Title:
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Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia) (English) |
Author:
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Mesiar, Radko |
Author:
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Sarkoci, Peter |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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46 |
Issue:
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4 |
Year:
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2010 |
Pages:
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585-599 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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copula |
Keyword:
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effect algebra |
Keyword:
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triangular norm |
MSC:
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03E72 |
MSC:
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06F25 |
MSC:
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60E05 |
idZBL:
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Zbl 1211.03077 |
idMR:
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MR2722089 |
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Date available:
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2010-10-22T05:19:23Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140771 |
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Reference:
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[1] Ahmad, N., Kim, H. K., McCann, R. J.: Extremal doubly stochastic measures and optimal transportation.Working paper, 2009. |
Reference:
|
[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 0821801 |
Reference:
|
[3] Alsina, C., Frank, M. J., Schweizer, B.: Problems on associative functions.Aequationes Math. 66 (2003), 128–140. Zbl 1077.39021, MR 2003460, 10.1007/s00010-003-2673-y |
Reference:
|
[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. Zbl 0798.60023, MR 1223530, 10.1016/0167-7152(93)90001-Y |
Reference:
|
[5] Alsina, C., Schweizer, B., Frank, M. J.: Associative Functions.World Scientific Publishing Company, Singapore 2006. Zbl 1100.39023, MR 2222258 |
Reference:
|
[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. Zbl 1175.62045, MR 2473107 |
Reference:
|
[7] Atanassov, K.: Intuitionistic Fuzzy Sets, Theory and Applications.Physica-Verlag, Heidelberg 1999. Zbl 0939.03057, MR 1718470 |
Reference:
|
[8] Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes.J. Multivariate Anal. 93 (2005), 313–339. Zbl 1070.60015, MR 2162641, 10.1016/j.jmva.2004.04.002 |
Reference:
|
[9] Butnariu, D., Klement, E. P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions.Kluwer Academic Publishers, Dordrecht 1993. Zbl 0804.90145 |
Reference:
|
[10] Couceiro, M.: On two generalizations of associativity.In: Proc. FSTA 2010 (E. P. Klement et al., eds.), p. 47, Liptovský Ján 2010. |
Reference:
|
[11] Cuculescu, I., Theodorescu, R.: Extreme value attractors for star unimodal copulas.CR Math. Acad. Sci. Paris 334 (2002) 689–692. Zbl 0996.60026, MR 1903371, 10.1016/S1631-073X(02)02322-1 |
Reference:
|
[12] Durante, F., Foschi, R., Sarkoci, P.: Distorted copulas: constructions and tail dependence.Comm. Statist. Theory Methods 2010. In press. Zbl 1194.62075, MR 2755652 |
Reference:
|
[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. Zbl 1158.62324, MR 2362234, 10.1142/S0218488507004753 |
Reference:
|
[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. Zbl 1204.03051, MR 2417853 |
Reference:
|
[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. |
Reference:
|
[16] Durante, F., Rodríguez-Lallena, J. A., Úbeda-Flores, M.: New constructions of diagonal patchwork copulas.Inform. Sci. 179 (2009), 3383–3391. Zbl 1190.62101, MR 2574347, 10.1016/j.ins.2009.06.007 |
Reference:
|
[17] Durante, F., Sempi, C.: Copulæ, and Schur-concavity.Internat. Math. J. 3 (2003), 893–905. Zbl 1231.60014, MR 1990502 |
Reference:
|
[18] Durante, F., Sempi, C.: Copula and semicopula transforms.Internat. J. Math. Math. Sci. (2005), 645–655. Zbl 1078.62055, MR 2172400, 10.1155/IJMMS.2005.645 |
Reference:
|
[19] Durante, F., Sempi, C.: Semicopulæ.Kybernetika 41 (2005), 315–328. Zbl 1249.26021, MR 2181421 |
Reference:
|
[20] Durante, F., Spizzichino, F.: Semi-copulas, capacities and families of level curves.Fuzzy Sets and Systems 161 (2009), 2009. |
Reference:
|
[21] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics.Found. Phys. 24 (1994), 1331–1352. MR 1304942, 10.1007/BF02283036 |
Reference:
|
[22] Frank, M. J.: On the simultaneous associativity of $F(x,y)$ and $x+y-F(x,y)$.Aeqationes Math. 19 (1979), 194–226. Zbl 0444.39003, MR 0556722, 10.1007/BF02189866 |
Reference:
|
[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. MR 1703371, 10.1006/jmva.1998.1809 |
Reference:
|
[24] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions.Cambridge University Press, Cambridge 2009. Zbl 1196.00002, MR 2538324 |
Reference:
|
[25] Gudder, S. P.: Sharply dominating effect algebras.Tatra Mt. Math. Publ. 15 (1998), 23–30. Zbl 0939.03073, MR 1655076 |
