Some remarks on the solutions to the functional equation I(x, y) = I(x, I(x, y)) for D-operations

Communications in Computer and Information Science

Volumn 80 PART 1, Issue , 2010, Pages 666-675

  Massanet, Sebastià ^a   Torrens, Joan ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS T-NORMS; CRISP LOGIC; FUNCTIONAL EQUATION; FUZZY IMPLICATIONS; ITERATIVE FUNCTIONAL EQUATIONS; T-CONORMS;

DATA PROCESSING; FUNCTIONAL ANALYSIS; FUZZY LOGIC; ITERATIVE METHODS; KNOWLEDGE BASED SYSTEMS; MATHEMATICAL OPERATORS;

INFORMATION MANAGEMENT;

EID: 84863167750     PISSN: 18650929     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-14055-6_70     Document Type: Conference Paper

References (19)

1. Aguiló, I., Suñer, J., Torrens, J.: A characterization of residual implications derived from uninorms. In: Proceedings of IFSA-EUSFLAT 2009, Lisbon, pp. 333-338 (2009)
2. Baczynski, M., Jayaram, B.: (S,N)-and R-implications: A state-of-the-art survey. Fuzzy Sets and Systems 159, 1836-1859 (2008)
3. Baczynski, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing, vol. 231. Springer, Heidelberg (2008)
4. Baczynski, M., Jayaram, B.: (U,N)-implications and their characterizations. Fuzzy Sets and Systems 160, 2049-2062 (2009)
5. Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practicioners. Springer, Heidelberg (2007)
6. Calvo, T., Mayor, G., Mesiar, R. (eds.): Aggregation operators. New trends and applications. Studies in Fuzziness and Soft Computing, vol. 97. Physica-Verlag, Heidelberg (2002)
7. Carbonell, M., Torrens, J.: Continuous R-implications generated from representable aggregation functions. Fuzzy Sets and Systems (accepted)
8. De Baets, B., Fodor, J.C.: Residual operators of uninorms. Soft Computing 3, 89-100 (1999)
9. Durante, F., Klement, E.P., Mesiar, R., Sempi, C.: Conjunctors and their residual implicators: Characterizations and construction methods. Mediterranean Journal of Mathematics 4, 343-356 (2007)
10. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation functions. Encyclopedia of Mathematics and its Applications, vol. 127. Cambridge University Press, Cambridge (2009)
11. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, London (2000)
12. Mas, M., Monserrat, M., Torrens, J.: QL versus D-implications. Kybernetika 42, 351-366 (2006)
13. Mas, M., Monserrat, M., Torrens, J.: Two types of implications derived from uninorms. Fuzzy Sets and Systems 158, 2612-2626 (2007)
14. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A survey on fuzzy implication functions. IEEE Transactions on Fuzzy Systems 15(6), 1107-1121 (2008)
15. Ruiz, D., Torrens, J.: Residual implications and co-implications from idempotent uninorms. Kybernetika 40, 21-38 (2004)
16. Ruiz-Aguilera, D., Torrens, J.: Distributivity of residual implications over conjunctive and disjunctive uninorms. Fuzzy Sets and Systems 158, 23-37 (2007)
17. Shi, Y., Ruan, D., Kerre, E.E.: On the characterization of fuzzy implications satisfying I(x, y) = I(x, I(x, y)). Information Sciences 117, 2954-2970 (2007)
18. Torra, V., Narukawa, Y.: Modeling decisiona. In: Information fusion and aggregation operators. Cognitive Technologies. Springer, Heidelberg (2007)
19. Xie, A., Qin, F.: Solutions of the functional equation I(x, y) = I(x.I(x.y)) for a continuous D-operation. Information Sciences (2010), doi:10.1016/j.ins.2010.01.023