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    Relation: mr:MR3607851; zbl:Zbl 06707377; reference:[1] Alsina, C., Frank, M. J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas.World Scientific, Singapore 2006. Zbl 1100.39023, MR 2222258, 10.1142/9789812774200; reference:[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. Zbl 0798.60023, MR 1223530, 10.1016/0167-7152(93)90001-y; reference:[3] Alvoni, E., Papini, P. L., Spizzichino, F.: On a class of transformations of copulas and quasi-copulas.Fuzzy Sets and Systems 160 (2009), 334-343. Zbl 1175.62045, MR 2473107, 10.1016/j.fss.2008.03.025; reference:[4] Birkhoff, G.: Lattice Theory.American Mathematical Society, Providence 1973. Zbl 0537.06001, MR 0227053; reference:[5] Clifford, A. H.: Naturally totally ordered commutative semigroups.Amer. J. Math. 76 (1954), 631-646. MR 0062118, 10.2307/2372706; reference:[6] Baets, B. De: Quasi-copulas: A bridge between fuzzy set theory and probability theory.In: Integrated Uncertainty Management and Applications. Selected Papers Based on the Presentations at the 2010 International Symposium on Integrated Uncertainty Managment and Applications (IUM 2010) (V.-N. Huynh, Y. Nakamori, J. Lawry, and M. Inuiguchi, eds.), Ishikawa 2010, p. 55. Springer, Berlin 2010. 10.1007/978-3-642-11960-6_6; reference:[7] Baets, B. De, Meyer, H. De, D{í}az, S.: On an idempotent transformation of aggregation functions and its application on absolutely continuous {A}rchimedean copulas.Fuzzy Sets and Systems 160 (2009), 733-751. Zbl 1175.62046, MR 2493272, 10.1016/j.fss.2008.04.001; reference:[8] Baets, B. De, Janssens, S., Meyer, H. De: On the transitivity of a parametric family of cardinality-based similarity measures.Internat. J. Approx. Reason. 50 (2009), 104-116. Zbl 1191.68706, MR 2519040, 10.1016/j.ijar.2008.03.006; reference:[9] Schuymer, B. De, Meyer, H. De, Baets, B. De: Cycle-transitive comparison of independent random variables.J. Multivariate Anal. 96 (2005), 352-373. Zbl 1087.60018, MR 2204983, 10.1016/j.jmva.2004.10.011; reference:[10] D{í}az, S., Montes, S., Baets, B. De: Transitivity bounds in additive fuzzy preference structures.IEEE Trans. Fuzzy Systems 15 (2007), 275-286. 10.1109/tfuzz.2006.880004; reference:[11] Dolati, A., Mohseni, S., Úbeda-Flores, M.: Some results on a transformation of copulas and quasi-copulas.Inform. Sci. 257 (2014), 176-182. Zbl 1321.62053, MR 3131786, 10.1016/j.ins.2013.09.023; reference:[12] Durante, F., Sarkoci, P., Sempi, C.: Shuffles of copulas.J. Math. Anal. Appl. 352 (2009), 914-921. Zbl 1160.60307, MR 2501937, 10.1016/j.jmaa.2008.11.064; reference:[13] Durante, F., Sempi, C.: Copula and semicopula transforms. Zbl 1078.62055, 10.1155/ijmms.2005.645; reference:[14] Durante, F., Sempi, C.: Principles of Copula Theory.CRC Press, Boca Raton 2015. MR 3443023, 10.1201/b18674; reference:[15] Fuchs, S., Schmidt, K. D.: Bivariate copulas: transformations, asymmetry and measures of concordance.Kybernetika 50 (2014), 109-125. MR 3195007, 10.14736/kyb-2014-1-0109; reference:[16] Genest, C., Quesada-Molina, J. J., Rodríguez-Lallena, J. A., Sempi, C.: A characterization of quasi-copulas.J. Multivariate Anal. 69 (1999), 193-205. Zbl 0935.62059, MR 1703371, 10.1006/jmva.1998.1809; reference:[17] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions.Cambridge