Performance Optimization of the Fuzzy Rule Interpolation Method “FIVE”

Dávid Vincze; Szilveszter Kovács

doi:10.20965/jaciii.2011.p0313

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JACIII Vol.15 No.3 pp. 313-320

doi: 10.20965/jaciii.2011.p0313

(2011)

Paper:

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Performance Optimization of the Fuzzy Rule Interpolation Method “FIVE”

Dávid Vincze and Szilveszter Kovács

Department of Information Technology, University of Miskolc, Miskolc, Hungary

Received:

January 5, 2011

Accepted:

March 28, 2011

Published:

May 20, 2011

Keywords:

fuzzy rule interpolation (FRI), FRI FIVE implementation, FRI performance optimization, FRIQlearning

Abstract

Fuzzy Rule Interpolation (FRI) methods are efficient structures for knowledge-representation with relatively few rules. In spite of their good knowledge representation efficiency, their high computational demand makes the FRI methods hardly suitable for embedded real-time applications, for which short reasoning time has a high importance. On the other hand, the fact that currently available devices have increased computational power gives the FRI methods an opportunity to appear in real-time embedded applications. Therefore, the need for a low-computation and lowresource-demand FRI method is emerging. The goal of this paper is to introduce some implementation details of such an FRI method, together with its brief time and space complexity analysis. The paper also gives some hints for further performance optimization possibilities.

Cite this article as:

D. Vincze and S. Kovács, “Performance Optimization of the Fuzzy Rule Interpolation Method “FIVE”,” J. Adv. Comput. Intell. Intell. Inform., Vol.15 No.3, pp. 313-320, 2011.

