Zsolt Csaba Johanyák, Domonkos Tikk, Szilveszter Kovács, Kok Wai Wong
Zs. Cs. Johanyák is with the Department of Information Technology, Kecskemét College, Kecskemét, H-6000 Hungary (e-mail: johanyak.csaba##AT##gamf.kefo.hu).
D. Tikk is with the Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, H-1117 Budapest, Hungary (e-mail:tikk##AT##tmit.bme.hu).
Sz. Kovács is with the Department of Information Technology, University of Miskolc, Miskolc, H-3515 Hungary (e-mail:szkovacs##AT##iit.uni-miskolc.hu). font>
K.W. Wong is with the School of Information Technology, Murdoch University, South St, Murdoch, Western Australia 6150 (e-mail:k.wong##AT##murdoch.edu.au)
Why Fuzzy Rule Interpolation is important?< p class="Text" style="text-indent:0in">Fuzzy systems use fuzzy rule base to make inference. A fuzzy rule base is fully covered (at level α ), if all input universes are covered by rules at level α. Such fuzzy rule bases are also called dense or complete rule bases. In practice, it means that for all the possible observations there exists at least one firing rule, whose antecedent part overlaps the input data at least partially at level α. If this condition is not satisfied, the rule base is considered sparse rule base, i.e. containing gaps. The classical fuzzy reasoning techniques like Zadeh’s, Mamdani’s, Larsen’s or even Sugeno’s cannot generate an acceptable output for such cases. Fuzzy rule based interpolation ( FRI) techniques were introduced to generate inference for sparse fuzzy rule base, thus extend the usage of sparse fuzzy rule base system. Basically, FRI techniques perform interpolative approximate reasoning by taking into consideration the existing fuzzy rules for cases where there is no fuzzy rules to fire.
The following are a list of papers on the background of Fuzzy Rule Interpolation.
L. T. Kóczy, K. Hirota, “Rule interpolation by α-level sets in fuzzy approximate reasoning”, In J. BUSEFAL, Automne, URA-CNRS. Vol. 46. Toulouse, France, 1991, pp. 115-123.
D. Tikk , P. Baranyi, “Comprehensive analysis of a new fuzzy rule interpolation method”, In IEEE Trans. Fuzzy Syst., vol. 8, pp. 281-296, June 2000.
Sz. Kovács, L. T. Kóczy, “Application of an approximate fuzzy logic controller in an AGV steering system, path tracking and collision avoidance strategy”, Fuzzy Set Theory and Applications, In Tatra Mountains Mathematical Publications, Mathematical Institute Slovak Academy of Sciences, vol.16, Bratislava, Slovakia, 1999, pp. 456-467.
K. W. Wong, T. D. Gedeon, and D. Tikk: “An improved multidimensional α-cut based fuzzy interpolation technique”, In Proc. Int. Conf Artificial Intelligence in Science and Technology (AISAT’2000), Hobart, Australia, 2000, pp. 29–32.
P. Baranyi, L. T. Kóczy, and Gedeon, T. D.: A Generalized Concept for Fuzzy Rule Interpolation. IEEE Trans. on Fuzzy Systems, vol. 12, No. 6, 2004, pp 820-837.
L. T. Kóczy, and K. Hirota, “Size Reduction by Interpolation in Fuzzy Rule Bases,” IEEE Transactions of System, Man and Cybernetics, Vol. 27, pp. 14–25, 1997.
Zs. Cs. Johanyák, Sz. Kovács, “A brief survey and comparison on various interpolation based fuzzy reasoning methods”, Acta Politechnica Hungarica, Journal of Applied Sciences at Budapest Tech Hungary, Vol 3, No 1, ISSN 1785-8860, pp. 91-105, 2006.
D. Tikk, I. Joó, L. T. Kóczy, P. Várlaki, B. Moser, and T. D. Gedeon. Stability of interpolative fuzzy KH-controllers. Fuzzy Sets and Systems, 125(1) pp. 105–119, January 2002. [
K. W. Wong, D. Tikk, T. D. Gedeon and L. T. Kóczy, “Fuzzy rule interpolation for multidimensional input spaces with applications: A case study”. IEEE Trans of Fuzzy Systems, 13(6), pp. 809–819, December 2005.
Kovács, Sz.: New Aspects of Interpolative Reasoning, Proceedings of the 6th. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, pp. 477-482, 1996.
Kóczy, L. T., Kovács, Sz.: On the preservation of the convexity and piecewise linearity in linear fuzzy rule interpolation, Tokyo Inst. Technol., Yokohama, Japan, Tech. Rep. TR 93-94/402, LIFE Chair Fuzzy Theory, 1993.
Zs. Cs Johanyák, Sz. Kovács, “Fuzzy set approximation based on linguistic term shifting”, MicroCad 2006, submitted for publication.
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