Tang-Kai Yin, Member, IEEEAbstract—This paper presents a characteristic-point-basedfuzzy inference system (CPFIS) for fuzzy modeling from trainingdata. The aim of the CPFIS is not only satisfactory precision performance,but also to employ as few purely linguistic fuzzy rulesas possible by using a minimization-based systematic trainingmethod. Characteristic points (CPs) are defined as the few datapoints among the original training data which, when they aredirectly mapped to fuzzy rules and thus form the entire rule base,allow the underlying system to be effectively modeled. Three minimization-based algorithms in a sequence are proposed to trainthe CPFIS: a gradient-projection method, a Gauss–Jordan-elimination-based column elimination, and back-propagation. TheCPs are determined by iterative computations of the first twominimization algorithms, after which the resulting fuzzy sets arefurther fine-tuned by the third algorithm. Experiments conductedon three benchmark problems showed th...