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Robust model estimation is a recurring problem in application areas such as robotics and computer vision. Taking inspiration from a notion of distance that arises in a natural way in fuzzy logic, this paper modifies the well-known robust estimator RANSAC making use of a Fuzzy Metric (FM) within the estimator main loop to encode the compatibility of each sample to the current model/hypothesis. Further, once a number of hypotheses have been explored, this FM-based RANSAC makes use of the same fuzzy metric to refine the winning model. The incorporation of this fuzzy metric permits us to express the distance between two points as a kind of degree of nearness measured with respect to a parameter, which is very appropriate in the presence of the vagueness or imprecision inherent to noisy data. By way of illustration of the performance of the approach, we report on the estimation accuracy achieved by FM-based RANSAC and other RANSAC variants for a benchmark comprising a large number of noisy datasets with varying proportion of outliers and different levels of noise. As it will be shown, FM-based RANSAC outperforms the classical counterparts considered.