Multi-argument distances and regular sum-based multidistances.

In this paper we consider the family of multi-argument functions called multidistances, introduced in some recent papers by J.Martin and G.Mayor, which extend to n-dimensional ordered lists of elements the usual concept of distance between a couple of points in a metric space. In particular Martin and Mayor investigated three classes of multidistances, that is Fermat, sum-based and OWA-based multidistances.In this note we focus our attention on a specific property of multidistances, i.e. regularity, and we provide an alternative proof about the regularity of the sum-based multidistances.