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Advances in Neural Network Research and Applications pp 173–183Cite as

Interval-Valued Fuzzy Control

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 67))

Abstract

In this paper, we introduce the concept of interval-valued fuzzy control. Based on the idea of the interpolation mechanism of fuzzy control, we propose the inference algorithm of interval-valued fuzzy inference and mathematical model of interval-valued fuzzy control, investigate the interpolation mechanism of interval-valued fuzzy control. Finally, we use a simulation experiment of interval-valued fuzzy control to illustrate our proposed algorithm reasonable.

This work is supported by grants from the National Natural Science Foundation of China (10971243).

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References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999)

    MATH  Google Scholar 

  3. Bustince, H., Burillo, P.: Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning. Fuzzy Sets and Systems 113, 205–219 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, S.M., Hsiao, W.H., Jong, W.T.: Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 91, 339–353 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, S.M., Hsiao, W.H.: Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets. Fuzzy Sets and Systems 113, 185–203 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chun, M.G.: A similarity-based bidirectional approximate reasoning method for decision-making systems. Fuzzy Sets and Systems 117, 269–278 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133, 227–235 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Deschrijver, G.: Arithmetic operators in interval-valued fuzzy set theory. Information Sciences 177, 2906–2924 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gorzalczany, M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems 21, 1–17 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gorzalczany, M.B.: An interval-valued fuzzy inference method -some basic properties. Fuzzy Sets and Systems 31, 243–251 (1989)

    Article  MathSciNet  Google Scholar 

  11. Li, H.X.: Interpolation mechanism of fuzzy control. Science in China, Ser. E 41(3), 312–320 (1998)

    Article  MATH  Google Scholar 

  12. Li, H.X.: Adaptive fuzzy controllers based on variable universe. Science in China, Ser. E 42(1), 10–20 (1999)

    Article  MATH  Google Scholar 

  13. Li, H.X.: Relationship between fuzzy controllers and PID controllers. Science in China, Ser. E 42(2), 215–224 (1999)

    Article  MATH  Google Scholar 

  14. Wang, P.Z., et al.: Mathematical theory of truth-valued flow inference. Fuzzy Sets and Systems 72, 221–238 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  15. Wu, W.M.: Principle and Method of Fuzzy Inference. Guizhou Science and technology Press, Guizhou (1994) (in Chinese)

    Google Scholar 

  16. Zadeh, L.A.: Fuzzy sets, Inform. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning(I). Inform. Sci. 8, 199–249 (1975)

    Article  MathSciNet  Google Scholar 

  18. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning (II) 8, 301–357 (1975)

    Google Scholar 

  19. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning(III). Inform. Sci. 9, 43–80 (1975)

    Article  MathSciNet  Google Scholar 

  20. Zadeh, L.A.: Toward a generalized theory of uncertainty(GTU)-—an outline. Information Sciences 172, 1–40 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Zeng, W.Y., Shi, Y.: Note on interval-valued fuzzy set. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds.) ICONIP 2004. LNCS, vol. 3316, pp. 20–25. Springer, Heidelberg (2004)

    Google Scholar 

  22. Zeng, W.Y., Li, H.X.: Inner product truth-valued flow inference, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems 13(6), 601–612 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  23. Zeng, W.Y., Shi, Y., Li, H.X.: Representation theorem of interval-valued fuzzy set, Internat. J. Uncer. Fuzzi. Knowloedge-Based Systems 14, 259–269 (2006)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Information Science and Technology, Beijing Normal University, Beijing, 100875, P.R. China

    Wenyi Zeng

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P.R. China

    Jiayin Wang

Authors
  1. Wenyi Zeng
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  2. Jiayin Wang
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Editor information

Editors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, 430074, Wuhan, Hubei, China

    Zhigang Zeng

  2. Department of Mechanical & Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

    Jun Wang

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Zeng, W., Wang, J. (2010). Interval-Valued Fuzzy Control. In: Zeng, Z., Wang, J. (eds) Advances in Neural Network Research and Applications. Lecture Notes in Electrical Engineering, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12990-2_20

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  • DOI: https://doi.org/10.1007/978-3-642-12990-2_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12989-6

  • Online ISBN: 978-3-642-12990-2

  • eBook Packages: EngineeringEngineering (R0)

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