Restricted equivalence functions

In this paper we present the concept of a restricted equivalence function. This concept arises on the one hand, from the definition of equivalence given by J. Fodor and M. Roubens, and on the other, from the properties usually demanded from the measures used for comparing images. We also study different methods for the construction of restricted equivalence functions from automorphisms and implication operators. Finally we analyze the manner of generating similarity measures of X. Liu and of J. Fan et al. from our restricted equivalence functions.