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Keywords:
semicopula; quasi-copula; Lipschitz condition; aggregation operator
semicopula; quasi-copula; Lipschitz condition; aggregation operator
Summary:
We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.
References:
[1] Alsina C., Frank M. J., Schweizer B.: Problems on associative functions. Aequationes Math. 66 (2003), 128–140 DOI 10.1007/s00010-003-2673-y | MR 2003460 | Zbl 1077.39021
[2] Alsina C., Nelsen R. B., Schweizer B.: On the characterization of a class of binary operations on distribution functions. Statist. Probab. Lett. 17 (1993), 85–89 DOI 10.1016/0167-7152(93)90001-Y | MR 1223530 | Zbl 0798.60023
[3] Axler S., Bourdon, P., Ramey W.: Harmonic Function Theory. (Graduate Texts in Mathematics 137.) Springer–Verlag, New York 2001 MR 1805196 | Zbl 0959.31001
[4] Baets B. De: Analytical solution methods for fuzzy relational equations. In: Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series (D. Dubois and H. Prade, eds.), Chapter 6, Vol. 1, Kluwer Academic Publishers, Dordrecht 2000, pp. 291–340 MR 1890236 | Zbl 0970.03044
[5] Baets B. De, Meyer H. De: Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity. Fuzzy Sets and Systems 152 (2005), 249–270 MR 2138509 | Zbl 1114.91031
[6] Baets B. De, Meyer H. De, Schuymer, B. De, Jenei S.: Cycle evaluation of transitivity of reciprocal relations. Soc. Choice Welfare. To appear
[7] Schuymer B. De, Meyer, H. De, Baets B. De: On some forms of cycle-transitivity and their relation to commutative copulas. In: Proc. EUSFLAT–LFA Conference, Barcelona 2005, pp. 178–182
[8] Bassan B., Spizzichino F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivariate Anal. 93 (2005), 313–339 DOI 10.1016/j.jmva.2004.04.002 | MR 2162641 | Zbl 1070.60015
[9] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: properties, classes and construction methods. In: Aggregation Operators. New Trends and Applications (T. Calvo, R. Mesiar, and G. Mayor, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–106 MR 1936383 | Zbl 1039.03015
[10] Denneberg D.: Non-additive Measure and Integral. Kluwer Academic Publishers, Dordrecht 1994 MR 1320048 | Zbl 0968.28009
[11] Durante F.: What is a semicopula? In: Proc. AGOP – Summer School on Aggregation Operators, Lugano 2005, pp. 51–56
[12] Durante F.: A new class of symmetric bivariate copulas. Preprint n. 19, Dipartimento di Matematica E. De Giorgi, Lecce, 2005 MR 2311801
[13] Durante F., Mesiar, R., Sempi C.: On a family of copulas constructed from the diagonal section. Soft Computing 10 (2006), 490–494 DOI 10.1007/s00500-005-0523-7 | Zbl 1098.60016
[14] Durante F., Quesada-Molina J. J., Sempi C.: A generalization of the Archimedean class of bivariate copulas. Ann. Inst. Statist. Math. (2006), to appear MR 2388803
[15] Durante F., Sempi C.: Semicopulæ. Kybernetika 41 (2005), 315–328 MR 2181421
[16] Genest C., Molina J. J. Quesada, Lallena J. A. Rodríguez, Sempi C.: A characterization of quasi-copulas. J. Multivariate Anal. 69 (1999), 193–205 DOI 10.1006/jmva.1998.1809 | MR 1703371
[17] Ricci R. Ghiselli, Mesiar R.: $k$-Lipschitz strict triangular norms. In: Proc. EUSFLAT–LFA Conference, Barcelona 2005, pp. 1307–1312
[18] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[19] Kolmogorov A. N.: Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer–Verlag, Berlin 1933. Reprinted in: Foundations of the Theory of Probability. Chelsea, Bronxm NY 1950 MR 0494348 | Zbl 0007.21601
[20] Mesiarová A.: $k$-Lipschitz aggregation operators. In: Proc. AGOP – Summer School on Aggregation Operators, Lugano 2005, pp. 89–92
[21] Mesiarová A.: Triangular norms and $k$-Lipschitz property. In: Proc. EUSFLAT–LFA Conference, Barcelona 2005, pp. 922–926
[22] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer–Verlag, New York 1999 DOI 10.1007/978-1-4757-3076-0 | MR 1653203 | Zbl 1152.62030
[23] Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M.: Best-possible bounds on sets of bivariate distribution functions. J. Multivariate Anal. 90 (2004), 348–358 DOI 10.1016/j.jmva.2003.09.002 | MR 2081783 | Zbl 1057.62038
[24] Nelsen R. B.: Copulas and quasi-copulas: an introduction to their properties and applications. In: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms (E. P. Klement and R. Mesiar, eds.), Elsevier, Amsterdam 2005, pp. 391–413 MR 2165243 | Zbl 1079.60021
[25] Rodríguez-Lallena J. A., Úbeda-Flores M.: A new class of bivariate copulas. Statist. Probab. Lett. 66 (2004), 315–325 DOI 10.1016/j.spl.2003.09.010 | MR 2045476 | Zbl 1102.62054
[26] Scarsini M.: Copulæ of capacities on product spaces. In: Distribution Functions with Fixed Marginals and Related Topics (L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds.), Institute of Mathematical Statistics (Lecture Notes – Monograph Series Volume 28), Hayward 1996, pp. 307–318 MR 1485540
[27] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North Holland, New York 1983. 2nd edition: Dover Publications, Mineola, New York 2005 MR 0790314 | Zbl 0546.60010
[28] Stromberg K. R.: An Introduction to Classical Real Analysis. Chapman & Hall, London 1981 MR 0604364 | Zbl 0454.26001
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