《A Probabilistic Neural-Fuzzy Learning System》.pdf

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