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Knowledge extraction techniques depend on the quality of the available data. In the best case, the deviation between the perceived information and the actual values of the variables is small and can be safely ignored. On other occasions this difference is relevant but a probability distribution can characterize the observation error. In the less favorable scenario, to which we will refer as ‘‘low quality data’’, the observation error is relevant but it cannot be aptly characterized by a unique probability distribution. Data with missing features, censored or comprising nested confidence intervals are particular cases of this. This special issue collects twelve papers about the extraction of knowledge from low quality data. On one hand, there are theoretical contributions, discussing different characterizations of the sources of uncertainty (possibility theory, interval data, fuzzy sets, imprecise probabilities, etc.). On the other hand, there are methodological and empirical studies, related to the design and validation of systems on the basis of incomplete and imprecise information, including algorithms for learning association rules, classification and regression models with uncertain attributes and/or labels. The first paper, titled ‘‘Partially supervised independent factor analysis using soft labels elicited from multiple experts: application to railway track circuit diagnosis’’ describes a new noiseless independent factor analysis model applied to the diagnosis of railway track circuits. Partial information from domain experts, expressed as belief functions, is combined with measurement data. The authors propose to handle the learning of this statistical model in a soft-supervised way using imperfect information on the system component states. In the second paper, ‘‘Singular spectral analysis of illknown signals and its application to predictive maintenance of windmills with SCADA records’’ a possibilistic generalization of the singular spectral analysis is proposed. This method produces a list of fuzzy bounds of the energy of an ill-known signal at different frequencies. By comparing these bounds to the expected energy of colored noise, those parts of the historical records of the supervision system of the windmill that are relevant for the prediction of mechanical failures can be identified. The third paper, ‘‘A fuzzy interval analysis approach to kriging with ill-known variogram and data’’, proposes an approach to handle epistemic uncertainty appearing in the kriging methodology (predicting a spatial phenomenon at non sampled locations from an estimated random function) when the collected data contains errors that can be modeled by intervals or fuzzy intervals, while at the same time the choice of parameter values for the theoretical variogram is not completely determined. These first three papers model the non random (epistemic) uncertainty in the data by means of families of probabilities. However, a different theoretical framework is assumed in both the fourth and the fifth papers. The minimization of a crisp distance between fuzzy sets is the basis of the work, ‘‘A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production’’, where a new generalization of the least-squares technique is introduced for solving a regression problem where the independent L. Sánchez (&) Computer Science Department, University of Oviedo, Campus de Viesques, 33071 Gijón, Asturias, Spain e-mail: luciano@uniovi.es

Guest editorial: special issue on “knowledge extraction from low quality data: theoretical, methodological and practical issues”