On integer-valued means and the symmetric maximum

Abstract

International audienceInteger-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

New Directions in Ordinal Evaluation: Sugeno Integrals and Beyond

“…[23] Let ϕ :L * →L be an anonymous and weakly associative function that satisfies (C1), (C2), (C3) onL 2 , and let R ∈ R. Then ϕ = R if and only if one (or, equivalently, all) of the following assertions hold:…”