© 2019 Instituto Politecnico Nacional. All rights reserved. The paper proposes a new class of fuzzy set similarity measures taking into account the proximity of membership values to the border values 0 and 1. These similarity measures take values in [0, 1] and generalize the crisp weak equality relation of fuzzy sets considered in the theory of fuzzy sets. We present the method constructing a contrast similarity measure using a bipolar function symmetric with respect to 0.5. As a particular case, we consider the similarity measure defined by the contrast intensification operation considered by Lotfi Zadeh.