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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 25))

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Abstract

The approximations we will discuss in this chapter are between discrete fuzzy expert systems, neural nets and fuzzy controllers. We first present the details of the structure of a discrete fuzzy expert system and a fuzzy controller before introducing all the approximation results. We call these “first” approximation results because in a latter chapter they will be fuzzyified and then called second approximation results. The second approximation results are concerned with approximations between fuzzy expert systems, fuzzy neural nets, fuzzy functions and fuzzy input-output controllers.

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References Chapter 4

  1. J.J. Buckley: Universal Fuzzy Controllers, Automatica 28 (1992), pp. 12451248.

    Google Scholar 

  2. J.J. Buckley: Approximations Between Nets, Controllers, Expert Systems and Processes, Proc. 2nd Intern. Conf. Fuzzy Logic and Neural Networks, Iizuka, Japan, July 17–22, 1992, Vol. 1, pp. 89–90.

    Google Scholar 

  3. J.J. Buckley: Approximations Paper: Part 1, Proc. of Third Intern. Workshop on Neural Networks and Fuzzy Logic, Vol. 1, NASA, Houston, Texas, June 1–3, 1992, pp. 170–173.

    Google Scholar 

  4. J.J. Buckley: Sugeno Type Controllers are Universal Controllers, Fuzzy Sets and Systems 53 (1993), pp. 299–304.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.J. Buckley: Applicability of the Fuzzy Controller, in P.-Z. Wang, K.F. Loe, (eds.) Between Mind and Computer, World Scientific Press, Singapore, 1993, pp. 47–54.

    Google Scholar 

  6. J.J. Buckley: System Stability and the Fuzzy Controller, in H.T. Nguyen, M. Sugeno, R. Tong, R. Yager (eds.) Theoretical Aspects of Fuzzy Control, Wiley, 1995, pp. 51–63.

    Google Scholar 

  7. J.J. Buckley: Stability and the Fuzzy Controller, Fuzzy Sets and Systems 77 (1996), pp. 167–173.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.J. Buckley: Erratum: Universal Fuzzy Controllers, Automatica 33 (1997), pp. 1771–1773.

    Article  MathSciNet  Google Scholar 

  9. J.J. Buckley: Approximation Aspects of Fuzzy Models, Handbook of Fuzzy Computation, Oxford Univ. Press. To appear.

    Google Scholar 

  10. J.J. Buckley: Erratum: Stability and the Fuzzy Controller, Fuzzy Sets and Systems, to appear.

    Google Scholar 

  11. J.J. Buckley and Y. Hayashi: Numerical Relationships Between Neural Networks, Continuous Functions and Fuzzy Systems, Fuzzy Sets and Systems 60 (1993), pp. 1–8.

    Article  MathSciNet  Google Scholar 

  12. J.J. Buckley and Y. Hayashi: Can Approximate Reasoning be Consistent, Fuzzy Sets and Systems 65 (1994) pp. 13–18.

    Article  MathSciNet  MATH  Google Scholar 

  13. J.J. Buckley, Y. Hayashi and E. Czogala: On the Equivalence of Neural Nets and Fuzzy Expert Systems, Proc. Intern. Joint Conf. Neural Networks, Baltimore, June 7–12, 1992, Vol. II, pp. 691–695.

    Google Scholar 

  14. J.J. Buckley, Y. Hayashi and E. Czogala: On the Equivalence of Neural Nets and Fuzzy Expert Systems. Fuzzy Sets and Systems 53 (1993), pp. 129–134.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y. Hayashi, J.J. Buckley and E. Czogala: Fuzzy Expert Systems Versus Neural Networks, Proc. Intern. Joint Conf. Neural Networks, Baltimore, June 7–12, 1992, Vol. II, pp. 720–726.

    Google Scholar 

  16. Y. Hayashi, J.J. Buckley and E. Czogala: Approximations Between Fuzzy Expert Systems and Neural Nets, Proc. 2nd Intern. Conf. Fuzzy Logic and Neural Networks, Iizuka, Japan, July 17–22, 1992, Vol. 1, pp. 135–139.

    Google Scholar 

  17. Y. Hayashi and J.J. Buckley: Approximations Between Fuzzy Expert Systems amd Neural Networks, J. of Approximate Reasoning 10 (1994), pp. 63–73.

    Article  MATH  Google Scholar 

  18. G.J. Klir and B. Yuan: Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, N.J., 1995.

    MATH  Google Scholar 

  19. FLOPS: URL: http://users.aol.com/wsiler

  20. R. Fuller and H.-J. Zimmermann: On Zadeh’s Compositional Rule of Inference, Proc. Fourth IFSA, Brussels, 1991, pp. 41–44.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Buckley, J.J., Feuring, T. (1998). First Approximation Results. In: Fuzzy and Neural: Interactions and Applications. Studies in Fuzziness and Soft Computing, vol 25. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1881-9_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1881-9_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11807-8

  • Online ISBN: 978-3-7908-1881-9

  • eBook Packages: Springer Book Archive

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