Advertisement

Complexity Reduction of a Generalised Rational Form

  • Peter Baranyi
  • Yeung Yam
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 553)

Abstract

This chapter is motivated by the fact that though fuzzy techniques are popular engineering tools, their utilisation is being restricted by their exponential complexity property. The objectives of this chapter are twofold: one is to find a general form for fuzzy system output covering the widest possible areas of applications, and the other is to present a complexity reduction algorithm for the general form.

Keywords

Fuzzy System Complexity Reduction Inference Algorithm Fuzzy Rule Base Fuzzy Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L.T. Kóczy and K. Hirota “Size reduction by interpolation in fuzzy rule bases”, IEEE Trans. on System Man and Cybernetics, Vol. 27, 1997, pp 14–25.CrossRefGoogle Scholar
  2. [2]
    L.T. Kóczy and K. Hirota “Fuzzy inference by compact rules”, Proc. of Int. Conf. on FL & NN (IIZUKA’ 90), Iizuka, Fukuoka, 1990, pp. 307–310.Google Scholar
  3. [3]
    E.P. Klement, L.T. Kóczy and B. Moser “Are fuzzy systems universal approximators?”, Int. Jour. General Systems, to appear.Google Scholar
  4. [4]
    D. Tikk “The nowhere denseness of Takagi-Sugeno-Kang type fuzzy controllers containing prerestricted number of rules”, Tatra Mountains Mathematical Publications. Google Scholar
  5. [5]
    A. Stoica “Fuzzy processing based on ?-cut mapping”, 5th IFSA World Congress, Seoul, pp. 1266–1269.Google Scholar
  6. [6]
    W. Yu and Z. Bien “Design of fuzzy logic controller with inconsistent rule base”, Jour. of intelligent and Fuzzy Systems, Vol. 2, 1994, pp 147–159Google Scholar
  7. [7]
    J. Bruinzeel, V. Lacróse, A. Titli and H.B. Verbruggen “Real time fuzzy control of complex systems using rule-base reduction methods”, 2nd World Aut. Con. (WAC’96), Monpellier, France, 1996.Google Scholar
  8. [8]
    M. Sugeno, M.F. Griffin, A. Bast, “Fuzzy hierarchical control of an unmanned Helicopter”, 5th IFSA World Congress, Seoul, 1993. pp. 1262–1265.Google Scholar
  9. [9]
    Y. Yam “Fuzzy approximation via grid point sampling and singular value decomposition”, IEEE Trans. on System Man and Cybernetics, Vol. 27, No. 6, 1997, pp. 933–951.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Y. Yam, P. Baranyi and C.T. Yang “Reduction of fuzzy rule base via singular value decomposition”, IEEE Trans. on Fuzzy Systems. Vol. 7, No. 2, ISSN 1063-6706, 1999, pp. 120–131.CrossRefGoogle Scholar
  11. [11]
    P. Baranyi, Y. Yam and C.T. Yang “Complexity reduction of the rational general form”, 8th IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE’99), Seoul, Korea, 1999, pp. 366–371.Google Scholar
  12. [12]
    P. Baranyi, A. Martinovics, Sz. Kovács, D. Tikk and Y. Yam “A general extension of the fuzzy SVD rule base reduction using arbitrary inference algorithm”, IEEE Int. Conf. System Man and Cybernetics (IEEE SMC’98), 1998, San Diego, California, USA, pp 2785–2790.Google Scholar
  13. [13]
    P. Baranyi, Y. Yam and C.T. Yang “Singular value decomposition of linguistic symbol-array”, IEEE Conf. on Systems Man and Cybernetics (IEEE SMC’99), 1999, Tokyo, Japan, pp.:III/822-III/826.Google Scholar
  14. [14]
