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We study the impact of fuzziness on the behavior of Fuzzy Rule-Based Classifiers (FRBCs) defined by trapezoidal fuzzy sets forming Strong Fuzzy Partitions. In particular, if an FRBC selects the class related to the rule with the highest activation (so-called Winner-Takes-All approach), then fuzziness, as quantified by the slope of the membership functions, has no impact in classifying data in regions of the input space where rules dominate. On the other hand, fuzziness affects the behaviour of the FRBC in regions where the confidence in classification is low. As a consequence, in the context of Explainable Artificial Intelligence, fuzziness is profitable in FRBCs only if classification is accompanied by an explanation of the confidence of the provided outputs. [ABSTRACT FROM AUTHOR]

Background: When the reads obtained from high-throughput RNA sequencing are mapped against a reference database, a significant proportion of them - known as multireads - can map to more than one reference sequence. These multireads originate from gene duplications, repetitive regions or overlapping genes. Removing the multireads from the mapping results, in RNA-Seq analyses, causes an underestimation of the read counts, while estimating the real read count can lead to false positives during the detection of differentially expressed sequences. Results: We present an innovative approach to deal with multireads and evaluate differential expression events, entirely based on fuzzy set theory. Since multireads cause uncertainty in the estimation of read counts during gene expression computation, they can also influence the reliability of differential expression analysis results, by producing false positives. Our method manages the uncertainty in gene expression estimation by defining the fuzzy read counts and evaluates the possibility of a gene to be differentially expressed with three fuzzy concepts: over-expression, same-expression and under-expression. The output of the method is a list of differentially expressed genes enriched with information about the uncertainty of the results due to the multiread presence. We have tested the method on RNA-Seq data designed for case-control studies and we have compared the obtained results with other existing tools for read count estimation and differential expression analysis. Conclusions: The management of multireads with the use of fuzzy sets allows to obtain a list of differential expression events which takes in account the uncertainty in the results caused by the presence of multireads. Such additional information can be used by the biologists when they have to select the most relevant differential expression events to validate with laboratory assays. Our method can be used to compute reliable differential expression events and to highlight possible false positives in the lists of differentially expressed genes computed with other tools. [ABSTRACT FROM AUTHOR]

Neuro-fuzzy networks have been successfully applied to extract knowledge from data in the form of fuzzy rules. However, one drawback with the neuro-fuzzy approach is that the fuzzy rules induced by the learning process are not necessarily understandable. The lack of readability is essentially due to the high dimensionality of the parameter space that leads to excessive flexibility in the modification of parameters during learning. In this paper, to obtain readable knowledge from data, we propose a new neuro-fuzzy model and its learning algorithm that works in a parameter space with reduced dimensionality. The dimensionality of the new parameter space is necessary and sufficient to generate human-understandable fuzzy rules, in the sense formally defined by a set of properties. The learning procedure is based on a gradient descent technique and the proposed model is general enough to be applied to other neuro-fuzzy architectures. Simulation studies on a benchmark and a real-life problem are carried out to embody the idea of the paper. [Copyright &y& Elsevier]