Significance measures for rules in probabilistic-fuzzy inference systems based on fuzzy transforms

Abstract

This paper defines a novel probabilistic-fuzzy inference system that considers fuzzy inputs and returns, as output, a probability distribution. In this way, it combines two different ways to represent uncertainty: the one modeled by fuzzy theory, that allows to represent reliable but vague information; and the one modeled by probability theory, that allows to represent undetermined but specific information. The novelty of this probabilistic-fuzzy inference system, with respect to the other existing in the literature, is that its inference engine combines quantile functions instead of distribution, probabilistic or density functions. Besides the formal definition of this novel kind of fuzzy inference systems, we propose: firstly, the construction of probabilistic-fuzzy rules by means of direct quantiles F-transforms; secondly, the definition of several significance measures for the obtained association rules; and finally, we present a set of experiments to validate all the assertions done throughout the paper.