Matching pairs of objects is a fundamental operation in data analysis. However, it requires to define a similarity measure between objects to be matched. The similarity measure may not be adapted to the various properties of each object. Consequently, designing a method to learn a measure of similarity between pairs of objects is an important generic problem in machine learning. In this paper, a general framework of fuzzy logical-based similarity measures based on T-equalities derived from residual implication functions is proposed. Then a model allowing to learn the parametric similarity measures is introduced. This is achieved by an online learning algorithm with an efficient implication-based loss function. Experiments on real datasets show that the learned measures are efficient at a wide range of scales, and achieve better results than existing fuzzy similarity measures. Moreover, the learning algorithm is fast, so that it can be used in real world applications, where computation times are a key-feature when one chooses an inference system.