This paper introduces a new class of fuzzy associative memories (FAMs) called tunable equivalence fuzzy associative memories, for short tunable E-FAMs or TE-FAMs, that are determined by the application of parametrized equivalence measures in the hidden nodes. Tunable E-FAMs belong to the class of Theta-FAMs that have recently appeared in the literature. In contrast to previous Theta-FAM models, tunable E-FAMs allow for the extraction of a fundamental memory set from the training data by means of an algorithm that depends on the evaluation of equivalence measures. Furthermore, we are able to optimize not only the weights corresponding to the contributions of the hidden nodes but also the contributions of the attributes of the data by tuning the parametrized equivalence measures used in a TE-FAM model. The computational effort involved in training tunable TE-FAMs is very low compared to the one of the previous Theta-FAM training algorithm. (C) 2015 Elsevier B.V. All rights reserved.292242260