Comparison of fuzzy functions with fuzzy rule base approaches

International Journal of Fuzzy Systems

Volumn 8, Issue 3, 2006, Pages 137-149

  Burhan Turksen I ^a,b   Celikyilmaz, Asli ^b  

^a TOBB UNIVERSITY OF ECONOMICS AND TECHNOLOGY   (Turkey)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

Fuzzy functions; Least squares; Membership values; Reasoning; Rule bases; Support vector machines for regression

Indexed keywords

FUZZY SETS; LEARNING SYSTEMS; LOGIC PROGRAMMING;

FUZZY FUNCTIONS; LEAST SQUARES; MEMBERSHIP VALUES; REASONING; RULE BASES; SUPPORT VECTOR MACHINES FOR REGRESSION;

FUNCTION EVALUATION;

EID: 33750914661     PISSN: 15622479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (48)

1. R.Babuska, and H.B. Verbruggen, "Constructing Fuzzy Models by Product Space Clustering," in H. Hellendoorn and D. Driankov(eds.), Fuzzy Model Identification: Selected Approaches, pp.53-90, Springer, Berlin, Germany, 1997.
2. J.C. Bezdek, "Fuzzy Mathematics in Pattern Classification," Ph.D. Thesis, applied Mathematics Centre, Cornell University, Ithaca, 1973.
3. Breiman, Leo, "Random Forests", Machine Learning, vol. 45, no. 1, pp. 5-32, October 2001.
4. A. Celikyilmaz, "Fuzzy Functions with Support Vector Machines.", M.A.Sc. Thesis, University of Toronto, 2005.
5. A. Celikyilmaz, I.B. Turksen, "Fuzzy Functions with Support Vector Machines.", Information Sciences, accepted.
6. A.Celmins, "Least Squares Model Fitting to Fuzzy Vector Data," Fuzzy Sets and Systems, vol. 22, pp. 245-269, 1987.
7. A. Celmins, "Multidimensional Least Squares Model Fitting of Fuzzy Models," Math. Modeling, vol. 9, pp. 669-690, 1987.
8. Y.-H.O. Chang, B.M. Ayyub, "Reliability Analysis in Fuzzy Regression," Proc., Annual Conf. of NAFIPS'93, Allentown, PA., USA, pp.93-97, 1993.
9. C. Chang., C. Lin, (2001), "LIBSVM: a library for support vector machines", Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm
10. P.-T. Chang, E.S. Lee, "Fuzzy Linear Regression with Spreads Unrestricted in Sign," Compt. Math. Appl., vol. 28, pp. 61-71, 1994.
11. M.R.Delgado, A.F. Gomez-Skennata and F.Martin, "Rapid Prototyping of Fuzzy Models," in H. Hellendoorn and D. Driankov(eds.), Fuzzy Model Identification: Selected Approaches, pp. 53-90, Springer, Berlin, Germany, 1997.
12. M. Demirci, "Fuzzy Functions and their Fundamental Properties," Fuzzy Sets and Systems, vol. 106, pp.239-246, 1999.
13. M. Demirci, "Foundations of Fuzzy Functions and Vague Algebra Based on Many-Valued Equivalence Relations, Part I: Fuzzy Functions and their Applications," I.J. General Systems, vol. 32, pp. 123-155, 2003.
14. M. Demirci, and J. Recasens, "Fuzzy Groups, Fuzzy Functions and Fuzzy Equivalence Relations," Fuzzy Sets and Systems, vol. 144, pp. 441-458, 2004.
15. P. Diamond, "Fuzzy Least Squares," Inform. Sci. vol. 46, pp. 141-157, 1998.
16. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications., Academic Press, New York, 1980
17. D. Dubois, H. Prade, "Towards Fuzzy Differential Calculaus: Part1: Integration of Fuzzy Mapping", Fuzzy Sets and Systems, vol. 8, pp. 1-17, 1982.
18. Emami, M.R., Turksen, I.B., Goldernberg, A.A., "Development of a Systematic Methodology of fuzzy logic modeling", IEEE Transactions on Fuzzy Systems, vol. 6, Issue 3, pp. 346-361, 1998.
19. R.J. Hathaway and J.C. Bezdek. "Switching regression models and fuzzy clustering," In IEEE Transactions on fuzzy systems, vol.1, no.3, pp.195-203, 1993.
20. U. Höhle, "Quotients with Respect to Similarity Relations", Fuzzy Sets and Systems, vol. 27, pp. 31-44, 1998.
21. E.H. Mamdani, S. Assilian, "An Experiment in Linguistic Syntesis with a Fuzzy Logic Controller," in E.H. Mamdani, B.R. Gains, "Fuzzy Reasonning and Its Applications", Academic Press, 1981.
