Fuzzy Rule Interpolation Methods Based on Sparse Rule Bases

Pan Su; Xueying Ren

doi:10.62051/ijcsit.v5n3.08

Authors

Pan Su
Xueying Ren

DOI:

https://doi.org/10.62051/ijcsit.v5n3.08

Keywords:

Fuzzy rule interpolation, Fuzzy inference, Sparse rule base, Membership function

Abstract

Fuzzy rule interpolation algorithms have broad applications in computational fuzzy inference systems. This paper systematically introduces interpolation methods based on α-cuts. It focuses on two classical α-cut-based interpolation methods: the KH fuzzy rule interpolation method and the Lagrange fuzzy rule interpolation method. Through theoretical analysis and comparative studies, the fundamental principles, performance characteristics, and limitations of these two interpolation algorithms are explored in depth. Based on this, a fuzzy inference system for the "tip calculation problem" was constructed using the MATLAB Fuzzy Toolbox. Empirical studies were conducted to verify the necessity and feasibility of applying fuzzy rule interpolation techniques in sparse rule bases. The results indicate that fuzzy rule interpolation methods effectively enhance inference performance in sparse rule bases, providing essential theoretical foundations and practical support for the application of fuzzy inference systems.

Downloads

Download data is not yet available.

References

[1] Terano, T, Asai, K, and Sugeno, M. Applied fuzzy systems. Boston, USA: Academic Press, 2014.

[2] Zimmermann, H. Fuzzy set theory and its applications. Berlin, Germany: Springer Business Media, 2011.

[3] Yang, J, Shang, C, Li, Y, Li, F, and Shen, Q. ANFIS Construction with Sparse Data via Group Rule Interpolation. IEEE Transactions on Cybernetics, DOI: 10.1109/TCYB.2019.2952267.

[4] Baranyi P, Koczy L T, Gedeon T D. A generalized concept for fuzzy rule interpolation [J]. IEEE Transactions on Fuzzy Systems, 2004, 12(6):820-837.

[5] Baranyi, P Z, Tikk, D, Yam, Y, Kóczy, LT, and Nádai, L.A new method for avoiding abnormal conclusion for α-cut based rule interpolation//Proceedings of the 1999 IEEE international fuzzy systems conference. Seoul, Korea, 1999: 1383–1388.

[6] Tikk, D and Baranyi, P. Comprehensive analysis of a new fuzzy rule interpolation method. IEEE Transactions on Fuzzy Systems, 2000, 8(3):281–296.

[7] R. Senge and E. Hüllermeier, "Top-Down Induction of Fuzzy Pattern Trees," in IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 241-252, April 2011, doi: 10.1109/TFUZZ.2010.2093532.

[8] Yam Y, Péter Baranyi, Tikk D, et al. Eliminating the Abnormality Problem of ɑ-cut Based Fuzzy Interpolation[C]// Eighth International Fuzzy Systems

[9] Dubois D, Prade H, Grabisch M. Gradual rules and the approximation of control laws [M]. John Wiley & Sons, Inc. 1995.

[10] Wang Tianjiang, Lu Zhengding, Li Fan. Fuzzy Interpolation Reasoning Based on Geometric Similarity [J]. Computer Science, 2004, (9): 169-171, 175.

[11] Chang, Y-C, Chen, S-M and Liau, C-J. Fuzzy interpolative reasoning for sparse fuzzy-rule-based systems based on the areas of fuzzy sets. IEEE Transactions on Fuzzy Systems, 2008, 16(5):1285–1301.

[12] Chen S M, Chen Z J. Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets [J]. Information Sciences, 2016, 329:503-523.

[13] Chen, S-M, Chang, Y-C, Chen, Z-J, and Chen, CL. Multiple fuzzy rules interpolation with weighted antecedent variables in sparse fuzzy rule-based systems. International Journal of Pattern Recognition and Artificial Intelligence, 2013, 27(05):1359002.

[14] Chen, S-M and Adam, S I. Adaptive fuzzy interpolation based on general representative values of polygonal fuzzy sets and the shift and modification techniques. Information Sciences, 2017, 414:147–157.

[15] Chen, S-M and Adam, S-I. Adaptive fuzzy interpolation based on ranking values of interval type-2 polygonal fuzzy sets. Information Sciences, 2018, 435:320–333.

[16] L. Yang and Q. Shen, "Adaptive fuzzy interpolation with prioritized component candidates," 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), Taipei, Taiwan, 2011, pp. 428-435.

[17] Cheng, S-H, Chen, S-M, and Chen, C-L. Adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets. Information Sciences, 2016, 342:176–190.

[18] Turksen I B, Zhong Z. An approximate analogical reasoning approach based on similarity measures [J]. IEEE Transactions on Systems Man & Cybernetics, 1988, 18(6):1049-1056.

[19] LászlóT. Kóczy, Hirota K. Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases [J]. Information Sciences, 2015, 71(1-2):169-201.

[20] Wang B, Zhang Q, Liu W, et al. Multidimensional Fuzzy Interpolative Reasoning Method Based on lambda-Width Similarity [C]// Eighth Acis International Conference on Software Engineering. IEEE Computer Society, 2007.

[21] Luo Chengzhong, Yu Fusheng, Zeng Wenyi. "Introduction to Fuzzy Sets" [M]. Beijing: Beijing Normal University Press, 2019.

[22] Shi Y, Mizumoto M. Some Considerations on Koczy's Linear Interpolative Reasoning Method [J]. Journal of Japan Society for Fuzzy Theory & Systems, 1995, 8(1):147-157.

[23] L Kóczy, Hirota K. Approximate reasoning by linear rule interpolation and general approximation [J]. International Journal of Approximate Reasoning, 1993, 9(3):197-225.

[24] Jenei S, Klement E P, Konzel R. Interpolation and extrapolation of fuzzy quantities – the multiple-dimensional case [J]. Soft Computing, 2002, 6(3-4):258-270.

[25] Shi Y, Mizumoto M. A Fuzzy Interpolative-Type Reasoning Based on Lagrange's Interpolation [C]. 16th Fuzzy System Symposium, Skita, 2000:15-18.