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An Interval-Valued Fuzzy Cerebellar Model Neural Network Based on Intuitionistic Fuzzy Sets

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Abstract

An interval-valued fuzzy cerebellar model neural network (IV-FCMNN) is proposed for the identification and control of uncertain systems. It is a more general model that uses the framework of a cerebellar model neural network (CMNN) and Atanassov intuitionistic fuzzy sets (AIFSs), so that the mathematical representation of a fuzzy event is more complete and the fuzzy neural network is more general. In some special cases, this neural network can be reduced to an interval-valued fuzzy neural network (IV-FNN), a fuzzy neural network (FNN), a fuzzy cerebellar model neural network (FCMNN) or a CMNN. Since the interval-type input data are used to realize this algorithm, the IV-FCMNN copes better with uncertainty and allows greater freedom of design. Therefore, the ability to learn, the approximation precision and the fuzzy semantic description of this network are much better than those of other models. In the proposed IV-FCMNN, a training algorithm that uses a gradient descent method is proposed to adjust the parameters and convergence is proved using the Lyapunov stability theorem. The variable learning rates are analyzed and the optimal learning rates are also determined. For demonstrating the effectiveness of the proposed IV-FCMNN, three types of applications, including multiple functions approximation, multi-dimensional classification and nonlinear dynamic system feedback control, are performed and the comparison with other models are also provided.

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Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive comments and based on which the presentation of this paper has been greatly improved. This work was supported by the Natural Science Foundation (2015J01275) of Science and Technology agency, Fujian, and the Science and Technology-Planned Project (3502Z20143034) of Xiamen, and the Foreign Science and Technology Special Cooperation (E201401400) of Xiamen University of Technology, and the National Science Council of the Republic of China under Grant NSC 98-2221-E-155-058-MY3.

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Authors and Affiliations

  1. School of Electrical Engineering and Automation, Xiamen University of Technology, Xiamen, 361024, China

    Jing Zhao

  2. Department of Electrical Engineering, Yuan Ze University, Chung Li, Tao-Yuan, 320, Taiwan, ROC

    Jing Zhao & Chih-Min Lin

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  1. Jing Zhao
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  2. Chih-Min Lin
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Correspondence to Chih-Min Lin.

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Zhao, J., Lin, CM. An Interval-Valued Fuzzy Cerebellar Model Neural Network Based on Intuitionistic Fuzzy Sets. Int. J. Fuzzy Syst. 19, 881–894 (2017). https://doi.org/10.1007/s40815-017-0321-2

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