Fuzzy If-Then Rules in Computational Intelligence pp 135-159 | Cite as

# Complexity Reduction of a Generalised Rational Form

Chapter

## 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
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## References

- [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]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]E.P. Klement, L.T. Kóczy and B. Moser “Are fuzzy systems universal approximators?”,
*Int. Jour. General Systems*, to appear.Google Scholar - [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]A. Stoica “Fuzzy processing based on ?-cut mapping”,
*5th IFSA World Congress*, Seoul, pp. 1266–1269.Google Scholar - [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]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]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]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]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]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]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]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]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]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]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]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]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]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]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]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]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]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]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]G. Farm “Curves and surfaces for computer aided geometric design”, Academic press 1997Google Scholar
- [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]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

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