Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
Kybernetika, Tome 46 (2010) no. 4, pp. 585-599 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
Classification : 03E72, 06F25, 60E05
Keywords: copula; effect algebra; triangular norm
@article{KYB_2010_46_4_a0,
     author = {Mesiar, Radko and Sarkoci, Peter},
     title = {Open problems posed at the tenth {International} conference on fuzzy set theory and applications {(FSTA} 2010, {Liptovsk\'y} {J\'an,} {Slovakia)}},
     journal = {Kybernetika},
     pages = {585--599},
     year = {2010},
     volume = {46},
     number = {4},
     mrnumber = {2722089},
     zbl = {1211.03077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a0/}
}
TY  - JOUR
AU  - Mesiar, Radko
AU  - Sarkoci, Peter
TI  - Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
JO  - Kybernetika
PY  - 2010
SP  - 585
EP  - 599
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a0/
LA  - en
ID  - KYB_2010_46_4_a0
ER  - 
%0 Journal Article
%A Mesiar, Radko
%A Sarkoci, Peter
%T Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
%J Kybernetika
%D 2010
%P 585-599
%V 46
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a0/
%G en
%F KYB_2010_46_4_a0
Mesiar, Radko; Sarkoci, Peter. Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia). Kybernetika, Tome 46 (2010) no. 4, pp. 585-599. http://geodesic.mathdoc.fr/item/KYB_2010_46_4_a0/

[1] Ahmad, N., Kim, H. K., McCann, R. J.: Extremal doubly stochastic measures and optimal transportation. Working paper, 2009.

[2] Alsina, C.: On Schur-concave $t$-norms and triangle functions. In: General inequalities, 4 (Oberwolfach, 1983), volume 71 of Internat. Schriftenreihe Numer. Math., pp. 241–248. Birkhäuser, Basel 1984. | MR

[3] Alsina, C., Frank, M. J., Schweizer, B.: Problems on associative functions. Aequationes Math. 66 (2003), 128–140. | DOI | MR | Zbl

[4] 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 | MR | Zbl

[5] Alsina, C., Schweizer, B., Frank, M. J.: Associative Functions. World Scientific Publishing Company, Singapore 2006. | MR | Zbl

[6] 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. | MR | Zbl

[7] Atanassov, K.: Intuitionistic Fuzzy Sets, Theory and Applications. Physica-Verlag, Heidelberg 1999. | MR | Zbl

[8] Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivariate Anal. 93 (2005), 313–339. | DOI | MR | Zbl

[9] Butnariu, D., Klement, E. P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions. Kluwer Academic Publishers, Dordrecht 1993. | Zbl

[10] Couceiro, M.: On two generalizations of associativity. In: Proc. FSTA 2010 (E. P. Klement et al., eds.), p. 47, Liptovský Ján 2010.

[11] Cuculescu, I., Theodorescu, R.: Extreme value attractors for star unimodal copulas. CR Math. Acad. Sci. Paris 334 (2002) 689–692. | DOI | MR | Zbl

[12] Durante, F., Foschi, R., Sarkoci, P.: Distorted copulas: constructions and tail dependence. Comm. Statist. Theory Methods 2010. In press. | MR | Zbl

[13] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Copulas with given diagonal sections: Novel constructions and applications. Internat. J. Uncertain. Fuzziness and Knowledge-Based Systems 18 (2007), 397–410. | DOI | MR | Zbl

[14] Durante, F., Mesiar, R., Papini, P. L.: The lattice-theoretic structure of the sets of triangular norms and semi-copulas. Nonlinear Analysis, Theory, Methods and Applications 69 (2008), 46–52. | MR | Zbl

[15] Durante, F., Mesiar, R., Sempi, C.: Copulas with given diagonal section: some new results. In: Proc. EUSFLAT-LFA Conference (E. Montseny and P. Sobrevilla, eds.), pp. 932–936, Barcelona 2005.

[16] Durante, F., Rodríguez-Lallena, J. A., Úbeda-Flores, M.: New constructions of diagonal patchwork copulas. Inform. Sci. 179 (2009), 3383–3391. | DOI | MR | Zbl

[17] Durante, F., Sempi, C.: Copulæ, and Schur-concavity. Internat. Math. J. 3 (2003), 893–905. | MR | Zbl

[18] Durante, F., Sempi, C.: Copula and semicopula transforms. Internat. J. Math. Math. Sci. (2005), 645–655. | DOI | MR | Zbl

[19] Durante, F., Sempi, C.: Semicopulæ. Kybernetika 41 (2005), 315–328. | MR | Zbl

[20] Durante, F., Spizzichino, F.: Semi-copulas, capacities and families of level curves. Fuzzy Sets and Systems 161 (2009), 2009.

[21] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1331–1352. | DOI | MR

[22] Frank, M. J.: On the simultaneous associativity of $F(x,y)$ and $x+y-F(x,y)$. Aeqationes Math. 19 (1979), 194–226. | DOI | MR | Zbl

[23] Genest, C., Quesada-Molina, J. J., Rodríguez-Lallena, J. A., Sempi, C.: A characterization of quasi-copulas. J. Multivariate Anal. 69 (1999), 193–205. | DOI | MR

[24] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge 2009. | MR | Zbl

[25] Gudder, S. P.: Sharply dominating effect algebras. Tatra Mt. Math. Publ. 15 (1998), 23–30. | MR | Zbl

[26] Gudder, S. P.: S-dominating effect algebras. Inter. J. Theor. Phys. 37 (1998), 915–923. | DOI | MR | Zbl

[27] Hestir, K., Williams, S. C.: Supports of doubly stochastic measures. Bernoulli 1 (1995), 217–243. | DOI | MR | Zbl

