Skip to main content

Optimization of SIRMs Fuzzy Model Using Łukasiewicz Logic

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7664)

Abstract

The purpose of this study is to prove the existence of single input rule modules which minimize the performance functional of the feedback control using SIRMs fuzzy reasoning method. A bounded product (Łukasiewicz t-norm) and a bounded sum (Łukasiewicz t-conorm) are applied to the operations in SIRMs fuzzy reasoning for interpreting “ands” and “ors” respectively.

Keywords

  • SIRMs approximate reasoning method
  • Bounded product
  • Bounded sum
  • Calculus of variations

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Metcalfe, G., Olivetti, N., Gabbay, D.: Proof Theory for Fuzzy Logics. Springer, Netherlands (2009)

    MATH  Google Scholar 

  2. Mizumoto, M.: Fuzzy Conditional Inference under Max-⊙ Composition. Inform. Sci. 27(2), 183–209 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Yubazaki, N., Yi, J., Hirota, K.: A Proposal of SIRMs (Single Input Rule Modules) Connected Fuzzy Inference Model for Plural Input Fuzzy Control. J. Japan Society for Fuzzy Theory Syst. 9(5), 699–709 (1997)

    Google Scholar 

  4. Seki, H., Ishii, H., Mizumoto, M.: On the Generalization of Single Input Rule Modules Connected Type Fuzzy Reasoning Method. In: Proc. Joint 3rd International Conference on Soft Computing and Intelligent Systems and 7th International Symposium on Advanced Intelligent Systems 2006, pp. 30–34 (2006)

    Google Scholar 

  5. Mitsuishi, T., Kawabe, J., Wasaki, K., Shidama, Y.: Optimization of Fuzzy Feedback Control Determined by Product-Sum-Gravity Method. J. Nonlin. Convex Anal. 1(2), 201–211 (2000)

    MathSciNet  MATH  Google Scholar 

  6. Mitsuishi, T., Shidama, Y.: Optimal Control Using Functional Type SIRMs Fuzzy Reasoning Method. In: Honkela, T., Duch, W., Girolami, M., Kaski, S. (eds.) ICANN 2011, Part II. LNCS, vol. 6792, pp. 237–244. Springer, Heidelberg (2011)

    Google Scholar 

  7. Mitsuishi, T., Terashima, T., Homma, T., Shidama, Y.: Fuzzy Approximate Reasoning Using Single Input Rule Modules in L ∞  Space. In: Proc. IEEE AFRICON, pp. 1–6 (2011)

    Google Scholar 

  8. Riesz, F., Sz.-Nagy, B.: Functional Analysis. Dover Publications, New York (1990)

    MATH  Google Scholar 

  9. Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. John Wiley & Sons, New York (1988)

    MATH  Google Scholar 

  10. Miller, R.K., Michel, A.N.: Ordinary Differential Equations. Academic Press, New York (1982)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mitsuishi, T., Terashima, T., Shidama, Y. (2012). Optimization of SIRMs Fuzzy Model Using Łukasiewicz Logic. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34481-7_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34481-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34480-0

  • Online ISBN: 978-3-642-34481-7

  • eBook Packages: Computer ScienceComputer Science (R0)