Fuzzy modeling based on generalized conjunction operations

IEEE Transactions on Fuzzy Systems

Volumn 10, Issue 5, 2002, Pages 678-683

  Batyrshin, Ildar ^b,c   Kaynak, Okyay ^a,d   Rudas, Imre ^a,e  

^a IEEE

^b Research Institute for Problems of Ecology and Mineral Wealth Use of Tatarstan Academy of Sciences   (Russian Federation)

^c KAZAN NATIONAL RESEARCH TECHNOLOGICAL UNIVERSITY   (Russian Federation)

^d BOGAZICI UNIVERSITY   (Turkey)

^e ÓBUDA UNIVERSITY   (Hungary)

Author keywords

Conjunction; Disjunction; Functions approximation; Fuzzy modeling; T norm

Indexed keywords

FUNCTION APPROXIMATION; FUZZY MODEL; PARAMETRIC CONJUNCTION OPERATIONS;

APPROXIMATION THEORY; CALCULATIONS; ERROR ANALYSIS; FUNCTION EVALUATION; MATHEMATICAL MODELS; MEMBERSHIP FUNCTIONS; PARAMETER ESTIMATION;

FUZZY SETS;

EID: 0036802273     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2002.803500     Document Type: Article

References (27)

1. C. Alsina, E. Trillas, and L. Valverde, "On some logical connectives for fuzzy sets theory," J. Math. Anal. Applicat., vol. 93, pp. 15-26, 1983.
2. I. Batyrshin and O. Kaynak, "Generation of generalized conjunction and disjunction operations," in Proc. IPMU-98, Paris, France, 1998, pp. 1762-1768.
3. ____, "Parametric classes of generalized conjunction and disjunction operations for fuzzy modeling," IEEE Trans. Fuzzy Syst., vol. 7, pp. 586-596, Oct. 1999.
4. I. Batyrshin, O. Kaynak, and I. Rudas, "Generalized conjunction and disjunction operations for fuzzy control," in Proc. EUFIT'98, vol. 1, Aachen, Germany, 1998, pp. 52-57.
5. I. Batyrshin, A. Bikbulatov, O. Kaynak, and I. Rudas, "Functions approximation based on the tuning of generalized connectives," in Proc. EUROFUSE-SIC '99, Budapest, Hungary 1999, pp. 556-561.
6. I. Batyrshin and M. Wagenknecht, "Contracting and expanding negations on [0, 1]," J. Fuzzy Math., vol. 6, no. 1, pp. 133-140, 1998.
7. M. Berger, "A new parametric family of fuzzy connectives and their application to fuzzy control," Fuzzy Sets Syst., vol. 93, pp. 1-16, 1998.
8. O. Cervinka, "Automatic tuning of parametric t-norms and t-conorms in fuzzy modeling," in Proc. 7th IFSA World Congr., vol. 3, Prague, Czech Republic, 1997, pp. 416-421.
9. J. C. Fodor, "A new look at fuzzy connectives," Fuzzy Sets Syst., vol. 57, pp. 141-148, 1993.
10. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization. New York: Academic, 1981.
11. M. M. Gupta and J. Qi, "Design of fuzzy logic controllers based on generalized T -operators," Fuzzy Sets Syst., vol. 40, pp. 473-489, 1991.
12. S. I. Horikawa, T. Furuhashi, and Y. Uchikawa, "A new type of fuzzy neural network based on a truth space approach for automatic acquisition of fuzzy rules with linguistic hedges," Int. J. Approx. Reason., vol. 13, pp. 249-268, 1995.
13. J.-S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing. A Computational Approach to Learning and Machine Intelligence. Upper Saddle River, NJ: Prentice-Hall, 1997.
14. J. M. Keller, R. Krishnapuram, Z. Chen, and O. Nasraoui, "Fuzzy additive hybrid operators for network-based decision making," Int. J. Intell. Syst., vol. 9, pp. 1001-1023, 1994.
15. E. P. Klement, "Construction of fuzzy σ-algebras using triangular norms," J. Math. Anal. Appl., vol. 85, pp. 543-565, 1982.
16. B. Kosko, Fuzzy Engineering. Upper Saddle River, NJ: Prentice-Hall, 1997.
17. G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty and Information. Upper Saddle River, NJ: Prentice-Hall, 1988.
18. R. Krishnapuram and J. Lee, "Fuzzy-connective-based hierarchical aggregation networks for decision making," Fuzzy Sets Syst., vol. 46, pp. 11-27, 1992.
19. M. Mizumoto, "Fuzzy controls under various fuzzy reasoning methods," Inform. Sci., vol. 45, pp. 129-151, 1988.
20. M. J. D. Powell, "Variable metric methods for constrained optimization," in Mathematical Programming: The State of the Art, A. Bachem, M. Grotschel, and B. Korte, Eds. New York: Springer-Verlag, 1983, pp. 288-311.
21. K. Schittowski, "NLQPL: A FORTRAN-subroutine solving constrained nonlinear programming problems," Ann. Oper. Res., vol. 5, pp. 485-500, 1985.
22. M. Sugeno, "An introductory survey of fuzzy control," Inform. Sci., 36, pp. 59-83, 1985.
23. I. B. Turksen et al., "Intelligent fuzzy system modeling," in Computational Intelligence-Soft Computing and Fuzzy-Neuro Integration With Applications, O. Kaynak et al., Eds. New York: Springer-Verlag, 1998, pp. 157-176.
24. L.-X. Wang, A Course in Fuzzy Systems and Control. Upper Saddle River, NJ: Prentice-Hall, 1997.
25. S. Weber, "A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms," Fuzzy Sets Syst., vol. 11, pp. 115-134, 1983.
26. T. Whalen, "Exact solutions for interacting rules in generalized modus ponens with parameterized implication functions," Inform. Sci., vol. 92, pp. 211-232, 1996.
27. L. A. Zadeh, "A fuzzy-set-theoretic interpretation of linguistic hedges," J. Cybern., vol. 2, no. 3, pp. 4-34, 1972.