About a new family of multidistances

In this paper the family of multi-argument functions called multidistances is considered, which have recently been introduced in some recent papers by J. Martin and G. Mayor. These refer to n-dimensional ordered lists of elements and extend the usual concept of distance between a couple of points in a metric space. In particular Martin and Mayor investigate three classes of multidistances, namely Fermat, sum-based and OWA-based multidistances. In this note we start by focusing on a specific property of multidistances, i.e. regularity, and alternative proof of the regularity of the sum-based multidistances is provided. Secondly a new family of multidistance functions are introduced, which are a generalization of the sum-based multidistances and which we call arithmetic–geometric multidistances.