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Fuzzy systems are universally acknowledged as valuable tools to model complex phenomena while preserving a readable form of knowledge representation. The resort to natural language for expressing the terms involved in fuzzy rules, in fact, is a key-factor to conjugate mathematical formalism and logical inference with human-centered interpretability. That makes fuzzy systems specifically suitable in every real-world context where people are in charge of crucial decisions. That is because the self-explanatory nature of fuzzy rules profitably supports expert assessments. Additionally, as far as interpretability is investigated, it appears that: a) the simple adoption of fuzzy sets in modeling is not enough to ensure interpretability; b) fuzzy knowledge representation must confront the problem of preserving the overall system accuracy, thus yielding a trade-off which is frequently debated. Such issues have attracted a growing interest in the research community and became to assume a central role in the current literature panorama of Computational Intelligence. This chapter gives an overview of the topics related to fuzzy system interpretability, facing the ambitious goal of proposing some answers to a number of open challenging questions: What is interpretability? Why interpretability is worth considering? How to ensure interpretability, and how to assess (quantify) it? Finally, how to design interpretable fuzzy models?

Computing with words (CWW) relies on linguistic representation of knowledge that is processed by operating at the semantical level defined through fuzzy sets. Linguistic representation of knowledge is a major issue when fuzzy rule based models are acquired from data by some form of empirical learning. Indeed, these models are often requested to exhibit interpretability, which is normally evaluated in terms of structural features, such as rule complexity, properties on fuzzy sets and partitions. In this paper we propose a different approach for evaluating interpretability that is based on the notion of cointension. The interpretability of a fuzzy rule-based model is measured in terms of cointension degree between the explicit semantics, defined by the formal parameter settings of the model, and the implicit semantics conveyed to the reader by the linguistic representation of knowledge. Implicit semantics calls for a representation of user's knowledge which is difficult to externalise. Nevertheless, we identify a set of properties - which we call "logical view" - that is expected to hold in the implicit semantics and is used in our approach to evaluate the cointension between explicit and implicit semantics. In practice, a new fuzzy rule base is obtained by minimising the fuzzy rule base through logical properties. Semantic comparison is made by evaluating the performances of the two rule bases, which are supposed to be similar when the two semantics are almost equivalent. If this is the case, we deduce that the logical view is applicable to the model, which can be tagged as interpretable from the cointension viewpoint. These ideas are then used to define a strategy for assessing interpretability of fuzzy rule-based classifiers (FRBCs). The strategy has been evaluated on a set of pre-existent FRBCs, acquired by different learning processes from a well-known benchmark dataset. Our analysis highlighted that some of them are not cointensive with user's knowledge, hence their linguistic representation is not appropriate, even though they can be tagged as interpretable from a structural point of view

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Introduction: Obstructive sleep apnea syndrome has become an important public health concern. Polysomnography is traditionally considered an established and effective diagnostic tool providing information on the severity of obstructive sleep apnea syndrome and the degree of sleep fragmentation. However, the numerous steps in the polysomnography test to diagnose obstructive sleep apnea syndrome are costly and time consuming. This study aimed to test the efficacy and clinical applicability of different machine learning methods based on demographic information and questionnaire data to predict obstructive sleep apnea syndrome severity. Materials and methods: We collected data about demographic characteristics, spirometry values, gas exchange (PaO2, PaCO2) and symptoms (Epworth Sleepiness Scale, snoring, etc.) of 313 patients with previous diagnosis of obstructive sleep apnea syndrome. After principal component analysis, we selected 19 variables which were used for further preprocessing and to eventually train seven types of classification models and five types of regression models to evaluate the prediction ability of obstructive sleep apnea syndrome severity, represented either by class or by apnea–hypopnea index. All models are trained with an increasing number of features and the results are validated through stratified 10-fold cross validation. Results: Comparative results show the superiority of support vector machine and random forest models for classification, while support vector machine and linear regression are better suited to predict apnea–hypopnea index. Also, a limited number of features are enough to achieve the maximum predictive accuracy. The best average classification accuracy on test sets is 44.7 percent, with the same average sensitivity (recall). In only 5.7 percent of cases, a severe obstructive sleep apnea syndrome (class 4) is misclassified as mild (class 2). Regression results show a minimum achieved root mean squared error of 22.17. Conclusion: The problem of predicting apnea–hypopnea index or severity classes for obstructive sleep apnea syndrome is very difficult when using only data collected prior to polysomnography test. The results achieved with the available data suggest the use of machine learning methods as tools for providing patients with a priority level for polysomnography test, but they still cannot be used for automated diagnosis.

A data stream classification method called DISSFCM (Dynamic Incremental Semi-Supervised FCM) is presented, which is based on an incremental semi-supervised fuzzy clustering algorithm. The method assumes that partially labeled data belonging to different classes are continuously available during time in form of chunks. Each chunk is processed by semi-supervised fuzzy clustering leading to a cluster-based classification model. The proposed DISSFCM is capable of dynamically adapting the number of clusters to data streams, by splitting low-quality clusters so as to improve classification quality. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method in data stream classification.

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Purpose The purpose of this paper is to propose a framework for intelligent analysis of Twitter data. The purpose of the framework is to allow users to explore a collection of tweets by extracting topics with semantic relevance. In this way, it is possible to detect groups of tweets related to new technologies, events and other topics that are automatically discovered. Design/methodology/approach The framework is based on a three-stage process. The first stage is devoted to dataset creation by transforming a collection of tweets in a dataset according to the vector space model. The second stage, which is the core of the framework, is centered on the use of non-negative matrix factorizations (NMF) for extracting human-interpretable topics from tweets that are eventually clustered. The number of topics can be user-defined or can be discovered automatically by applying subtractive clustering as a preliminary step before factorization. Cluster analysis and word-cloud visualization are used in the last stage to enable intelligent data analysis. Findings The authors applied the framework to a case study of three collections of Italian tweets both with manual and automatic selection of the number of topics. Given the high sparsity of Twitter data, the authors also investigated the influence of different initializations mechanisms for NMF on the factorization results. Numerical comparisons confirm that NMF could be used for clustering as it is comparable to classical clustering techniques such as spherical k-means. Visual inspection of the word-clouds allowed a qualitative assessment of the results that confirmed the expected outcomes. Originality/value The proposed framework enables a collaborative approach between users and computers for an intelligent analysis of Twitter data. Users are faced with interpretable descriptions of tweet clusters, which can be interactively refined with few adjustable parameters. The resulting clusters can be used for intelligent selection of tweets, as well as for further analytics concerning the impact of products, events, etc. in the social network.