Inferência fuzzy e a aproximação universal

Abstract

Fuzzy theory is an area of applied mathematics that provides a solid theoretical foundation for translating subjective concepts used in everyday life into mathematical models. Among the different branches of fuzzy theory are fuzzy inference engines, models that deduce conclusions from rule bases that represent human knowledge. The use of fuzzy inference engines is common in areas such as biology, automation and industry. Despite being widely used, there is usually little understanding of the mathematical foundations that ensure the usefulness of these models. In this context, the objective of this paper is to present and demonstrate the Universal Approximation Theorem for Fuzzy Inference Engines. Through a theoretical and analytical study based on bibliographic references, the paper presents sufficient conditions (singleton fuzzifier, Gaussian membership functions, product inference and center-average defuzzifier) that ensure that fuzzy inference engines are universal approximators of continuous functions defined on a compact subset of $\mathbb{R}^n$. Furthermore, the paper provides a solid basis to further studies in the area.