From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets

Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this article, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from
$L$
to
$L^{n}$
and present a new similarity construction on
$L^{n}$
. proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.