Similarity of fuzzy sets, application to Rn as a substratum

In this paper we apply to real spaces the concept of similarity relation on fuzzy sets. The underlying topological space is said to play the role of an expression substratum. These relations can be used to define relative positions of expression of fuzzy sets. Groups of homeomorphisms of a topological space are important, they are representative of the symmetries of the space. We give very simple examples to clarify these rather abstract notions. (C) 2000 Elsevier Science B.V. All rights reserved.