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References

[1] L. T. Kóczy and Sz. Kovács, “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.
[2] D. Tikk and P. Baranyi, “Comprehensive analysis of a new fuzzy rule interpolation method,” In IEEE Trans. Fuzzy Syst., Vol.8, No.3, pp. 281-296, June, 2000.
[3] P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A Generalized Concept for Fuzzy Rule Interpolation,” IEEE Trans. on Fuzzy Systems, Vol.12, No.6, pp. 820-837, 2004.
[4] S. Jenei, “Interpolating and extrapolating fuzzy quantities revisited – an axiomatic approach,” Soft Comput., Vol.5, pp. 179-193, 2001.
[5] S. Jenei, E. P. Klement, and R. Konzel, “Interpolation and extrapolation of fuzzy quantities – The multiple-dimensional case,” Soft Comput., Vol.6, pp. 258-270, 2002.
[6] K. W. Wong, D. Tikk, T. D. Gedeon, and L. T. Kóczy, “Fuzzy Rule Interpolation for Multidimensional Input Spaces With Applications,” IEEE Trans. on Fuzzy Systems, Vol.13, No.6, pp. 809-819, December, 2005.
[7] Zs. Cs. Johanyák, “Sparse fuzzy model identification Matlab toolbox – RuleMaker toolbox,” Proc. of IEEE 6th Int. Conf. on Computational Cybernetics ICCC 2008, Stara Lesná, Slovakia, pp. 69-74, 2008.
[8] Zs. Cs. Johanyák and Sz. Kovács, “Fuzzy Rule Interpolation Based on Polar Cuts, Computational Intelligence,” Theory and Applications, Springer Berlin Heidelberg, pp. 499-511, 2006.
[9] Zs. Cs. Johanyák and Sz. Kovács, “Fuzzy Rule Interpolation by the Least Squares Method,” 7th Int. Symposium of Hungarian Researchers on Computational Intelligence (HUCI 2006), Budapest, pp. 495-506, November 24-25, 2006.
[10] Zs. Cs. Johanyák and Sz. Kovács, “Vague Environment-based Twostep Fuzzy Rule Interpolation Method,” 5th Slovakian-Hungarian Joint Symposium on Applied Machine Intelligence and Informatics (SAMI 2007), Poprad, Slovakia, pp. 189-200, January 25-26, 2007.
[11] Sz. Kovács, “New Aspects of Interpolative Reasoning,” Proc. of the 6th. Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, pp. 477-482, 1996.
[12] Sz. Kovács, and L.T. Kóczy, “Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rule base as a Practical Alternative of the Classical CRI,” Proc. of the 7th Int. Fuzzy Systems Association World Congress, Prague, Czech Republic, pp. 144-149, 1997.
[13] Sz. Kovács and L.T. Kóczy, “The use of the concept of vague environment in approximate fuzzy reasoning,” Fuzzy Set Theory and Applications, Tatra Mountains Mathematical Publications, Mathematical Institute Slovak Academy of Sciences, Bratislava, Slovak Republic, Vol.12, pp. 169-181, 1997.
[14] Sz. Kovács, “Extending the Fuzzy Rule Interpolation “FIVE” by Fuzzy Observation,” Advances in Soft Computing, Computational Intelligence, Theory and Applications, Bernd Reusch (Ed.), Springer Germany, pp. 485-497, 2006.
[15] F. Klawonn, “Fuzzy Sets and Vague Environments,” Fuzzy Sets and Systems, Vol.66, pp. 207-221, 1994.
[16] D. Shepard, “A two dimensional interpolation function for irregularly spaced data,” Proc. 23rd ACM Int. Conf., pp. 517-524, 1968.
[17] Zs. Cs. Johanyák, D. Tikk, Sz. Kovács, and K. W. Wong, “Fuzzy Rule Interpolation Matlab Toolbox – FRI Toolbox,” Proc. of the IEEE World Congress on Computational Intelligence (WCCI’06), 15th Int. Conf. on Fuzzy Systems (FUZZ-IEEE’06), July 16-21, Vancouver, BC, Canada, Omnipress., pp. 1427-1433, 2006.
[18] The FRI Toolbox.
http://fri.gamf.hu/
[19] Sz. Kovács and L.T. Kóczy, “Application of the Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rulebase in the Fuzzy Logic Controlled Path Tracking Strategy of Differential Steered AGVs”, Computational Intelligence – Theory and Applications, Lecture Notes in Computer Science, Vol.1226, Springer, pp. 456-467, Germany, 1997.
[20] D. Vincze and Sz. Kovács, “Fuzzy Rule Interpolation-based Qlearning,” SACI 2009, 5th Int. Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, pp. 55-59, May 28-29, 2009.
[21] Sz. Kovács, “Interpolative Fuzzy Reasoning in Behaviour-based Control,” Advances in Soft Computing, Vol.2, Computational Intelligence, Theory and Applications, Bernd Reusch (Ed.), Springer, Germany, pp. 159-170, 2005.
[22] D. Vincze and Sz. Kovács, “Behaviour Based Control with Fuzzy Automaton in Vehicle Navigation,” Production Systems and Information Engineering, Vol.5, University of Miskolc, Hungary, pp. 151-166, 2009.
[23] D. Vincze and Sz. Kovács, “Incremental Rule Base Creation with Fuzzy Rule Interpolation-Based Q-Learning,” I. J. Rudas et al. (Eds.), Computational Intelligence in Engneering, Studies in Computational Intelligence, Vol.313, Springer-Verlag, Berlin Heilderberg, pp. 191-203, 2010.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] L. T. Kóczy and Sz. Kovács, “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.

[2] [2] D. Tikk and P. Baranyi, “Comprehensive analysis of a new fuzzy rule interpolation method,” In IEEE Trans. Fuzzy Syst., Vol.8, No.3, pp. 281-296, June, 2000.

[3] [3] P. Baranyi, L. T. Kóczy, and T. D. Gedeon, “A Generalized Concept for Fuzzy Rule Interpolation,” IEEE Trans. on Fuzzy Systems, Vol.12, No.6, pp. 820-837, 2004.

[4] [4] S. Jenei, “Interpolating and extrapolating fuzzy quantities revisited – an axiomatic approach,” Soft Comput., Vol.5, pp. 179-193, 2001.

[5] [5] S. Jenei, E. P. Klement, and R. Konzel, “Interpolation and extrapolation of fuzzy quantities – The multiple-dimensional case,” Soft Comput., Vol.6, pp. 258-270, 2002.

[6] [6] K. W. Wong, D. Tikk, T. D. Gedeon, and L. T. Kóczy, “Fuzzy Rule Interpolation for Multidimensional Input Spaces With Applications,” IEEE Trans. on Fuzzy Systems, Vol.13, No.6, pp. 809-819, December, 2005.

[7] [7] Zs. Cs. Johanyák, “Sparse fuzzy model identification Matlab toolbox – RuleMaker toolbox,” Proc. of IEEE 6th Int. Conf. on Computational Cybernetics ICCC 2008, Stara Lesná, Slovakia, pp. 69-74, 2008.

