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 datasets, 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.