S-norm aggregation of infinite collections

Abstract

The aggregation of membership values by means of the iterate application of an s-norm is of cardinal relevance for the development of any general theory of approximate reasoning which relies on a sup- t model for relation composition. Here we present a definition of s-norm aggregation for possibly infinite collections, which can be demonstrated to generalize previous approaches consistently. It provides a common framework in which classical sup-t and finite s- t compositions can be analyzed as well as other significant cases. General properties of the s-norm aggregation concept, its specialization for the class of continuous s-norms and its relationship with fuzzy measure theory are discussed.