Obtaining fuzzy rules from interval-censored data with genetic algorithms and a random sets-based semantic of the linguistic labels

Fuzzy memberships can be understood as coverage functions of random sets. This interpretation makes sense in the context of fuzzy rule learning: a random-sets-based semantic of the linguistic labels is compatible with the use of fuzzy statistics for obtaining knowledge bases from data. In particular, in this paper we formulate the learning of a fuzzy-rule-based classifier as a problem of statistical inference. We propose to learn rules by maximizing the likelihood of the classifier. Furthermore, we have extended this methodology to interval-censored data, and propose to use upper and lower bounds of the likelihood to evolve rule bases. Combining descent algorithms and a co-evolutionary scheme, we are able to obtain rule-based classifiers from imprecise data sets, and can also identify the conflictive instances in the training set: those that contribute the most to the indetermination of the likelihood of the model.