abstract. In this article we study interpolation properties for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the-modality easily follow from this result. Furthermore , these properties are extended to the system ILP. Failure of arrow interpolation for ILW is established by providing an expl...

This paper proposes a mechanism that helps improve the interpretability of linguistic fuzzy ruled based systems with common adaptive defuzzification methods. Adaptive defuzzification significantly improves the system accuracy, but introduces weights associated with each rule of the rule base, decreasing the system interpretability. The suggested mechanism is based on three goals: 1) reducing th...

The paper deals with the interpretability problem of 1 order Takagi-Sugeno systems and interpolation issues in particular. Interpolation improvement is carried out by a corrective secondary model (essentially a black box) complementing the primary (interpretable) model. Optimization technique for this two-model configuration is developed. Experimental results suggest that this approach achieves...

Recently, Word2Vec tool has attracted a lot of interest for its promising performances in a variety of natural language processing (NLP) tasks. However, a critical issue is that the dense word representations learned in Word2Vec are lacking of interpretability. It is natural to ask if one could improve their interpretability while keeping their performances. Inspired by the success of sparse mo...

In this paper we develop the theory of cardinals in the theory COPY. This is the theory of two total, jointly injective binary predicates in a second order version, where we may quantify over binary relations. The only second order axioms of the theory are the axiom asserting the existence of an empty relation and the adjunction axiom, which says that we may enrich any relation R with a pair x,...

Fuzzy systems are capable to model the inherent uncertainties in real world problems and implement human decision making. In this paper two issues related to fuzzy systems development are addressed and solutions are proposed and implemented. First issue is related to the high dimensional data sets. Such kinds of data sets lead to explode the search space of generated rules and results into dete...

Interpretability is a fundamental requirement for fuzzy models that has not been exhaustively addressed in literature. This paper rises some fundamental questions concerning interpretability with the aim of promoting deeper insights in the study and application of this property in fuzzy modeling.

We extend the Ahlbrandt–Ziegler analysis of interpretability in א0-categorical structures by showing that existential interpretation is controlled by the monoid of self–embeddings and positive existential interpretation of structures without constant endomorphisms is controlled by the monoid of endomorphisms in the same way as general interpretability is controlled by the automorphism group.

3 Illustration of interpretability of trees 7 3.1 Interpretability of single decision trees . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1.1 Local approach with two multiple-output trees . . . . . . . . . . . . . . . . . . . 9 3.1.2 Global approach with one single-output tree . . . . . . . . . . . . . . . . . . . . 12 3.2 Clustering with ensembles of trees . . . . . . . . . . . . ....

Brain decoding is a popular multivariate approach for hypothesis testing in neuroimaging. Linear classifiers are widely employed in the brain decoding paradigm to discriminate among experimental conditions. Then, the derived linear weights are visualized in the form of multivariate brain maps to further study the spatio-temporal patterns of underlying neural activities. It is well known that th...