We propose Fuzzy Jaccard Index (Fuji) — a scale-invariant score for similarity assessment of two ranked/ordered lists. Fuji improves upon the Jaccard index by incorporating a membership function that takes into account the particular ranks, thus producing both more stable and more accurate similarity estimates. We provide theoretical insights into the properties of the Fuji score as well as propose an efficient algorithm for computing it. We also present empirical evidence of its performance in different synthetic scenarios. Finally, we demonstrate its utility in a typical machine learning setting — comparing feature ranking lists, relevant to a given machine learning task. In many practical applications, in particular originating from high-dimensional domains, where only a small percentage of the whole feature space might be relevant, a robust and confident feature ranking leads to interpretable findings, efficient computation and good predictive performance. In such cases, Fuji correctly distinguishes between existing feature ranking approaches, while being more robust and efficient than the benchmark similarity scores.