Kernel aggregation operators and their marginals. (English) Zbl 1043.03040

Summary: Binary kernel aggregation operators, that is, monotone binary operators on \([0,1]\) with the Chebyshev norm equal to 1 are studied. Marginal functions of such operators are shown to be 1-Lipschitz. Several constructions of kernel aggregation operators with fixed marginal functions are given, including maximal and minimal kernel aggregation operators with prescribed marginals. Finally, kernel aggregation operators uniquely determined by their marginals are characterized.


03E72 Theory of fuzzy sets, etc.
68T37 Reasoning under uncertainty in the context of artificial intelligence
Full Text: DOI


[1] Calvo, T.; Kolesárová, A.; Komornı́ková, M.; Mesiar, R., Aggregation operators: properties, classes and construction methods, (), 3-106 · Zbl 1039.03015
[2] T. Calvo, R. Mesiar, Stability of aggregation operators, Proc. EUSFLAT’ 2001, Leicester, 2001, pp. 475-478.
[3] Fodor, J.C.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0827.90002
[4] Genest, C.; Quesada Molina, J.J.; Rodrı́guez Lallena, J.A.; Sempi, C., A characterization of quasi-copulas, J. multivariate anal., 69, 193-205, (1999) · Zbl 0935.62059
[5] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, Trends in logic, Vol. 8, (2000), Kluwer Academic Publishers Dordrecht/London/Boston · Zbl 0972.03002
[6] Kolesárová, A., Möbius Fitting aggregation operators, Kybernetika, 38, 3, 259-273, (2002) · Zbl 1265.28042
[7] A. Kolesárová, J. Mordelová, 1-Lipschitz and kernel aggregation operators, Proc. AGOP’ 2001, Oviedo, Spain, 2001, pp. 71-76.
[8] J. Lázaro, T. Rückschlossová, T. Calvo, Shift invariant binary aggregation operators. Fuzzy Sets and Systems (2004), in this issue doi:10.1016/j.fss.2003.10.031.
[9] Mas, G.; Mayor, G.; Torrens, J., T-operators, Internat. J. uncertainty knowledge-based systems, 7, 31-50, (1999) · Zbl 1087.03515
[10] J. Mordelová, E. Muel, Kernel aggregation operators, Proc. AGOP’ 2001, Oviedo, Spain, 2001, pp. 95-98.
[11] Nelsen, R.B., An introduction to copulas, Lecture notes in statistics, Vol. 139, (1999), Springer Berlin · Zbl 0909.62052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.