    P. Baranyi, Y. Yam, C.T. Yang and A. Várkonyi-Kóczy “Practical extension of the SVD based reduction technique for extremely large fuzzy rule bases”, IEEE Int. Workshop on Intelligent Signal Processing, (WISP’99), 1999, Budapest, Hungary, pp. 29–33.Google Scholar
  15. [15]
    C.T. Yang, P. Baranyi, Y. Yam and Sz. Kovács “SVD reduction of a fuzzy controller in an AGV steering system”, EFDAN’99, Dortmund, Germany, 1999, pp 118–124Google Scholar
  16. [16]
    P. Baranyi, I. Mihálcz, P. Korondi, Z. Gubinyi and H. Hashimoto “Fuzzy rule base reduction for robot finger furnished with shape memory alloy”, IEEE 24th Industrial Electronics Society Conference (IEEE IECON’98), 1998, pp 6–11.Google Scholar
  17. [17]
    P. Baranyi and Y. Yam “Singular value-based approximation with non-singleton fuzzy rule base”, 7th Int. Fuzzy Systems Association World Congress (IFSA’97), Prague, 1997, pp. 127–132.Google Scholar
  18. [18]
    P. Baranyi and Y. Yam “Singular value-based approximation with Takagi-Sugeno type fuzzy rule base”, 6th IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE’97), Barcelona, Spain, 1997, pp. 265–270.Google Scholar
  19. [19]
    P. Baranyi, Y. Yam and L.T. Kóczy “Multi variables singular value based rule interpolation”, IEEE Int. Conf. System Man and Cybernetics USA, 1997, pp. 1598–1603.Google Scholar
  20. [20]
    L. Wang, R. Langari, and J. Yen “Principal components, B-splines, and fuzzy systems reduction”, in Fuzzy Logic for the applications to Complex systems, W. Chiang and J. Lee, Eds. Singapurer World Scientific, 1996, pp. 255–259.Google Scholar
  21. [21]
    Sz. Kovács and L.T. Koczy “The use of the concept of vague environment in approximate fuzzy reasoning”, Fuzzy Set Theory and Applications, Tatra Mountains Mathematical Publications, Math. Inst. Slovak Academy of S. 1997, vol. 12, pp.169–181.MATHGoogle Scholar
  22. [22]
    P. Baranyi, T.D. Gedeon and L.T. Koczy “A general interpolation technique in fuzzy rule bases with arbitrary membership functions”, IEEE Int. Conf S.M.C, Beijing, China, 1996, pp. 510–515.Google Scholar
  23. [23]
    P. Baranyi, D. Tikk, Y. Yam, L.T. Koczy and L. Nádai “A new method for avoiding abnormal conclusion for ?-cut based rule interpolation”, 8th IEEE Int. Conf. on Fuzzy Systems (FUZZ-IEEE’99), Seoul, Korea, 1999Google Scholar
  24. [24]
    M.F. Kawaguchi and M. Miyakoshi “Fuzzy spline interpolation in sparse fuzzy rule bases”, Proc. of 5th Int. Conf on Soft Comp. and Inf /Int. Systems IIZUKA 98, Iizuka, Japan, 1998, pp 664–667.Google Scholar
  25. [25]
    G. Farm “Curves and surfaces for computer aided geometric design”, Academic press 1997Google Scholar
  26. [26]
    M. Mizumoto “Fuzzy controls by product-sum-gravity method”, Advancement of Fuzzy Thory and Systems in China and Japan, Eds. Liu and Mizumoto, International Academic Publishers, cl.l.-c.1.4.1990.Google Scholar
  27. [27]
    T. Takagi and M. Sugeno “Fuzzy identification of systems and its applications to modelling and control”, IEEE Trans. On System Mans and Cybernetics Vol.15, 1985, 116–132.MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Peter Baranyi
    • 1
  • Yeung Yam
    • 2
  1. 1.Research Group for Mechanics of the Hungarian Academy of Science and Dept. Telecommunication and TelematicsTechnical University of BudapestBudapestHungary
  2. 2.Department of Mechanical and Automation EngineeringChinese University of Hong KongShatin, N.T., Hong KongP.R China

Personalised recommendations