Interpolation with function space representation of membership functions

IEEE Transactions on Fuzzy Systems

Volumn 14, Issue 3, 2006, Pages 398-411

  Yam, Yeung ^a   Wong, Man Lung ^a   Baranyi, Péter ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUZZY SETS; INTERPOLATION; MEMBERSHIP FUNCTIONS;

EXTENSIBILITY FUNCTIONS; FUNCTION SPACE REPRESENTATION; SPANNING SET;

FUZZY CONTROL;

EID: 33745145789     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2006.876332     Document Type: Article

References (16)

1. L. T. Kóczy and K. Hirota, "Approximate reasoning by linear rule interpolation and general approximation," Int. J. Approx. Reason., vol. 9, pp. 197-225, 1993.
2. L. T. Kóczy and K. Hirota, "Interpolatiive reasoning with insufficient evidence in sparse fuzzy rule bases," Inform. Sci., vol. 71, pp. 169-201, 1993.
3. P. Baranyi, T. D. Gedeon, and L. T. Kóczy, "A general interpolation technique in fuzzy rule bases with arbitrary membership functions," in Proc. IEEE Int. Conf. Systems, Man, and Cybernetics, ch. China, Beijing, 1996, pp. 510-515.
4. T. D. Gedeon and L. T. Kóczy, "Conservation of fuzziness in rule interpolation," in Proc. Intelligent Technologies Int. Symp. on New Trends in the Control of Large Scale Systems, vol. 1, Herlany, Slovakia, 1996, pp. 13-19.
5. L. T. Kóczy, K. Hirota, and T. D. Gedeon, "Fuzzy rule interpolation by the conservation of relative fuzziness," Hirota Lab., Dept. Intell. Comput. Syst. Sci., Tokyo Inst. Technol., Yokohama, Japan, Tech. Rep. TR 97-2, 1997.
6. Y. Yam and L. T. Kóczy, "Cartesian representation for fuzzy interpolation," in Proc. 37th Conf. Decision and Control, Tampa, FL, Dec. 16-18, 1998, pp. 2936-2937.
7. Y. Yam and L. T. Kóczy, "Representing membership functions as points in high dimensional spaces for fuzzy interpolation and extrapolation," IEEE Trans. Fuzzy Syst., vol. 8, no. 6, pp. 761-772, Dec. 2000.
8. Y. Yam, M. L. Wong, and P. Baranyi, "Interpolation as mapping between cartesian spaces," in Proc. Int. Conf. Intelligent Technologies (InTech'2000), Bangkok, Thailand, 2000, pp. 450-459.
9. Y. Yam, P. Baranyi, D. Tikk, and L. T. Kóczy, "Eliminating the abnormality problem of α-cut based fuzzy interpolation," in Proc. 8th Int. Fuzzy Systems Association World Congr (IFSA'99), Taipei, Taiwan, Aug. 17-20, 1999, pp. 762-766.
10. Y. Yam, V. Kreinovich, and H. T. Hung, "Extracting fuzzy sparse rule base by cartesian representation and clustering," in Proc. 2000 IEEE Int. Conf. Systems, Man, and Cybernetics, Nashville, TN, pp. 3778-3783.
11. M. L. Wong, Y. Yam, and P. Baranyi, "Representing membership functions as elements in function space," in Proc. Amer Control Conf., vol. 3, 2001, pp. 1922-1927.
12. J. N. Reddy, Applied Functional Analysis and Variational Methods in Engineering. New York: McGraw-Hill, 1986.
13. W. J. Wang and C. H. Chiu, "Entropy change in extension principle," Fuzzy Sets Syst., vol. 103, pp. 153-162, 1999.
14. P. Baranyi, D. Tikk, Y. Yam, and L. T. Kóczy, "Investigation of a new α-cut based fuzzy interpolation method," Dept. Mech. Automat. Eng., Chinese Univ. Hong Kong, Tech. Rep. CUHK-MAE-99-06, 1999.
15. M. L. Wong, "Further investigations of geometric representation approach to fuzzy inference and interpolation," M.Phil. thesis, Dept. Mech. Automat. Eng., Chinese Univ. Hong Kong, 2002.
16. A. D. Belegundu and T. R. Chandrupada, Optimization Concepts and Applications in Engineering. Upper Saddle River, NJ: Prentice-Hall, Inc., 1999.