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898 IEEE TRANSACTIONS ON FUZZY SYSTEMS, VOL. 16, NO. 4, AUGUST 2008
A Probabilistic Neural-Fuzzy Learning System
for Stochastic Modeling
Han-Xiong Li, Senior Member, IEEE, and Zhi Liu
Abstract—A probabilistic fuzzy neural network (PFNN) with a handling inexact information [11], and the performance can be
hybrid learning mechanism is proposed to handle complex stochas- enhanced when integrating with NNs [12]. Though the FNN
tic uncertainties. Fuzzy logic systems (FLSs) are well known for can effectively handle vagueness and even time-varying non-
vagueness processing. Embedded with the probabilistic method,
an FLS will possess the capability to capture stochastic uncertain- linearity, however, it may not be able to process the stochastic
ties. Further enhanced with the neural learning, it will be able to uncertainties.
work under time-varying stochastic environment. Integrated with As probabilistic methods and fuzzy techniques are good at
a statistical process control (SPC) based monitoring method, the processing stochastic and nonstochastic uncertainties, respec-
PFNN can maintain the robust modeling performance. Finally, the tively [13], it would be more valuable if these two methods
successful simulation demonstrates the modeling effectiveness of
the proposed PFNN under the time-varying stochastic conditions. could be combined into one. The stochastic fuzzy system was
proposed to model and control a dynamic system perturbed with
Index Terms—Intelligent learning, probabilistic fuzzy logic sys- stochastic uncertainty [1
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