On S-generalized multidistances and their aggregation

Abstract

We introduce a new class of multidistances, they are called S-generalized multidistances, defined by means of a t-conorm S. The main properties of them are analyzed and some examples are given. We have also established some relations between a multidistance and an S-generalized multidistance through the additive generator of the t-conorm. In this context, we study how to combine a collection of (Sk)k=1)-generalized multidistances in order to obtain a new S-generalized multidistance. In addition, we prove that properties of the S-generalized multidistances are preserved through the aggregation process. Finally, we give some characterizations of the aggregation functions of a family of (Sk)k=1)-generalized multidistances based on another aggregation function and the additive generators of the involved t-conorms.