Reduction of attributes in averaged similarities

Similarity Relations may be constructed from a set of fuzzy attributes. Each fuzzy attribute generates a simple similarity, and these simple similarities are combined into a complex similarity afterwards. The Representation Theorem establishes one such way of combining similarities, while averaging them is a different and more realistic approach in applied domains. In this paper, given an averaged similarity by a family of attributes, we propose a method to find families of new attributes having fewer elements that generate the same similarity. More generally, the paper studies the structure of this important class of fuzzy relations.