Fuzzy rule interpolation for multidimensional input spaces with applications: A case study

IEEE Transactions on Fuzzy Systems

Volumn 13, Issue 6, 2005, Pages 809-819

  Wong, Kok Wai ^a   Tikk, Domonkos ^b   Gedeon, Tamás D ^c   Kóczy, László T ^b,d  

^a MURDOCH UNIVERSITY   (Australia)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^c AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^d SZÉCHENYI ISTVÁN UNIVERSITY   (Hungary)

Author keywords

Fuzzy rule interpolation; Multidimensional input spaces; Sparse fuzzy rules

Indexed keywords

COMPUTATIONAL COMPLEXITY; FUZZY SETS; INTERPOLATION; PETROLEUM ENGINEERING;

FUZZY RULE INTERPOLATION; MULTIDIMENSIONAL INPUT SPACES; SPARSE FUZZY RULES;

KNOWLEDGE BASED SYSTEMS;

EID: 30344465742     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2005.859316     Document Type: Article

References (47)

1. L. A. Zadeh, "Fuzzy sets," Inform. Control, vol. 8, pp. 338-353, 1965.
2. E. H. Mamdami and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," Int. J. Man Mach. Stud., vol. 7, pp. 1-13, 1975.
3. M. Sugeno and T. Takagi, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, Cybern., vol. SMC-15, no. 1, pp. 116-132, Feb. 1985.
4. 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.
5. L. T. Kóczy and K. Hirota, "Interpolation and size reduction in fuzzy rule bases," Tokyo Inst. Technol., Tech. Rep. 93-94/401, LIFE Chair of Fuzzy Theory, 1993.
6. P. Baranyi and L. T. Kóczy, "Multidimensional fuzzy rule inter- and extrapolation based on geometric solution," in Proc. 7th Int. Power Electronics and Motion Control Conference (PEMC'96), vol. 3, Budapest, Hungary, 1996, pp. 443-447.
7. D. Tikk and P. Baranyi, "Comprehensive analysis of a new fuzzy rule interpolation method," IEEE Trans. Fuzzy Syst., vol. 8, no. 3, pp. 281-296, Jun. 2000.
8. L. T. Kóczy and K. Hirota, "Size reduction by interpolation in fuzzy rule bases," IEEE Trans. Syst., Man, Cybern., vol. 27, no. 1, pp. 14-25, Feb. 1997.
9. D. G. Burkhard and P. P. Bonissone, "Automated fuzzy knowledge base generation and tuning," in Proc. IEEE Int. Conf. Fuzzy Systems, San Diego, CA, 1992, pp. 179-196.
10. L. T. Kóczy and K. Hirota, "Approximate inference in hierarchical structured rule bases," in Proc. 5th IFSA World Congr. (IFSA'93), Seoul, Korea, 1993, pp. 1262-1265.
11. D. Dubois and H. Prade, "Gradual rules in approximate reasoning," Inform. Sci., vol. 61, pp. 103-122, 1992.
12. I. B. Türkşen and Z. Zhong, "An approximate analogical reasoning approach based on similarity measures," IEEE Trans. Syst., Man, Cybern., vol. 18, no. 6, pp. 1049-1056, D 1988.
13. I. B. Türkşen and Z. Zhong, "An approximate analogical reasoning approach of functions," in Proc. 2nd Int. Conf. Fuzzy Logic and Neural Networks (IZUKA'92), Iizuka, Japan, 1992, pp. 629-632.
14. L. Ding, L. Shen, and M. Mukaidono, "Revision principle for approximate reasoning, based on linear revising method," in Proc. 2nd Int. Conf. Fuzzy Logic and Neural Networks (IZUKA'92), Iizuka, Japan, 1992, pp. 305-308.
15. Z. Shen, L. Ding, and M. Mukaidono, "Fuzzy resolution principle," in Proc. IEEE 22nd Int. Symp. Multi-Valued Logic (IEEE-ISMVL), Fukuoka, Japan, 1998, pp. 210-215.
16. Z. Shen, L. Ding, and M. Mukaidono, "Methods of revision principle," in Proc. 5th IFSA World Congress (IFSA'93), Seoul, Korea, 1993, pp. 246-249.
17. L. T. Kóczy, "Computational complexity of various fuzzy inference algorithms," Ann. Univ. Sci., vol. 12, pp. 151-158, 1991.
18. 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 of Fuzzy Theory, 1993.
19. L. T. Kóczy and Sz. Kovács, "Shape of the fuzzy conclusion generated by linear interpolation in trapezoidal fuzzy rule bases," in Proc. 2nd Eur. Congr. Intelligent Techniques and Soft Computing, Aachen, Germany, 1994, pp. 1666-1670.
20. S. Kawase and Q. Chen, "On fuzzy reasoning by Kóczy's linear rule interpolation," Teikyo Heisei Univ., Heisei, Japan, 1996.
21. Y. Shi and M. Mizumoto, "On Kóczy's interpolative reasoning method in sparse rule bases," in Proc. 10th Fuzzy Syst. Symp., Osaka, Japan, 1994, pp. 211-224.
