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

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.& COPY; 2023 Published by Elsevier B.V.

Automated summary

This paper introduces a novel probabilistic-fuzzy inference system that combines fuzzy theory and probability theory to represent uncertainty. The system uses quantile functions in its inference engine, distinguishing it from existing systems that use distribution or probability functions. The paper also presents methods for constructing probabilistic-fuzzy rules, defining significance measures for association rules, and validating the proposed system through experiments.