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Approximation and its implementation process of the stochastic hybrid fuzzy system

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Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. School of Mathematics Science, Tianjin Normal University, Tianjin, 300387, China

    Guijun Wang & Xiaoping Li

  2. Mathematical group, Yaohua Middle school in Tianjin City, Tianjin, 300000, China

    Xiaolin Sui

Authors
  1. Guijun Wang
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  2. Xiaolin Sui
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  3. Xiaoping Li
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Correspondence to Guijun Wang.

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Wang, G., Sui, X. & Li, X. Approximation and its implementation process of the stochastic hybrid fuzzy system. Int. J. Mach. Learn. & Cyber. 8, 1423–1437 (2017). https://doi.org/10.1007/s13042-015-0369-y

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  • DOI: https://doi.org/10.1007/s13042-015-0369-y

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