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Approximating Fuzzy Control Strategies via CRI

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Fuzzy Sets and Systems — IFSA 2003 (IFSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2715))

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Abstract

We start from the observation that Zadeh’s compositional rule of inference (CRI) is a strategy to determine approximately a roughly given control function.

From this point of view the problem to solve a system of fuzzy relation equations also becomes the problem to determine approximately such a control strategy. This gives a natural interpretation for approximate solutions of unsolvable systems of relation equations.

Therefore we discuss and generalize some approaches and results about approximate solutions of systems of relation equations.

Finally we discuss here how a choice of the t-norm which is involved in the sup-t-composition modifies the solvability behavior.

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Author information

Authors and Affiliations

  1. Institute for Logic, Leipzig University, Leipzig, Germany

    Siegfried Gottwald

  2. IRAFM, Ostrava University, Ostrava, Czech Republic

    Vilem Novák & Irina Perfilieva

Authors
  1. Siegfried Gottwald
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  2. Vilem Novák
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  3. Irina Perfilieva
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Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Taner Bilgiç

  2. Dept. of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Department of Electrical and Electronics Engineering, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Okyay Kaynak

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Gottwald, S., Novák, V., Perfilieva, I. (2003). Approximating Fuzzy Control Strategies via CRI. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_24

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  • DOI: https://doi.org/10.1007/3-540-44967-1_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40383-8

  • Online ISBN: 978-3-540-44967-6

  • eBook Packages: Springer Book Archive

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