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Australasian Joint Conference on Artificial Intelligence

AI 2007: AI 2007: Advances in Artificial Intelligence pp 529–538Cite as

Continuity of Fuzzy Approximate Reasoning and Its Application to Optimization

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4830))

Abstract

This paper describes a mathematical framework for studying a nonlinear feedback control. The fuzzy control discussed here is the nonlinear feedback control in which the feedback laws are determined by IF-THEN type fuzzy production rules through approximate reasoning introduced by Nakamori. To prove existence of optimal control, we applied compactness of a set of membership functions in L 2 space and continuity of the approximate reasoning, and prepared some propositions concerning approximate reasoning of Nakamori model. By considering fuzzy optimal control problems as problems of finding the minimum (maximum) value of the integral cost (benefit) function on an appropriate set of membership functions, the existence of fuzzy optimal control is shown.

The paper was supported in part by Grant-in-Aid for Young Scientists (B) #19700225 from Japan Society for the Promotion of Science (JSPS).

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Author information

Authors and Affiliations

  1. University of Marketing and Distribution Sciences, Kobe 651-2188, Japan

    Takashi Mitsuishi

  2. Shinshu University, Nagano 380-8553, Japan

    Yasunari Shidama

Authors
  1. Takashi Mitsuishi
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  2. Yasunari Shidama
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Editor information

Mehmet A. Orgun John Thornton

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© 2007 Springer-Verlag Berlin Heidelberg

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Mitsuishi, T., Shidama, Y. (2007). Continuity of Fuzzy Approximate Reasoning and Its Application to Optimization. In: Orgun, M.A., Thornton, J. (eds) AI 2007: Advances in Artificial Intelligence. AI 2007. Lecture Notes in Computer Science(), vol 4830. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76928-6_54

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  • DOI: https://doi.org/10.1007/978-3-540-76928-6_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76926-2

  • Online ISBN: 978-3-540-76928-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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