Survey on two-step fuzzy rule interpolation methods

Authors

  • Antónia Berecz Dénes Gábor Applied University, Institute of Technology and Principle Science, H-1115 Budapest, Etele út 68.
  • Zsolt Csaba Johanyák Kecskemét College, GAMF Faculty, Kalmár Sándor Institute of Information Technology, H-6000 Kecskemét, Izsáki út 10.

Keywords:

fuzzy interference, two-step rule interpolation methods, GM, IGRV, FRIPOC, LESFRI

Abstract

Fuzzy Rule Interpolation (FRI) is a wide applied tool for fuzzy inference when the rule base is sparse, i.e. it does not ensure a full coverage of the input space, and the compositional reasoning methods are not able to produce a proper output in case of each possible observation. This paper surveys a relevant group of FRI techniques called two-step methods that follow the concepts of the generalized methodology of fuzzy rule interpolation (GM) introduced by Baranyi, Kóczy and Gedeon.

Author Biography

  • Antónia Berecz, Dénes Gábor Applied University, Institute of Technology and Principle Science, H-1115 Budapest, Etele út 68.

    corresponding author
    berecz@gdf.hu

References

Baranyi, P., Kóczy, L. T. (1996): A General and Specialised Solid Cutting Method for Fuzzy Rule Interpolation. In: Journal BUSEFAL. URA-CNRS : Toulouse, France. 66. 13–22.

Baranyi, P., Kóczy, L. T., Gedeon, T. D. (2004): A Generalized Concept for Fuzzy Rule Interpolation. In: IEEE Transaction on Fuzzy Systems, 12(6), 820–837. https://doi.org/10.1109/TFUZZ.2004.836085

Huang, Z. H., Shen, Q. (2004): Fuzzy interpolation with generalized representative values. In: Proceedings of the UK Workshop on Computational Intelligence. 161–171.

Johanyák Zs. Cs. (2006a): Fuzzy halmaz-interpoláció legkisebb négyzetek módszerével. Gép, 10, 51–57.

Johanyák, Zs. Cs., Kovács, Sz. (2006b): Fuzzy Rule Interpolation Based on Polar Cuts. In: Computational Intelligence, Theory and Applications, Springer : Berlin Heidelberg, 499–511. https://doi.org/10.1007/3-540-34783-6_49

Johanyák, Zs. Cs., Kovács, Sz. (2006c): Fuzzy Rule Interpolation by the Least Squares Method. In: Proceedings of the 7th International Symposium of Hungarian Researchers on Computational Intelligence (HUCI 2006), Budapest, Hungary, 495–506.

Johanyák, Zs. Cs., Kovács, Sz. (2006d): Fuzzy set approximation using polar co- ordinates and linguistic term shifting. 4th Slovakian-Hungarian Joint Symposium on Applied Machine Intelligence (SAMI 2006), Herl'any, Slovakia, 219–227.

Johanyák, Zs. Cs. (2007): Fuzzy szabály-interpolációs módszerek és mintaadatok alapján történő automatikus rendszergenerálás, Ph.D. értekezés, Miskolci Egyetem, Hatvany József Informatikai Tudományok Doktori Iskola

Kóczy, L. T., Hirota, K. (1991): Rule interpolation by α-level sets in fuzzy approximate reasoning. Journal BUSEFAL, URA-CNRS : Toulouse, France. 46. 115–123.

Mamdani, E. H., Assilian, S. (1975): An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man Machine Studies, 7(1), 1–13. https://doi.org/10.1016/S0020-7373(75)80002-2

Shen, Z., Ding, L., Mukaidono, M. (1993): Methods of revision principle. Proceedings of the 5th IFSA World Congress, Seoul, Korea. 246–249. p.

Shepard, D. (1968): A two dimensional interpolation function for irregularly spaced data. Proceedings of the 23rd ACM International Conference, New York, USA, 517–524. https://doi.org/10.1145/800186.810616

Takagi, T., Sugeno, M. (1985): Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on System, Man and Cybernetics, 15(1), 116–132. https://doi.org/10.1109/TSMC.1985.6313399

Tikk, D., Baranyi, P. (2000): Comprehensive analysis of a new fuzzy rule interpolation method. IEEE Transactions on Fuzzy Systems, 8(3), 281–296. https://doi.org/10.1109/91.855917

Yan, S., Mizumoto, M., Qiao, W. Z. (1996): An Improvement to Kóczy and Hirota's Interpolative Reasoning in Sparse Fuzzy Rule Bases. International Journal of Approximate Reasoning, 15(3), 185–201. https://doi.org/10.1016/S0888-613X(96)00054-0

Zadeh, L. A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on System, Man and Cybernetics, 3(1), 28–44. https://doi.org/10.1109/TSMC.1973.5408575

Published

2008-07-15

How to Cite

Berecz, A., & Johanyák, Z. C. (2008). Survey on two-step fuzzy rule interpolation methods. Acta Agraria Kaposváriensis, 12(2), 39-51. https://journal.uni-mate.hu/index.php/aak/article/view/1910