Semicopulæ

Fabrizio Durante; Carlo Sempi

Kybernetika (2005)

  • Volume: 41, Issue: 3, page [315]-328
  • ISSN: 0023-5954

Abstract

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We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, t -norm.

How to cite

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Durante, Fabrizio, and Sempi, Carlo. "Semicopulæ." Kybernetika 41.3 (2005): [315]-328. <http://eudml.org/doc/33756>.

@article{Durante2005,
abstract = {We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, $t$-norm.},
author = {Durante, Fabrizio, Sempi, Carlo},
journal = {Kybernetika},
keywords = {semicopula; copula; quasi-copula; aggregation operator; $t$-norm; semicopula; copula; quasi-copula; aggregation operator; -norm},
language = {eng},
number = {3},
pages = {[315]-328},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Semicopulæ},
url = {http://eudml.org/doc/33756},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Durante, Fabrizio
AU - Sempi, Carlo
TI - Semicopulæ
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 3
SP - [315]
EP - 328
AB - We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, $t$-norm.
LA - eng
KW - semicopula; copula; quasi-copula; aggregation operator; $t$-norm; semicopula; copula; quasi-copula; aggregation operator; -norm
UR - http://eudml.org/doc/33756
ER -

References

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  1. Agell N., On the concavity of t-norms and triangular functions, Stochastica 8 (1984), 91–95 (1984) Zbl0567.26010MR0780142
  2. Alsina C., Nelsen R. B., Schweizer B., 10.1016/0167-7152(93)90001-Y, Statist. Probab. Lett. 17 (1993), 85–89 (1993) Zbl0798.60023MR1223530DOI10.1016/0167-7152(93)90001-Y
  3. Bassan B., Spizzichino F., 10.1016/j.jmva.2004.04.002, J. Multivariate Anal. 93 (2005), 313–339 Zbl1070.60015MR2162641DOI10.1016/j.jmva.2004.04.002
  4. 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 Zbl1039.03015MR1936383
  5. Calvo T., Mesiar R., Stability of aggregation operators, In: Proc. EUSFLAT 2001, Leicester 2001, pp. 475–478 MR1821982
  6. Calvo T., Pradera A., 10.1016/j.fss.2003.10.029, Fuzzy Sets and Systems 142 (2004), 15–33 Zbl1081.68105MR2045340DOI10.1016/j.fss.2003.10.029
  7. Dunford N., Schwartz J. T., Linear Operators, Part I: General Theory. Wiley, New York 1958 Zbl0635.47003MR1009162
  8. Durante F., Sempi C., On the characterization of a class of binary operations on bivariate distribution functions, Submitted Zbl1121.60010
  9. Fredricks G. A., Nelsen R. B., Copulas constructed from diagonal sections, In: Distributions With Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1997, pp. 129–136 (1997) Zbl0906.60022MR1614666
  10. Fredricks G. A., Nelsen R. B., The Bertino family of copulas, In: Distributions with given marginals and statistical problems (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena, eds.), Kluwer Academic Publishers, Dordrecht 2002, pp. 81–91 Zbl1135.62334MR2058982
  11. Genest C., Molina J. J. Quesada, Lallena J. A. Rodríguez, Sempi C., 10.1006/jmva.1998.1809, J. Multivariate Anal. 69 (1999), 193–205 (1999) MR1703371DOI10.1006/jmva.1998.1809
  12. Kelley J. L., General Topology, Van Nostrand, New York 1955; reprinted by Springer, New York – Heidelberg – Berlin 1975 (1955) Zbl0066.16604MR0070144
  13. Klement E. P., Mesiar, R., Pap E., Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000 Zbl1087.20041MR1790096
  14. Kolesárová A., 1 -Lipschitz aggregation operators and quasi-copulas, Kybernetika 39 (2003), 615–629 MR2042344
  15. Mikusiński P., Sherwood, H., Taylor M. D., The Fréchet bounds revisited, Real Anal. Exchange 17 (1991), 759–764 (1991) MR1171416
  16. Nelsen R. B., 10.1007/978-1-4757-3076-0, (Lecture Notes in Statistics 139.) Springer–Verlag, New York 1999 Zbl1152.62030MR1653203DOI10.1007/978-1-4757-3076-0
  17. Nelsen R. B., Fredricks G. A., Diagonal copulas, In: Distributions With Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1997, pp. 121–128 (1997) Zbl0906.60021MR1614665
  18. Nelsen R. B., Quesada-Molina J. J., Schweizer, B., Sempi C., Derivability of some operations on distribution functions, In: Distributions With Fixed Marginals and Related Topics (L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds.), (IMS Lecture Notes – Monogr. Ser. 28), Inst. Math. Statist., Hayward 1996, pp. 233–243 (1996) MR1485535
  19. Nelsen R. B., Flores M. Úbeda, The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas, Submitted 
  20. Schweizer B., Sklar A., Probabilistic Metric Spaces, Elsevier, New York 1983 Zbl0546.60010MR0790314
  21. Sklar A., Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 (1959) MR0125600
  22. Sklar A., Random variables, joint distribution functions and copulas, Kybernetika 9 (1973), 449–460 (1973) Zbl0292.60036MR0345164
  23. Suarez F., Gil P., 10.1016/0165-0114(86)90028-X, Fuzzy Sets and Systems 18 (1986), 67–81 (1986) Zbl0595.28011MR0825620DOI10.1016/0165-0114(86)90028-X
  24. Szász G., Introduction to Lattice Theory, Academic Press, New York 1963 Zbl0126.03703MR0166118
  25. Flores M. Úbeda, Cópulas y quasicópulas: interrelaciones y nuevas propiedades, Aplicaciones. Ph. D. Dissertation. Universidad de Almería, Servicio de Publicaciones de la Universidad de Almería 2002 

Citations in EuDML Documents

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  1. Fabrizio Durante, José Quesada-Molina, Carlo Sempi, Semicopulas: characterizations and applicability
  2. Susanne Saminger, Bernard De Baets, Hans De Meyer, On the dominance relation between ordinal sums of conjunctors
  3. Zuming Peng, The study on semicopula based implications
  4. Michał Boczek, Marek Kaluszka, On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application
  5. Gaspar Mayor, Radko Mesiar, Joan Torrens, On quasi-homogeneous copulas
  6. Rachele Foschi, Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach
  7. Radko Mesiar, Peter Sarkoci, Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)

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