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On the Symmetry of Interval Type-2 Fuzzy Logic Controllers Using Different Type-Reduction Methods

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Proceedings of 2013 Chinese Intelligent Automation Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 254))

Abstract

In order to deepen the theoretical understanding of the interval type-2 (IT2) fuzzy logic controllers (FLCs), it is meaningful to explore the fundamental properties of IT2FLCs, e.g. continuity, monotonicity, smoothness, adaptiveness, novelty, stability and robustness. This paper studies another fundamental property—the symmetry, which is always required in real-world control applications. Symmetric conditions are derived to ensure the symmetry of FLCs, including both IT2FLCs and type-1 FLCs (T1FLCs). For IT2FLCs, we consider three most commonly-used type-reduction and defuzzification methods—the Karnik–Mendel (KM) method, the uncertainty bound (UB) method and the Begian-Melek-Mendel (BMM) method. At last, an application is given to verify the correctness of the derived results.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (61105077, 61273149, 61074149 and 61273326), and the Excellent Young and Middle-Aged Scientist Award Grant of Shandong Province of China (BS2012DX026).

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Authors and Affiliations

  1. School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan, 250101, China

    Chengdong Li, Guiqing Zhang & Ming Wang

  2. Institute of Automation, Chinese Academy of Sciences, Beijing, 100090, China

    Jianqiang Yi

Authors
  1. Chengdong Li
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  2. Guiqing Zhang
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  3. Jianqiang Yi
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  4. Ming Wang
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Corresponding author

Correspondence to Chengdong Li .

Editor information

Editors and Affiliations

  1. , Department of Computer Science, Tsinghua University, Qinghua, Beijing, 100084, China, People's Republic

    Zengqi Sun

  2. Tsinghua University, Qinghua, Beijing, 100084, China, People's Republic

    Zhidong Deng

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Li, C., Zhang, G., Yi, J., Wang, M. (2013). On the Symmetry of Interval Type-2 Fuzzy Logic Controllers Using Different Type-Reduction Methods. In: Sun, Z., Deng, Z. (eds) Proceedings of 2013 Chinese Intelligent Automation Conference. Lecture Notes in Electrical Engineering, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38524-7_47

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  • DOI: https://doi.org/10.1007/978-3-642-38524-7_47

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38523-0

  • Online ISBN: 978-3-642-38524-7

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