same system with and without anticipation and with a similar EFS from state-of-the-art. The experiments demonstrates improvements in both cases.

Various strategies and techniques have been proposed for the generation of questions/answers tests in Intelligent Tutoring Systems by using OWL (Web Ontology Language) ontolo- gies. Currently there have been no known methods to utilize SWRL rules for this task. This paper presents a system and a set of strategies that can be used in order to automatically generate multiple choice questions from SWRL rules. The aim of the proposed framework is to support further research in the area and to be a testbed for the development of more advanced assessment techniques.