Abstract
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.
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References
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Studies in fuzziness and soft computing, vol 221. Springer, Berin
Calvo T, Mayor G, Mesiar R (eds) (2002) Aggregation Operators. Physica Verlag, Heidelberg
Grabisch M, Marichal J-L, Mesiar R, Pap E (2009) Aggregation functions. Cambridge University Press, Cambridge
Halaš R, Pócs J (2016) On the clone of aggregation functions on bounded lattices. Inf Sci 329:381–389. https://doi.org/10.1016/j.ins.2015.09.038
Halaš R, Mesiar R, Pócs J (2016) Generators of Aggregation Functions and Fuzzy Connectives. IEEE Trans Fuzzy Syst 24(6):1690–1694. https://doi.org/10.1109/TFUZZ.2016.2544353
Jech T (2002) Set theory, 3rd Millennium ed, rev. and expanded. Springer, Berlin.
Kerkhoff S, Pöschel R, Schneider FM (2014) A short introduction to clones. Electron Notes Theor Comput Sci 303:107–120. https://doi.org/10.1016/j.entcs.2014.02.006
Lau D (2006) Function algebras on finite sets. Springer, Berlin
Stone MH (1948) The generalized Weierstrass approximation theorem. Math Mag 21(4):167–184. https://doi.org/10.2307/3029750
Acknowledgements
Radomír Halaš was supported by the Grant Agency of the Czech Republic (GAČR) no. 18-06915S and by the project MSMT Mobility 7AMB17AT054. Radko Mesiar was supported by the Slovak Research and Development Agency under the contract no. APVV-14-0013 and by the IGA project of the faculty of Science Palacký University Olomouc no. PrF2018012. Jozef Pócs was supported by the Slovak Research and Development Agency under the contract no. APVV-16-0073 and by the IGA project of the faculty of Science Palacký University Olomouc no. PrF2018012.
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Halaš, R., Mesiar, R. & Pócs, J. On generation of aggregation functions on infinite lattices. Soft Comput 23, 7279–7286 (2019). https://doi.org/10.1007/s00500-018-3375-7
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DOI: https://doi.org/10.1007/s00500-018-3375-7