On Bisymmetric Operators on a Finite Chain

IEEE Transactions on Fuzzy Systems

Volumn 11, Issue 5, 2003, Pages 647-651

  Mas, Margarita ^a   Monserrat, Miquel ^a   Torrens, Joan ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

Associativity; Bisymmetry; Finite chain; Label; Smoothness; t conorm; t norm; t operator

Indexed keywords

FUZZY SETS; SET THEORY; THEOREM PROVING;

BINARY OPERATORS;

LOGIC DEVICES;

EID: 0142258235     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2003.817851     Document Type: Article

References (15)

1. J. Aczél, Lectures on Functional Equations and their Applications. New York: Academic, 1966.
2. J. C. Fodor, "An extension of Fung-Fu's theorem," Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst., vol. 4, no. 3, pp. 235-243, 1996.
3. J. C. Fodor, "Smooth associative operations on finite ordinal scales," IEEE Trans. Fuzzy Syst., vol. 8, pp. 791-795, Dec. 2000.
4. J. C. Fodor and J.-L. Marichal, "On nonstrict means," Aequationes Math., vol. 54, pp. 308-327, 1997.
5. M. Gehrke, C. Walker, and E. Walker, "Averaging operators on the unit interval," Int. J. Intell. Syst., vol. 14, pp. 883-898, 1999.
6. L. Godo and C. Sierra, "A new approach to connective generation in the framework of expert systems using fuzzy logic," in Proc. XVIIIth ISMVL, Palma, Italy, 1988, pp. 157-162.
7. J. L. Marichal, "On the associativity functional equation," Fuzzy Sets Syst., vol. 114, pp. 381-389, 2000.
8. M. Mas, G. Mayor, and J. Torrens, "t-operators and uninorms on a finite chain," Int. J. Intell. Syst., vol. 14, pp. 909-922, 1999.
9. _, "t-operators," Int. J. Uncertainty, Fuzziness, Knowledge-Based Syst., vol. 7, pp. 31-50, 1999.
10. M. Mas, M. Monserrat, and J. Torrens, "On left and right uninorms on a finite chain," in Proc. EUSFLAT'01, Leicester, U.K., 2001, pp. 458-462.
11. G. Mayor and J. Torrens, "On a class of operators for expert systems," Int. J. Intell. Syst., vol. 8, pp. 771-778, 1993.
12. B. Moser, E. Tsiporkova, and P. Klement, "Convex combinations in terms of triangular norms: A charactrizattion of idempotent, bisymmetrical and self-dual compensatory operators," Fuzzy Sets Syst., vol. 104, pp. 97-108, 1999.
13. S. Ovchinnikov, "On some bisymmetric functions on closed intervals," Estudios de Lògica Borrosa y sus Aplicaciones, pp. 353-364, 1993.
14. W. Sander, "Associative aggregation operators," in Aggregation Operators: New Trends and Applications. ser. Studies in Fuzziness and Soft Computing, T. Calvo, G. Mayor, and R. Mesiar, Eds. Heidelberg, Germany: Physica-Verlag, 2002, vol. 97, pp. 124-158.
15. R. R. Yager, "Non-numeric multi-criteria multi-person decision making," Group Decisions Negotiation, vol. 2, pp. 81-93, 1993.