Linguistic cost-sensitive learning of genetic fuzzy classifiers for imprecise data

Cost-sensitive classification is based on a set of weights defining the expected cost of misclassifying an object. In this paper, a Genetic Fuzzy Classifier, which is able to extract fuzzy rules from interval or fuzzy valued data, is extended to this type of classification. This extension consists in enclosing the estimation of the expected misclassification risk of a classifier, when assessed on low quality data, in an interval or a fuzzy number. A cooperative-competitive genetic algorithm searches for the knowledge base whose fitness is primal with respect to a precedence relation between the values of this interval or fuzzy valued risk. In addition to this, the numerical estimation of this risk depends on the entrywise product of cost and confusion matrices. These have been, in turn, generalized to vague data. The flexible assignment of values to the cost function is also tackled, owing to the fact that the use of linguistic terms in the definition of the misclassification cost is allowed.