On integer-valued means and the symmetric maximum

Miguel Couceiro (1) , Michel Grabisch (2, 3)

1 ORPAILLEUR - Knowledge representation, reasonning
2 PSE - Paris School of Economics
3 CES - Centre d'économie de la Sorbonne

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.

Mots clés: decomposability; symmetric maximum; nonassociative algebra; integer means

Domaines: Mathématiques [math]

Miguel Couceiro, Michel Grabisch. On integer-valued means and the symmetric maximum. Aequationes Mathematicae, 2017, 91 (2), pp.353-371. ⟨10.1007/s00010-016-0460-9⟩. ⟨hal-01404593⟩