Some new characterizations and properties of quasi-copulas

Fuzzy Sets and Systems

Volumn 160, Issue 6, 2009, Pages 717-725

  Rodríguez Lallena, José Antonio ^a   Úbeda Flores, Manuel ^a  

^a UNIVERSITY OF ALMERÍA   (Spain)

Author keywords

1 Lipschitz aggregation operators; Conjunctive aggregation operators; Copulas; Fuzzy connectives and aggregation operators; Quasi copulas; Tracks

Indexed keywords

1-LIPSCHITZ AGGREGATION OPERATORS; CONJUNCTIVE AGGREGATION OPERATORS; COPULAS; FUZZY CONNECTIVES AND AGGREGATION OPERATORS; QUASI-COPULAS; TRACKS;

EID: 58849094152     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2008.02.007     Document Type: Article

References (23)

1. Alsina C. On quasi-copulas and metrics. In: Cuadras C., Fortiana J., and Rodríguez-Lallena J.A. (Eds). Distributions with Given Marginals and Statistical Modelling (2002), Kluwer Academic Publishers, Dordrecht 1-8
2. Alsina C., Nelsen R.B., and Schweizer B. On the characterization of a class of binary operations on distribution functions. Statist. Probab. Lett. 17 (1993) 85-89
3. Calvo T., Kolesárová A., Komorníková M., and Mesiar R. Aggregation operators: properties, classes and construction methods. In: Calvo T., Mayor G., and Mesiar R. (Eds). Aggregation Operators: New Trends and Applications (2002), Physica-Verlag, Heidelberg 3-104
4. Cuculescu I., and Theodorescu R. Copulas: diagonals and tracks. Rev. Roumaine Math. Pures Appl. 46 (2001) 731-742
5. De Baets B., De Meyer H., and Úbeda-Flores M. Extremes of the mass distribution associated with a trivariate quasi-copula. C. R. Math. 344 (2007) 587-590
6. Dubois D., and Prade H. On the use of aggregation operations in information fusion processes. Fuzzy Sets and Systems 142 (2004) 143-161
7. Durante F., Mesiar R., Papini P.L., and Sempi C. 2-Increasing binary aggregation operators. Inform. Sci. 177 (2007) 111-129
8. Durante F., and Papini P.L. A weakening of Schur-concavity for copulas. Fuzzy Sets and Systems 158 (2007) 1378-1383
9. Genest C., Quesada-Molina J.J., Rodríguez-Lallena J.A., and Sempi C. A characterization of quasi-copulas. J. Multivariate Anal. 69 (1999) 193-205
10. Janssens S., De Baets B., and De Meyer H. Bell-type inequalities for quasi-copulas. Fuzzy Sets and Systems 148 (2004) 263-278
11. Klement E.P., and Kolesárová A. 1-Lipschitz aggregation operators, quasi-copulas and copulas with given diagonals. In: López-Díaz M., Gil M.A., Grzegorzewski P., Hryniewicz O., and Lawry J. (Eds). Soft Methodology and Random Information Systems (2004), Springer, Berlin 205-211
12. Klement E.P., and Kolesárová A. Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators. Kybernetika 41 (2005) 329-348
13. Klement E.P., and Kolesárová A. Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section. Monatsh. Math. 152 (2007) 151-167
14. Kolesárová A. 1-Lipschitz aggregation operators and quasi-copulas. Kybernetika 39 (2003) 615-629
15. Nelsen R.B. An Introduction to Copulas. second ed. (2006), Springer, New York
16. Nelsen R.B., Quesada-Molina J.J., Rodríguez-Lallena J.A., and Úbeda-Flores M. Some new properties of quasi-copulas. In: Cuadras C., Fortiana J., and Rodríguez-Lallena J.A. (Eds). Distributions with Given Marginals and Statistical Modelling (2002), Kluwer Academic Publishers, Dordrecht 187-194
17. R.B. Nelsen, J.J. Quesada-Molina, B. Schweizer and C. Sempi, Derivability of some operations on distribution functions, in: L. Rüschendorf, B. Schweizer and M.D. Taylor (Eds.), Distributions with Fixed Marginals and Related Topics, IMS Lecture Notes-Monograph Series Number 28, Hayward, 1996, pp. 233-243.
18. Nelsen R.B., and Úbeda-Flores M. The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. C. R. Math. 341 (2005) 583-586
19. Rodríguez-Lallena J.A., and Úbeda-Flores M. Best-possible bounds on sets of multivariate distribution functions. Comm. Statist. Theory Methods 33 (2004) 805-820
20. Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959) 229-231
21. Sklar A. Random variables, joint distribution functions, and copulas. Kybernetika 9 (1973) 449-460
22. E.F. Wolff, Measures of dependence derived from copulas, Thesis, University of Massachusetts in Amherst, 1977.
23. Wolff E.F. N-dimensional measures of dependence. Stochastica 4 (1980) 175-188