Semi-overlap functions and novel fuzzy reasoning algorithms with applications

In order to get a more general result related on fuzzy implications that induced by aggregation functions, we relax the definition of general overlap functions, more precisely, removing its right-continuous, and introduce a new kind of aggregation function, which called semi-overlap function. Subsequently, we explore some of their related algebraic properties and its corresponding residual implications. Moreover, serval scholars have provided kinds of methods for fuzzy modus ponens (FMP, for short) problems, such as Zadeh's compositional rule of inference (CRI, for short), Wang's triple I method (TIM, for short) and quintuple implication principle (QIP, for short). Compared with CRI and TIM, QIP has some advantages in solving FMP problems. Based on the above theory foundation of semioverlap functions and their residual implications, we further consider the QIP for FMP problems. Finally, we propose a new classification algorithm that based on semi-overlap functions and QIP, which called SO5I-FRC algorithm. Through the comparative tests, the average accuracy of SO5I-FRC algorithm is higher than FARC-HD algorithm. The experimental results indicate that semi-overlap functions and QIP have certain advantages and a wide range of applications in classification problems. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This study relaxes the definition of general overlap functions and introduces semi-overlap functions. It explores their algebraic properties and residual implications, and considers the application of QIP in fuzzy modus ponens problems. A new classification algorithm based on semi-overlap functions and QIP is proposed, and its performance is compared with another algorithm.