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. (c) 2017 Elsevier Inc. All rights reserved.