A formal and empirical analysis of the fuzzy gamma rank correlation coefficient

The so-called gamma coefficient is a well-known rank correlation measure frequently used to quantify the strength of dependence between two variables with ordered domains. To increase the robustness of this measure toward noise in the data, a generalization of the gamma coefficient has recently been developed on the basis of fuzzy order relations. The goal of this paper is threefold. First, we analyze some formal properties of the fuzzy gamma coefficient. Second, we complement the original experiments, which have been conducted on a simple artificial data set, by a more extensive empirical evaluation using real-world data. On the basis of these empirical results, we provide some basic insights and offer an explanation for the effectiveness of the fuzzy gamma coefficient. Third, we propose an alternative motivation for the measure, based on the idea of (fuzzy) equivalence relations induced by limited precision in the perception of measurements.