Approximation and its implementation process of the stochastic hybrid fuzzy system

  • Guijun WangEmail author
  • Xiaolin Sui
  • Xiaoping Li
Original Article


The stochastic Mamdani and Takagi–Sugeno fuzzy systems are firstly unified in a random environment, and the resulting stochastic hybrid fuzzy system is established according to some stochastic parameters. Secondly, A canonical representation of the stochastic process with orthogonal increments is presented by the properties of the Lebesgue–Stieltjes measure and stochastic integral, the approximation of the stochastic hybrid fuzzy system in the mean square sense is proved. Finally, an implementation process of this system is described through a simulation example, and the surface figure of the covariance function shows that the stochastic hybrid fuzzy system has excellent approximation capability.


Stochastic process Stochastic integral Covariance function Stochastic hybrid fuzzy system Approximation in mean square 



This work has been supported by National Natural Science Foundation China (Grant No. 61374009).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematics ScienceTianjin Normal UniversityTianjinChina
  2. 2.Mathematical groupYaohua Middle school in Tianjin CityTianjinChina

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