On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms

IEEE Transactions on Fuzzy Systems

Volumn 12, Issue 1, 2004, Pages 45-61

  Deschrijver, Glad ^a   Cornelis, Chris ^a   Kerre, Etienne E ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

transform; Archimedean property; Intuitionistic fuzzy set; Intuitionistic fuzzy triangular norm and conorm; Nilpotency; Representation theorem

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; FUZZY SETS; MAPPING; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; THEOREM PROVING; UNCERTAIN SYSTEMS;

Φ-TRANSFORM; ARCHIMEDEAN PROPERTY; INTUITIONISTIC FUZZY SET; INTUITIONISTIC FUZZY TRIANGULAR NORM AND CONORM; NILPOTENCY; REPRESENTATION THEOREM;

FUZZY CONTROL;

EID: 1542303729     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2003.822678     Document Type: Article

References (29)

1. K. T. Atanassov, "Intuitionistic Fuzzy Sets," Central Tech. Library, Bulgarian Academy Science, Sofia, Bulgaria, Rep. No. 1697/84, 1983.
2. C. Cornelis and G. Deschrijver, "The compositional rule of inference in an intuitionistic fuzzy logic setting," in Proc. ESSLLI 2001 Student Session, K. Striegnitz, Ed., 2001, pp. 83-94.
3. C. Cornelis and E. E. Kerre, "On the structure and interpretation of an intuitionistic fuzzy expert system," in Proc. EUROFUSE 2002, B. De Baets, J. Fodor, and G. Pasi, Eds., 2002, pp. 173-178.
4. C. Cornelis, C. V. D. Donck, and E. E. Kerre, "Sinha-dougherty approach to the fuzzification of set inclusion revisited," Fuzzy Sets Syst., vol. 134, no. 2, pp. 283-295, 2003.
5. C. Cornelis and E. E. Kerre, Inclusion-Based Approximate Reasoning. ser. Lecture Notes in Computer Science 2074, V. Alexandrov, J. Dongarra, B. Juliano, R. Renner, and C. Tan, Eds. New York: Springer-Verlag, 2001, pt. II, pp. 221-230.
6. _, "A fuzzy inference methodology based on the fuzzification of set inclusion," in Recent Advances in Intelligent Paradigms and Applications, A. Abraham, L. Jain, and J. Kacprzyk, Eds. Berlin, Germany: Physica-Verlag, 2002, pp. 71-89.
7. P. Grzegorzewski and E. Mrówka, "Soft querying via intuitionistic fuzzy sets," in Proc. 9th Int. Conf. Information Processing Management Uncertainty Knowledge-Based Systems, 2002, pp. 1845-1849.
8. N. N. Morsi and A. A. Fahmy, "On generalized modus ponens with multiple rules and a residuated implication," Fuzzy Sets Syst., vol. 129, pp. 267-274, 2002.
9. R. Yager and V. Kreinovich, "Universal approximation theorem for uninorm-based fuzzy systems modeling," Fuzzy Sets Syst., vol. 140, no. 2, pp. 331-339, 2002.
10. G. Deschrijver and E. E. Kerre, "On the composition of intuitionistic fuzzy relations," Fuzzy Sets Syst., vol. 136, no. 3, pp. 333-361, 2003.
11. _, "On the cuts of intuitionistic fuzzy compositions," Kuwait J. Sci. Eng., 2004, submitted for publication.
12. C. Cornelis, G. Deschrijver, M. De Cock, and E. E. Kerre, "Intuitionistic fuzzy relational calculus: an overview," in Proc. 1st Int. IEEE Symp. Intelligent Systems: Methodology, Models, Applications Emerging Technologies, vol. 1, 2002, pp. 340-345.
13. B. De Baets and E. E. Kerre, "Fuzzy relations and applications," Adv. Electron. Electron Phys., vol. 89, pp. 255-324, 1994.
14. W. Bandler and L. Kohout, "Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and artificial systems," in Theory and Application to Policy Analysis and Information Systems, P. Wang and S. Chang, Eds. New York: Plenum, 1980, pp. 341-367.
15. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norms. Dordrecht, The Netherlands: Kluwer, 2002.
16. P. Smets and P. Magrez, "Implication in fuzzy logic," Int. J. Approx. Reason., vol. 1, pp. 327-347, 1987.
17. M. Eisenberg, Axiomatic Theory of Sets and Classes. New York: Holt, Rinehart, and Winston, 1971.
18. K. T. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets Syst., vol. 20, pp. 87-96, 1986.
19. _, Intuitionistic Fuzzy Sets. Heidelberg, Germany: Physica-Verlag, 1999.
20. G. Deschrijver and E. E. Kerre, "On the relationship between some extensions of fuzzy set theory," Fuzzy Sets Syst., vol. 133, no. 2, pp. 227-235, 2003.
21. J. Goguen, "L-fuzzy sets," J. Math. Anal. Appl., vol. 18, pp. 145-174, 1967.
22. H. Bustince, J. Kacprzyk, and V. Mohedano, "Intuitionistic fuzzy generators - application to intuitionistic fuzzy complementation," Fuzzy Sets Syst., vol. 114, pp. 485-504, 2000.
23. G. Deschrijver, C. Cornelis, and E. E. Kerre, "Intuitionistic fuzzy connectives revisited," in Proc. 9th Int. Conf. Information Processing Management Uncertainty Knowledge-Based Systems, 2002, pp. 1839-1844.
24. C. Cornelis, G. Deschrijver, and E. E. Kerre, "Classification of intuitionistic fuzzy implicators: An algebraic approach," in Proc. 6th Joint Conf. Information Sciences, H. J. Caulfield, S. Chen, H. Chen, R. Duro, V. Honaver, E. E. Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang, and Y. Yang, Eds., 2002, pp. 105-108.
25. E. Hewitt and K. Stromberg, Real and Abstract Analysis. New York: Springer-Verlag, 1965.
26. E. Szmidt and J. Kacprzyk, "Distances between intuitionistic fuzzy sets," Fuzzy Sels Syst., vol. 114, pp. 505-518, 2000.
27. E. Sagan, Advanced Calculus. Boston, MA: Houghton Mifflin, 1974.
28. D. Dubois and H. Prade, "Fuzzy logics and generalized modus ponens revised," Int. J. Cybern. Syst., vol. 15, pp. 293-331, 1984.
29. C. Cornelis, G. Deschrijver, and E. E. Kerre, "Implication in intuitionistic and interval-valued fuzzy set theory: Construction, classification, application," J. Approx. Reason., vol. 35, no. 1, pp. 55-95, 2004.