Sách A Characteristic-Point-Based Fuzzy Inference System Aimed to Minimize the Number of Fuzzy Rules

Tang-Kai Yin, Member, IEEE
Abstract—This paper presents a characteristic-point-based
fuzzy inference system (CPFIS) for fuzzy modeling from training
data. The aim of the CPFIS is not only satisfactory precision performance,
but also to employ as few purely linguistic fuzzy rules
as possible by using a minimization-based systematic training
method. Characteristic points (CPs) are defined as the few data
points among the original training data which, when they are
directly 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 train
the CPFIS: a gradient-projection method, a Gauss–Jordan-elimination-
based column elimination, and back-propagation. The
CPs are determined by iterative computations of the first two
minimization algorithms, after which the resulting fuzzy sets are
further fine-tuned by the third algorithm. Experiments conducted
on three benchmark problems showed that the CPFIS used one of
the smallest number of fuzzy rules among the reported results for
other methods. The Gaussian membership functions in both the
input and output fuzzy sets and the small number of fuzzy rules
make the rule interpretation of the CPFIS much easier than that
of other methods, thus enhancing human-computer cooperation
in knowledge discovery.