University Press, Cambridge 2009. Zbl 1206.68299, MR 2538324, 10.1017/cbo9781139644150; reference:[18] Hájek, P., Mesiar, R.: On copulas, quasicopulas and fuzzy logic.Soft Computing 12 (2008), 1239-1243. Zbl 1152.03018, 10.1007/s00500-008-0286-z; reference:[19] Janssens, S., Baets, B. De, Meyer, H. De: Bell-type inequalities for commutative quasi-copulas.Fuzzy Sets and Systems 148 (2004), 263-278. MR 2100199, 10.1016/j.fss.2004.03.015; reference:[20] Kalická, J.: On some construction methods for 1-Lipschitz aggregation functions.Fuzzy Sets and Systems 160 (2009), 726-732. Zbl 1175.62047, MR 2493271, 10.1016/j.fss.2008.06.017; reference:[21] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000. Zbl 1087.20041, MR 1790096, 10.1007/978-94-015-9540-7; reference:[22] Klement, E. P., Mesiar, R., Pap, E.: Invariant copulas.Kybernetika 38 (2002), 275-285. Zbl 1264.62045, MR 1944309; reference:[23] Klement, E. P., Mesiar, R., Pap, E.: Transformations of copulas.Kybernetika 41 (2005), 425-436. Zbl 1243.62019, MR 2180355; reference:[24] Ling, C. M.: Representation of associative functions.Publ. Math. Debrecen 12 (1965), 189-212. Zbl 0137.26401, MR 0190575; reference:[25] Montes, I., Miranda, E., Montes, S.: Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance.European J. Oper. Res. 2342 (2014), 209-220. Zbl 1305.91106, MR 3141610, 10.1016/j.ejor.2013.09.013; reference:[26] Montes, I., Miranda, E., Pelessoni, R., Vicig, P.: Sklar's theorem in an imprecise setting.Fuzzy Sets and Systems 278 (2015), 48-66. MR 3383206, 10.1016/j.fss.2014.10.007; reference:[27] Nelsen, R. B.: An Introduction to Copulas. Second edition.Springer, New York 2006. MR 2197664, 10.1007/0-387-28678-0; reference:[28] Nelsen, R. B., Quesada-Molina, J. J., Rodríguez-Lallena, J. A., Úbeda-Flores, M.: Some new properties of quasi-copulas.In: Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez-Lallena, edis.), Kluwer Academic Publishers, Dordrecht 2002, pp. 187-194. Zbl 1135.62339, MR 2058992, 10.1007/978-94-017-0061-0_20; reference:[29] Nelsen, R. B., Úbeda-Flores, M.: The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas.Comptes Rendus Mathematique 341 (2005), 583-586. Zbl 1076.62053, MR 2182439, 10.1016/j.crma.2005.09.026; reference:[30] Pelessoni, R., Vicig, P., Montes, I., Miranda, E.: Imprecise copulas and bivariate stochastic orders.In: Proc. EUROFUSE 2013, Oviedo 2013, pp. 217-224.; reference:[31] Sainio, E., Turunen, E., Mesiar, R.: A characterization of fuzzy implications generated by generalized quantifiers.Fuzzy Sets and Systems 159 (2008), 491-499. Zbl 1176.03013, MR 2388105, 10.1016/j.fss.2007.09.018; reference:[32] Schweizer, B., Sklar, A.: Associative functions and abstract semigroups.Publ. Math. Debrecen 10 (1963), 69-81. MR 0170967; reference:[33] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces.North-Holland, New York 1983. Zbl 0546.60010, MR 0790314; reference:[34] Sklar, A.: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR 0125600; reference:[35] Sklar, A.: Random variables, joint distribution functions, and copulas.Kybernetika 9 (1973), 449-460. Zbl 0292.60036, MR 0345164; reference:[36] Walley, P.: Statistical Reasoning with Imprecise Probabilities.Chapman and Hall, London 1991. Zbl 0732.62004, MR 1145491

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