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2-increasing binary aggregation operators. (English) Zbl 1142.68541

Summary: In this work we investigate the class of binary aggregation operators (=agops) satisfying the 2-increasing property, obtaining some characterizations for agops having other special properties (e.g., quasi-arithmetic mean, Choquet-integral based, modularity) and presenting some construction methods. In particular, the notion of \(P\)-increasing function is used in order to characterize the composition of 2-increasing agops. The lattice structure (with respect to the pointwise order) of some subclasses of 2-increasing agops is presented. Finally, a method is given for constructing copulas beginning from 2-increasing and 1-Lipschitz agops.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] Benvenuti, P.; Mesiar, R., Integrals with respect to a general fuzzy measure, () · Zbl 1048.28003
[2] ()
[3] T. Calvo, A. Kolesárová, M. Komornı´ková, R. Mesiar, Aggregation operators: properties, classes and construction methods, in: [4], pp. 3-106.
[4] ()
[5] Choquet, G., Theory of capacities, Ann. inst. Fourier Grenoble, 5, 131-295, (1953-1954) · Zbl 0064.35101
[6] Denneberg, D., Non-additive measure and integral, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0826.28002
[7] Durante, F., Generalized composition of binary aggregation operators, Int. J. uncertain. fuzz. knowl.-based syst., 13, 567-577, (2005) · Zbl 1137.62353
[8] F. Durante, C. Sempi, On the characterization of a class of binary operations on bivariate distribution functions, Publ. Math. Debrecen, in press. · Zbl 1121.60010
[9] Fredricks, G.A.; Nelsen, R.B., Copulas constructed from diagonal sections, (), 129-136 · Zbl 0906.60022
[10] Genest, C.; Quesada-Molina, J.J.; Rodríguez-Lallena, J.A.; Sempi, C., A characterization of quasi-copulas, J. multivariate anal., 69, 193-205, (1999) · Zbl 0935.62059
[11] Gottwald, S., Mathematical fuzzy logic as a tool for the treatment of vague information, Inform. sci., 172, 41-71, (2005) · Zbl 1079.03014
[12] E.P. Klement, A. Kolesárová, R. Mesiar, C. Sempi, Copulas constructed from the horizontal section, submitted for publication. · Zbl 1130.60017
[13] A. Kolesárová, E.P. Klement, On affine sections of 1-Lipschitz aggregation operators, in: Proceedings Joint EUSFLAT-LFA Conference, Barcelona, 2005, pp. 1293-1296.
[14] Kolesárová, A., 1-Lipschitz aggregation operators and quasi-copulas, Kybernetika, 39, 615-629, (2003) · Zbl 1249.60018
[15] Kolesárová, A.; Mordelová, J.; Muel, E., Kernel aggregation operators and their marginals, Fuzzy sets syst., 142, 35-50, (2004) · Zbl 1043.03040
[16] R. Mesiar, B. De Baets, New construction methods for aggregation operators, in: Proceedings IPMU, Madrid, 2000, pp. 701-706.
[17] Mesiar, R., A note on moderate growth of t-conorms, Fuzzy sets syst., 122, 357-359, (2001) · Zbl 1013.03062
[18] Nelsen, R.B., An introduction to copulas, Lecture notes in statistics, vol. 139, (1999), Springer New York · Zbl 0909.62052
[19] Nelsen, R.B.; Úbeda Flores, M., The lattice – theoretic structure of sets of bivariate copulas and quasi-copulas, C.R. math. acad. sci. Paris, 341, 583-586, (2005) · Zbl 1076.62053
[20] Pasi, G.; Yager, R.R., Modeling the concept of majority opinion in group decision making, Inform. sci., 176, 390-414, (2006) · Zbl 1126.91016
[21] Yager, R.R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE trans. syst. man. cybernet., 18, 183-190, (1988) · Zbl 0637.90057
[22] Yager, R.R., On global requirements for implication operators in fuzzy modus ponens, Fuzzy sets syst., 106, 3-10, (1999) · Zbl 0931.68117
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