Performance analysis of fuzzy systems based on quintuple implications method

To improve the quality of approximate reasoning in fuzzy system, quintuple implication principle (QIP) to resolve fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) problems has been proposed by Zhou et al. [32]. The same approximation as Mamdani-type fuzzy inference can be reached by fuzzy reasoning with QIP method for Gödel implication. It therefore is essential to establish some fundamental properties of fuzzy inference system with QIP method. This paper mainly investigates the robustness and universal approximation capability of fuzzy inference system with QIP method. Firstly, we present the QIP solutions of FMP and FMT for R-, S-, QL-, f- and g-implications. And then the robustness of fuzzy inference system with QIP method is discussed. Finally, we study the universal approximation properties of multiple-input and single-output (MISO) fuzzy systems with QIP method for R-, S- and QL-implications. These results reveal that the QIP method possesses better performance in fuzzy rule-based system.