Reference:
|
[26] Gudder, S. P.: S-dominating effect algebras.Inter. J. Theor. Phys. 37 (1998), 915–923. Zbl 0932.03072, MR 1624277, 10.1023/A:1026637001130 |
Reference:
|
[27] Hestir, K., Williams, S. C.: Supports of doubly stochastic measures.Bernoulli 1 (1995), 217–243. Zbl 0844.60002, MR 1363539, 10.2307/3318478 |
Reference:
|
[28] Hilbert, D.: Mathematical problems.Bull. Amer. Math. Soc. 8 (1901/02), 437–479. MR 1557926, 10.1090/S0002-9904-1902-00923-3 |
Reference:
|
[29] Janiš, V.: T-Norm based cuts of intuitionistic fuzzy sets.Inform. Sci. 180 (2010), 1134–1137. Zbl 1188.03036, MR 2580107, 10.1016/j.ins.2009.11.039 |
Reference:
|
[30] Jaworski, P.: On copulas and their diagonals.Inform. Sci. 179 (2009), 2863–2871. Zbl 1171.62332, MR 2547755, 10.1016/j.ins.2008.09.006 |
Reference:
|
[31] Jenča, G.: Blocks of homogeneous effect algebras.Bull. Austr. Math. Soc. 64 (2001), 81–98. Zbl 0985.03063, MR 1848081, 10.1017/S0004972700019705 |
Reference:
|
[32] Jenča, G.: Finite homogeneous and lattice ordered effect algebras.Discrete Mathematics 272 (2003), 197–214. Zbl 1031.03078, MR 2009543, 10.1016/S0012-365X(03)00256-5 |
Reference:
|
[33] Jenča, G.: Sharp and meager elements in orthocomplete homogeneous effect algebras.Order 27 (2010), 41–61. Zbl 1193.03084, MR 2601154, 10.1007/s11083-009-9137-5 |
Reference:
|
[34] Jenča, G.: Coexistence in interval effect algebras.Proc. Amer. Math. Soc. To appear. |
Reference:
|
[35] Jenča, G., Pulmannová, S.: Orthocomplete effect algebras.Proc. Amer. Math. Soc. 131 (2003), 2663–2671. Zbl 1019.03046, MR 1974321, 10.1090/S0002-9939-03-06990-9 |
Reference:
|
[36] Jenča, G., Riečanová, Z.: On sharp elements in lattice ordered effect algebras.BUSEFAL 80 (1999), 24–29. |
Reference:
|
[37] Jwaid, T., Baets, B. De: Double conic copulas.In: Proc. FSTA 2010 (E. P. Klement et al., eds.), p. 73, Liptovský Ján 2010. |
Reference:
|
[38] Kalina, M.: On central atoms of Archimedean atomic lattice effect algebras.Kybernetika 46 (2010), 609–620. Zbl 1214.06002, MR 2722091 |
Reference:
|
[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 2241786 |
Reference:
|
[40] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000. Zbl 1010.03046, MR 1790096 |
Reference:
|
[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. Zbl 1054.62064, MR 1895466 |
Reference:
|
[42] Klement, E. P., Mesiar, R., Pap, E.: Problems on triangular norms and related operators.Fuzzy Sets and Systems 145 (2004), 471–479. Zbl 1050.03019, MR 2075842 |
Reference:
|
[43] Klement, E. P., Mesiar, R., Pap, E.: Archimax copulas and invariance under transformations.C R Math. Acad. Sci. Paris 340 (2005), 755–758. Zbl 1126.62040, MR 2141065, 10.1016/j.crma.2005.04.012 |
Reference:
|
[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. |
Reference:
|
[45] Marinacci, M., Montrucchio, L.: Ultramodular functions.Math. Oper. Res. 30 (2005), 311–332. Zbl 1082.52006, MR 2142035, 10.1287/moor.1040.0143 |
Reference:
|
[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 1392780 |
Reference:
|
[47] Mesiarová, A.: Triangular Norms and their Diagonal Functions.Master Thesis, Comenius University, Bratislava 2002. |
Reference:
|
[48] McNeil, A. J., Nešlehová, J.: Multivariate Archimedean copulas, $d$-monotone functions and $L_{1}$-norm symmetric distributions.Ann. Statist. 37 (2009), 3059–3097. MR 2541455, 10.1214/07-AOS556 |
Reference:
|
[49] Moynihan, R.: Infinite $\tau _{T}$ products of distribution functions.J. Austral. Math. Soc. Ser. A 26 (1978), 227–240. MR 0511607, 10.1017/S1446788700011721 |
Reference:
|
[50] Nelsen, R. B.: An Introduction to Copulas.Second edition. Springer Science+Business Media, New York 2006. Zbl 1152.62030, MR 2197664 |
Reference:
|
[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. Zbl 1076.62053, MR 2182439, 10.1016/j.crma.2005.09.026 |
Reference:
|
[52] Post, E. L.: Polyadic groups.Trans. Amer. Math. Soc. 48 (1940), 208–350. Zbl 0025.01201, MR 0002894, 10.1090/S0002-9947-1940-0002894-7 |
Reference:
|
[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. MR 1268029, 10.1007/BF01832957 |
Reference:
|
[54] Riečanová, Z.: Orthogonal sets in effect algebras.Demonstratio Math. 34 (2001), 525–532. Zbl 0989.03071, MR 1853730 |
Reference:
|
[55] Riečanová, Z.: MacNeille completion of Archimedean lattice effect algebras and their sublattice effect algebras.Preprint. |
Reference:
|
[56] Riečanová, Z., Junde, Wu: States on sharply dominating effect algebras.Science in China Series A: Mathematics 51 (2008), 907–914. Zbl 1155.81012, MR 2395393, 10.1007/s11425-007-0163-8 |
Reference:
|
[57] Royden, H. L.: Real Analysis.Third edition. Macmillan Publishing Company, New York 1988. Zbl 0704.26006, MR 1013117 |
Reference:
|
[58] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces.North-Holland, New York 1983. Zbl 0546.60010, MR 0790314 |
Reference:
|
[59] Tawn, J.: Bivariate extreme value theory: Models and estimation.Biometrika 75 (1988), 397–415. Zbl 0653.62045, MR 0967580, 10.1093/biomet/75.3.397 |
Reference:
|
[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. |
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