Semi-overlap functions and novel fuzzy reasoning algorithms with applications - Zhang, Xiaohong; Wang, Mei; Bedregal, Benjamín; Li, Mengyuan; Liang, Rong (Information sciences, 2022)
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 semi-overlap 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.