22. Y. Shi and M. Mizumoto, "Some considerations on Kóczy's interpolative reasoning method," in Proc. FUZZ-IEEE/IFES '95, Yokohama, Japan, 1995, pp. 2117-2122.
23. Y. Shi and M. Mizumoto, "A note on reasoning conditions of Koczy's interpolative reasoning method," Fuzzy Sets Syst., vol. 96, no. 3, pp. 373-379, 1998.
24. G. Vass, L. Kalmár, and L. T. Kóczy, "Extension of the fuzzy rule interpolation method," in Proc. Int. Conf on Fuzzy Sets Theory and its Applications, Liptovský, Czechoslovakia, Jan. 1992.
25. P. Baranyi and T. D. Gedeon, "Rule interpolation by spatial geometric representation," in Proc. IPMU'96, Granada, Spain, 1996, pp. 483-488.
26. 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 SMC, 1996, pp. 510-515.
27. P. Baranyi and L. T. Kóczy, "A general and specialised solid cutting method for fuzzy role interpolation," in BUSEFAL, vol. 67, 1996, pp. 13-22.
28. P. Baranyi, L. T. Kóczy, and T. D. Gedeon, "A generalized concept for fuzzy rule interpolation," IEEE Trans. Fuzzy Syst. vol. 12, no. 6, pp. 820-832, Dec. 2004.
29. P. Baranyi, S. Mizik, L. T. Kóczy, T. D. Gedeon, and I. Nagy, "Fuzzy rule base interpolation based on semantic revision," in Proc. IEEE Int. Conf. SMC, San Diego, CA, 1998, pp. 1306-1311.
30. T. D. Gedeon and L. T. Kóczy, "Conservation of fuzziness in rule interpolation," in Proc. Symp. New Trends in Control of Large Scale Systems, vol. 1, Herl'any, Slovakia, 1996, pp. 13-19.
31. 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. 97/2, 1997.
32. Sz. Kovács, "New aspect of interpolative reasoning," in Proc. IPMU'96, Granada, Spain, 1996, pp. 477-482.
33. Sz. Kovács and L. T. Kóczy, "Fuzzy rule interpolation in vague environment," in Proc. 3rd Eur. Congr. Intelligent Techniques and Soft Computing (EUFIT'95), Aachen, Germany, 1995, pp. 95-98.
34. Sz. Kovács and L. T. Kóczy, "The use of the concept of vague environment in approximate fuzzy reasoning," Tatra Mountains Math. Publ., vol. 12, pp. 169-181, 1997.
35. D. Tikk, P. Baranyi, T. D. Gedeon, and L. Muresan, "Generalization of a rule interpolation method resulting always in acceptable conclusion," Tatra Mountains Math. Publ., vol. 21, pp. 73-91, 2001.
36. S. Jenei, "A new approach for interpolation and extrapolation of compact fuzzy quantities," in Proc. 21st Linz Seminar on Fuzz set Theory, Linz, Austria, 2000, pp. 13-18.
37. S. Jenei, "Interpolation and extrapolation of fuzzy quantities revisited - (I) an axiomatic approach," Soft Comput., vol. 5, pp. 179-193, 2001.
38. S. Jenei, E. P. Klement, and R. Konzel, "Interpolation and extrapolation of fuzzy quantities - (II) the multiple-dimensional case," Soft Comput., vol. 6, no. 3-4, pp. 258-270, 2002.
39. L. T. Kóczy and K. Hirota, "Ordering, distance and closeness of fuzzy sets," Fuzzy Sets Syst., vol. 59, no. 3, pp. 281-293, Nov. 1993.
40. D. Tikk, P. Baranyi, Y. Yam, and L. T. Kóczy, "Stability of a new interpolation method," in Proc. IEEE Int. Conf. System, Man, and Cybernetics (IEEE SMC'99), vol. III, Tokyo, Japan, 1999, pp. 7-9.
41. Y. Yam and L. T. Kóczy, "Representing membership functions as points in high dimensional spaces for fuzzy interpolation and extrapolation," Dept. Mech. Automat. Eng., Chinese Univ., Hong Kong, Tech. Rep. CUHK-MAE-97-03, 1997.
42. M. Rider, The Geological Interpretation of Well Logs, 2nd ed. Caithness, Scotland: Whittles, 1996.
43. E. R. Crain, The Log Analysis Handbook Volume 1: Quantitative Log Analysis Methods. Tulsa, OK: Penn Well, 1986.
44. G. B. Asquith and C. R. Gibson, "Basic well log analysis for geologists," AAPG Methods Expl. Ser., vol. 3, pp. 91-95, 1982.
45. C. C. Fung, K. W. Wong, and P. M. Wong, "A self-generating fuzzy rules inference systems for petrophysical properties prediction," in Proc. IEEE Int. Conf. Intelligent Processing Systems, Beijing, China, 1997, pp. 205-208.
46. D. Bradley, The Hydrocyclone. New York: Pergamon, 1965.
47. A. Gupta and H. Eren, "Mathematical modeling and on-line control of hydrocyclones," Proc. Aus. IMM, vol. 295, no. 2, pp. 31-41, 1990.