[28] Hilbert, D.: Mathematical problems. Bull. Amer. Math. Soc. 8 (1901/02), 437–479. | DOI | MR

[29] Janiš, V.: T-Norm based cuts of intuitionistic fuzzy sets. Inform. Sci. 180 (2010), 1134–1137. | DOI | MR | Zbl

[30] Jaworski, P.: On copulas and their diagonals. Inform. Sci. 179 (2009), 2863–2871. | DOI | MR | Zbl

[31] Jenča, G.: Blocks of homogeneous effect algebras. Bull. Austr. Math. Soc. 64 (2001), 81–98. | DOI | MR | Zbl

[32] Jenča, G.: Finite homogeneous and lattice ordered effect algebras. Discrete Mathematics 272 (2003), 197–214. | DOI | MR | Zbl

[33] Jenča, G.: Sharp and meager elements in orthocomplete homogeneous effect algebras. Order 27 (2010), 41–61. | DOI | MR | Zbl

[34] Jenča, G.: Coexistence in interval effect algebras. Proc. Amer. Math. Soc. To appear.

[35] Jenča, G., Pulmannová, S.: Orthocomplete effect algebras. Proc. Amer. Math. Soc. 131 (2003), 2663–2671. | DOI | MR | Zbl

[36] Jenča, G., Riečanová, Z.: On sharp elements in lattice ordered effect algebras. BUSEFAL 80 (1999), 24–29.

[37] Jwaid, T., Baets, B. De: Double conic copulas. In: Proc. FSTA 2010 (E. P. Klement et al., eds.), p. 73, Liptovský Ján 2010.

[38] Kalina, M.: On central atoms of Archimedean atomic lattice effect algebras. Kybernetika 46 (2010), 609–620. | MR | Zbl

[39] Klement, E. P., Mesiar, R.: Open problems posed at the Eight International Conference on Fuzzy Set Theory and Applications (FSTA 2006, Liptovský Ján, Slovakia). Kybernetika 42 (2006), 225–235. | MR

[40] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. | MR | Zbl

[41] Klement, E. P., Mesiar, R., Pap, E.: Uniform approximation of associative copulas by strict and non-strict copulas. Illinois J. Math. 45 (2001), 1393–1400. | MR | Zbl

[42] Klement, E. P., Mesiar, R., Pap, E.: Problems on triangular norms and related operators. Fuzzy Sets and Systems 145 (2004), 471–479. | MR | Zbl

[43] Klement, E. P., Mesiar, R., Pap, E.: Archimax copulas and invariance under transformations. C R Math. Acad. Sci. Paris 340 (2005), 755–758. | DOI | MR | Zbl

[44] Kolesárová, A., Mordelová, J., Stupňanová, A.: Aggregation functions as extensions of fuzzy measures. In: Proc. FSTA 2010 (E. P. Klement et al., eds.), p. 80, Liptovský Ján 2010.

[45] Marinacci, M., Montrucchio, L.: Ultramodular functions. Math. Oper. Res. 30 (2005), 311–332. | DOI | MR | Zbl

[46] Mesiar, R., Novák, V.: Open problems from the 2nd International Conference on Fuzzy Sets Theory and Its Applications. Fuzzy Sets and Systems 81 (1996), 185–190. | MR

[47] Mesiarová, A.: Triangular Norms and their Diagonal Functions. Master Thesis, Comenius University, Bratislava 2002.

[48] McNeil, A. J., Nešlehová, J.: Multivariate Archimedean copulas, $d$-monotone functions and $L_{1}$-norm symmetric distributions. Ann. Statist. 37 (2009), 3059–3097. | DOI | MR

[49] Moynihan, R.: Infinite $\tau _{T}$ products of distribution functions. J. Austral. Math. Soc. Ser. A 26 (1978), 227–240. | DOI | MR

[50] Nelsen, R. B.: An Introduction to Copulas. Second edition. Springer Science+Business Media, New York 2006. | MR | Zbl

[51] Nelsen, R. B., Úbeda-Flores, M.: The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas. CR Math. Acad. Sci. Paris 341 (2005), 583–586. | DOI | MR | Zbl

[52] Post, E. L.: Polyadic groups. Trans. Amer. Math. Soc. 48 (1940), 208–350. | DOI | MR | Zbl

[53] Quesada-Molina, J. J., Rodríguez-Lallena, J.-A.: Some remarks on the existence of doubly stochastic measures with latticework hairpin support. Aequationes Math. 47 (1994), 164–174. | DOI | MR

[54] Riečanová, Z.: Orthogonal sets in effect algebras. Demonstratio Math. 34 (2001), 525–532. | MR | Zbl

[55] Riečanová, Z.: MacNeille completion of Archimedean lattice effect algebras and their sublattice effect algebras. Preprint.

[56] Riečanová, Z., Junde, Wu: States on sharply dominating effect algebras. Science in China Series A: Mathematics 51 (2008), 907–914. | DOI | MR | Zbl

[57] Royden, H. L.: Real Analysis. Third edition. Macmillan Publishing Company, New York 1988. | MR | Zbl

[58] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, New York 1983. | MR | Zbl

[59] Tawn, J.: Bivariate extreme value theory: Models and estimation. Biometrika 75 (1988), 397–415. | DOI | MR | Zbl

[60] Vasiliev, T.: Four extended level operators of membership/non-membership over intuitionistic fuzzy sets. In: Proc. Twelfth International Conference on Intuitionistic Fuzzy Sets, Vol. 2 (J. Kacprzyk and K. Atanassov, eds.), Sofia 2008. Notes on Intuitionistic Fuzzy Sets 14 (2008), 100–107.