On integer-valued means and the symmetric maximum
- 68 Downloads
Integer-valued means, satisfying the decomposability condition of Kolmogoroff/Nagumo, are necessarily extremal, i.e., the mean value depends only on the minimal and maximal inputs. To overcome this severe limitation, we propose an infinite family of (weak) integer means based on the symmetric maximum and computation rules. For such means, their value depends not only on extremal inputs, but also on 2nd, 3rd, etc., extremal values as needed. In particular, we show that this family can be characterized by a weak version of decomposability.
KeywordsInteger means nonassociative algebra symmetric maximum decomposability
Mathematics Subject Classification26E60 08A99 06A99
Unable to display preview. Download preview PDF.
- 4.Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Number 127 in Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2009)Google Scholar
- 5.Kolmogoroff, A.: Sur la notion de moyenne. Atti delle Reale Accademia Nazionale dei Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. 12, 323–343 (1930)Google Scholar
- 6.Marichal, J.-L., Teheux, B.: Barycentrically associative and preassociative functions. Acta Math. Hungar. 145, 468–488 (2015)Google Scholar