[1] Xing Zongyi, Hu Weili, Jia Limin,. Study on the tradeoff between interpretabilityand precision in fuzzy modeling [J]. Journal of Southeast University (English Edition), 2004, 20 (4): 472-476. [doi:10.3969/j.issn.1003-7985.2004.04.016]

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Study on the tradeoff between interpretabilityand precision in fuzzy modeling()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

20

Issue:

2004 4

Page:

472-476

Research Field:

Automation

Publishing date:

2004-12-30

Info

Title:

Study on the tradeoff between interpretabilityand precision in fuzzy modeling

Author(s):

Xing Zongyi¹;  Hu Weili¹;  Jia Limin²

¹Department of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
²School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

Keywords:

fuzzy modeling;  precision;  interpretability;  fuzzy clustering

PACS:

TP273

DOI:

10.3969/j.issn.1003-7985.2004.04.016

Abstract:

An approach to identifying fuzzy models considering both interpretability and precision is proposed. Firstly, interpretability issues about fuzzy models are analyzed. Then, a heuristic strategy is used to select input variables by increasing the number of input variables, and the Gustafson-Kessel fuzzy clustering algorithm, combined with the least square method, is used to identify the fuzzy model. Subsequently, an interpretability measure is described by the product of the number of input variables and the number of rules, while precision is weighted by root mean square error, and the selection objective function concerning interpretability and precision is defined. Given the maximum and minimum number of input variables and rules, a set of fuzzy models is constructed. Finally, the optimal fuzzy model is selected by the objective function, and is optimized by a genetic algorithm to achieve a good tradeoff between interpretability and precision. The performance of the proposed method is illustrated by the well-known Box-Jenkins gas furnace benchmark; the results demonstrate its validity.

References:

[1] Gomez-Skarmeta A F, Delgado M, Vila M A. About the use of fuzzy clustering techniques for fuzzy model identification [J]. Fuzzy Sets and Systems, 1999, 106(2): 179-188.
[2] Tsoukalas L H, Uhrig R E. Fuzzy and neural approaches in engineering [M]. New York: Wiley, 1997.
[3] Cordon O, Herrera F, Hoffmann F, et al. Genetic fuzzy systems: evolutionary tuning and learning of fuzzy rule bases [M]. Singapore: World Scientific, 2001.
[4] Babuska R, Bersini H, Linkens D A, et al. Future prospects for fuzzy systems and technology [EB/OL].http: //www.erudit.de/erudit/newsletters/news61/pag e5.htm. 2000-11-21/2004-09-17.
[5] Takagi T, Sugeno M. Fuzzy identification of systems and its application to modeling and control [J]. IEEE Trans on Systems, Man and Cybernetics, 1985, 15(1): 116-132.
[6] Xing Zongyi, Hu Weili, Jia Limin. A fuzzy clustering based approach for generating interpretable fuzzy models [A]. In: Proc of the Third International Conference on Machine Learning and Cybernetics [C]. Shanghai, 2004. 2093-2097.
[7] Xing Zongyi, Jia Limin. Research on input variable selection for numeric data based fuzzy modeling [A]. In: Proc of Int Conf on Machine Learning and Cybernetics [C]. Xi’an, 2003. 2737-2740.
[8] Bezdek J C. Pattern recognition with fuzzy objective algorithm [M]. New York: Plenum Press, 1981.
[9] Gustafson D E, Kessel W C. Fuzzy clustering with a fuzzy covariance matrix [A]. In: Proc of IEEE Conf on Decision and Control [C]. San Diego, 1979. 761-766.
[10] Setnes M, Roubos H. Transparent fuzzy modeling using fuzzy clustering and GA’s. [A]. In: Proc of IEEE Int Conf on Fuzzy Systems [C]. Seou, 1999. 198-202.

Memo

Memo:

Biographies: Xing Zongyi(1974—), male, doctor, xingzongyi@com.cn; Hu Weili(1941—), male, professor, hwl1002@mail.njust.edu.cn.

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