We prove that if $$G(R)=G_\pi (\Phi ,R)$$ $$(E(R)=E_{\pi }(\Phi , R))$$ is an (elementary) Chevalley group of rank $$> 1$$ R a local ring (with $$\frac{1}{2}$$ for the root systems $${{\textbf{A}}}_2, {{\textbf{B}}}_l, {{\textbf{C}}}_l, {{\textbf{F}}}_4, {{\textbf{G}}}_2$$ and with $$\frac{1}{3}$$ $${{\textbf{G}}}_{2})$$ then G(R) (or (E(R)) regularly bi-interpretable R. As consequence this the...

We present the Mind the Gap Model (MGM), an approach for interpretable feature extraction and selection. By placing interpretability criteria directly into the model, we allow for the model to both optimize parameters related to interpretability and to directly report a global set of distinguishable dimensions to assist with further data exploration and hypothesis generation. MGM extracts disti...

The use of fuzzy logic for the modeling of processes (such as a technical process or the behavior of a human operator in a process) is often motivated by the interpretability of the resulting fuzzy system/model. In fuzzy models, the dependencies of the variables of the considered process are described by qualitative (linguistic) if–then rules, which correspond to the way in which human knowledg...

We study the use of feed-forward convolutional neural networks for the unsupervised problem of mining recurrent temporal patterns mixed in multivariate time series. Traditional convolutional autoencoders lack interpretability for two main reasons: the number of patterns corresponds to the manually-fixed number of convolution filters, and the patterns are often redundant and correlated. To recov...

Enhanced fuzzy modeling by multivariable fuzzy membership functions is described. From the interpretability issues viewpoint conventionally fuzzy modeling is carried out by means of decomposition of multivariable membership functions via projections on each variable component. However, due to decomposition there involves an error while reconstructing the model output from the contributions of e...

Albert Visser introduced five different categories of interpretations between theories INT0 (the category of synonymy), INT1 (the category of homotopy), INT2 (the category of weak homotopy), INT3 (the category of equivalence), and INT4 (the category of mutual interpretability) [Vis04]. The objects in these categories are first order theories, the morphisms are interpretations up to some level o...

A neuro-fuzzy system based on a radial basis function network and using support vector learning is considered for non-linear modeling. In order to reduce the number of fuzzy rules, and improve the system interpretability, the proposed method proceeds in two phases. Firstly, the input-output data is clustered according to the subtractive clustering method. Secondly the parameters of the network,...

This paper presents an algorithm to extract rules relating input/output data and including prior knowledge. The rules are created in the environment of fuzzy systems. The fuzzy sets describing the system are constructed within a framework of linguistic integrity to guarantee its interpretability in the linguistic context. Two algorithms are presented in this paper. The main algorithm is the aut...

The chapter introduces a simple learning methodology, the cooperative rules (COR) one, that improves the accuracy of linguistic fuzzy models preserving the highest interpretability. Its operation mode involves a combinatorial search of fuzzy rules performed over a set of previously generated candidate ones. The accuracy is achieved by developing a smart search space reduction and by inducing th...