22. M. Mizimoto, "Method of Fuzzy Inference Suitable for Fuzzy Control," J.of Soc.Instrument Control Engineering, vol.58, pp. 959-963, 1989.
23. Nakanishi H., Türkşen I.B., Sugeno M., "A Review and Comparison of Six Reasoning Methods", Fuzzy Sets and Systems, vol. 57, pp. 257-295, 1993.
24. Pal, N.R., Bezdek, J.C., "On Cluster Validity for the Fuzzy C-Means Model", IEEE Transactions on Fuzzy Systems, vol. 3, no.3, 1995.
25. D. Savic and W. Pedryzc, "Evolution of Fuzzy Linear Regression Models," Fuzzy sets and systems, vol. 39, pp. 51-63, 1991.
26. A.J. Smola, B. Scholkopf, "A Tutorial on Support Vector Regression", NeuroColT2 Technical Report Series, NC2-Tr-1998-030, 1998.
27. Sugeno M., Yasukawa T., "A Fuzzy Logic Based Approach to Qualitative Modelling", IEEE Transactions on Fuzzy Systems, vol. 1, pp. 7-31, 1993.
28. T.Takagi and M.Sugeno, "Fuzzy Identification of Systems and Its Applications to Modeling and Control," IEEE Transactions on Systems, Man and Cybernetics, vol.SMC-15, no.1, pp.116-132, 1985.
29. H. Tanaka, "Fuzzy Data Analysis by Possibilistic Linear Models," Fuzzy Sets and Systems, vol. 24, pp. 363-375, 1991.
30. H. Tanaka, H. Ishibuchi, "Identification of Possibilistic Linear Systems by Quadratic Membership Functions of Fuzzy Parameters," Fuzzy Sets and Systems, vol. 41, pp. 145-160, 1991.
31. H. Tanaka, H. Ishibuchi, S. Yoshikawa, "Exponential Possibility Regression Analysis", Fuzzy Sets and Systems, vol. 69, pp. 305-318, 1995.
32. H. Tanaka, S. Vegima, K. Asai, "Linear Regression Analysis with Fuzzy Model," IEEE Trans. On Systems, Man, Cybernetics, SMC-2, pp. 903-907, 1982.
33. I.B. Türkşn, "Interval Valued Fuzzy Sets Based on Normal Forms," Fuzzy Sets and Systems, vol. 20, pp.191-210, 1986.
34. I.B. Türkşen, "Four Methods of Approximate Reasoning with Interval-valued Fuzzy Sets", Int. J. of Approximate Reasoning, vol. 3, pp.121-142, 1989
35. I.B. Türkşen, "Interval-valued fuzzy sets and compensatory AND," Fuzzy Sets and Systems, vol. 51, pp. 295-307, 1992
36. I.B. Türkşen, "Interval valued fuzzy sets and fuzzy connectives," Interval Computations, pp. 125-142, 1993.
37. I.B. Türkşen, "Interval valued fuzzy sets and fuzzy measures", Proc. of First Int. Conf. Of NAFIPS, pp. 317-321, 1994.
38. I.B. Türkşen, "Fuzzy Normal Forms", Fuzzy Sets and Systems, vol. 69, pp. 319-346, 1995.
39. I.E. Türkşen, "Type I and "Interval-Valued" Type II Fuzzy Sets and Logics", In P. Wang (Ed.), Advances in Fuzzy Set Theory and Technology, 1995.
40. I.B. Türkşen, "Non-specificity and interval-valued fuzzy sets," Fuzzy Sets and Systems, vol. 80, pp. 87-100, 1996.
41. I.B. Türkşen, "Type I and Type II fuzzy system modeling," Fuzzy Sets and Systems, vol. 106, pp. 11-34, 1999.
42. I.B. Türkşen, "Type 2 representation and reasoning for CWW," Fuzzy Sets and Systems, vol. 127, pp. 17-36, 2006.
43. I.B. Türkşen, "Fuzzy Functions with LSE," Applied Soft Computing, (forthcoming)
44. Ö. Uncu and I.E. Türkşen, "A Novel Fuzzy System Modeling Approach: Multidimensional Structure Identification and Inference", Proc. of Tenth IEEE International Conference on Fuzzy Systems, Melbourne, Australia, December, pp. 557-562, 2001.
45. N.V.Vapnik, Statistical Learning Theory, John Wiley and Sons, New York, 1998.
46. Z. Yue, Q. Zhong, W. Guangyuan, "Solving Process for a system of first-order differential equations", Fuzzy Sets and Systems vol. 95, pp. 333-347, 1998.
47. L.A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, pp. 338-353, 1965.
48. L.A. Zadeh, "The Concept of a Linguistic Variable and its Application to Approximate Reasoning," Information Sciences, vol.8, pp. 199-249, 1975.