[8] [8] Zs. Cs. Johanyák and Sz. Kovács, “Fuzzy Rule Interpolation Based on Polar Cuts, Computational Intelligence,” Theory and Applications, Springer Berlin Heidelberg, pp. 499-511, 2006.

[9] [9] Zs. Cs. Johanyák and Sz. Kovács, “Fuzzy Rule Interpolation by the Least Squares Method,” 7th Int. Symposium of Hungarian Researchers on Computational Intelligence (HUCI 2006), Budapest, pp. 495-506, November 24-25, 2006.

[10] [10] Zs. Cs. Johanyák and Sz. Kovács, “Vague Environment-based Twostep Fuzzy Rule Interpolation Method,” 5th Slovakian-Hungarian Joint Symposium on Applied Machine Intelligence and Informatics (SAMI 2007), Poprad, Slovakia, pp. 189-200, January 25-26, 2007.

[11] [11] Sz. Kovács, “New Aspects of Interpolative Reasoning,” Proc. of the 6th. Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, pp. 477-482, 1996.

[12] [12] Sz. Kovács, and L.T. Kóczy, “Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rule base as a Practical Alternative of the Classical CRI,” Proc. of the 7th Int. Fuzzy Systems Association World Congress, Prague, Czech Republic, pp. 144-149, 1997.

[13] [13] Sz. Kovács and L.T. Kóczy, “The use of the concept of vague environment in approximate fuzzy reasoning,” Fuzzy Set Theory and Applications, Tatra Mountains Mathematical Publications, Mathematical Institute Slovak Academy of Sciences, Bratislava, Slovak Republic, Vol.12, pp. 169-181, 1997.

[14] [14] Sz. Kovács, “Extending the Fuzzy Rule Interpolation “FIVE” by Fuzzy Observation,” Advances in Soft Computing, Computational Intelligence, Theory and Applications, Bernd Reusch (Ed.), Springer Germany, pp. 485-497, 2006.

[15] [15] F. Klawonn, “Fuzzy Sets and Vague Environments,” Fuzzy Sets and Systems, Vol.66, pp. 207-221, 1994.

[16] [16] D. Shepard, “A two dimensional interpolation function for irregularly spaced data,” Proc. 23rd ACM Int. Conf., pp. 517-524, 1968.

[17] [17] Zs. Cs. Johanyák, D. Tikk, Sz. Kovács, and K. W. Wong, “Fuzzy Rule Interpolation Matlab Toolbox – FRI Toolbox,” Proc. of the IEEE World Congress on Computational Intelligence (WCCI’06), 15th Int. Conf. on Fuzzy Systems (FUZZ-IEEE’06), July 16-21, Vancouver, BC, Canada, Omnipress., pp. 1427-1433, 2006.

[18] [18] The FRI Toolbox.
http://fri.gamf.hu/

[19] [19] Sz. Kovács and L.T. Kóczy, “Application of the Approximate Fuzzy Reasoning Based on Interpolation in the Vague Environment of the Fuzzy Rulebase in the Fuzzy Logic Controlled Path Tracking Strategy of Differential Steered AGVs”, Computational Intelligence – Theory and Applications, Lecture Notes in Computer Science, Vol.1226, Springer, pp. 456-467, Germany, 1997.

[20] [20] D. Vincze and Sz. Kovács, “Fuzzy Rule Interpolation-based Qlearning,” SACI 2009, 5th Int. Symposium on Applied Computational Intelligence and Informatics, Timisoara, Romania, pp. 55-59, May 28-29, 2009.

[21] [21] Sz. Kovács, “Interpolative Fuzzy Reasoning in Behaviour-based Control,” Advances in Soft Computing, Vol.2, Computational Intelligence, Theory and Applications, Bernd Reusch (Ed.), Springer, Germany, pp. 159-170, 2005.

[22] [22] D. Vincze and Sz. Kovács, “Behaviour Based Control with Fuzzy Automaton in Vehicle Navigation,” Production Systems and Information Engineering, Vol.5, University of Miskolc, Hungary, pp. 151-166, 2009.

[23] [23] D. Vincze and Sz. Kovács, “Incremental Rule Base Creation with Fuzzy Rule Interpolation-Based Q-Learning,” I. J. Rudas et al. (Eds.), Computational Intelligence in Engneering, Studies in Computational Intelligence, Vol.313, Springer-Verlag, Berlin Heilderberg, pp. 191-203, 2010.