Genetic learning of fuzzy rules based on low quality data

Genetic Fuzzy Systems (GFS) are based on the use of Genetic Algorithms for designing fuzzy systems, and for providing them with learning and adaptation capabilities. In this context, fuzzy sets represent linguistic granules of information, contained in the antecedents and consequents of the rules, whereas the data used in the genetic learning is assumed to be crisp. GFS seldom deal with fuzzy-valued data. In this paper we address this problem, and propose a set of techniques that can be incorporated to different GFS in order to learn a Knowledge Base (KB) from interval and fuzzy data for regression problems. Details will be given about the representation of non-standard data with fuzzy sets, about the needed changes in the reasoning method of the Fuzzy Rule Based System, and also about a new generalization of the mean squared error to vague data. In addition, we will show that the learning process requires a genetic algorithm that must be capable of optimizing a multicriteria fitness function, containing both crisp and interval-valued criteria. Lastly, we benchmark our procedures with some machine learning related datasets and a real-world problem of marketing, and the techniques proposed here are shown to improve the generalization properties of other KBs obtained from crisp training data.