On generation of aggregation functions on infinite lattices. (English) Zbl 1418.06002

Summary: We describe supremum-dense subsets of aggregation functions, which are defined on infinite complete lattices. Also some restriction on the size of a generating set with respect to number of arguments involved in a generating process is discussed.


06B05 Structure theory of lattices
06A15 Galois correspondences, closure operators (in relation to ordered sets)
03E75 Applications of set theory
Full Text: DOI


[1] Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Studies in fuzziness and soft computing, vol 221. Springer, Berin · Zbl 1123.68124
[2] Calvo T, Mayor G, Mesiar R (eds) (2002) Aggregation Operators. Physica Verlag, Heidelberg · Zbl 0983.00020
[3] Grabisch M, Marichal J-L, Mesiar R, Pap E (2009) Aggregation functions. Cambridge University Press, Cambridge · Zbl 1196.00002
[4] Halaš, R.; Pócs, J., On the clone of aggregation functions on bounded lattices, Inf Sci, 329, 381-389, (2016) · Zbl 1390.06006
[5] Halaš, R.; Mesiar, R.; Pócs, J., Generators of Aggregation Functions and Fuzzy Connectives, IEEE Trans Fuzzy Syst, 24, 1690-1694, (2016)
[6] Jech T (2002) Set theory, 3rd Millennium ed, rev. and expanded. Springer, Berlin.
[7] Kerkhoff, S.; Pöschel, R.; Schneider, FM, A short introduction to clones, Electron Notes Theor Comput Sci, 303, 107-120, (2014) · Zbl 1341.08003
[8] Lau D (2006) Function algebras on finite sets. Springer, Berlin · Zbl 1105.08001
[9] Stone, MH, The generalized Weierstrass approximation theorem, Math Mag, 21, 167-184, (1948)
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.