On the standard fuzzy metric: generalizations and application to model estimation

Different approaches to obtain a notion of metric in the context of fuzzy setting can be found in the literature. In this paper, we deal with the concept due to George and Veeramani, which is defined by means of continuous triangular norms. Different authors have addressed the study of such a concept from a theoretical point of view. In this paper, we provide a new methodology to induce fuzzy metrics which generalize the celebrated standard fuzzy metric. The aforementioned methodology allows us to approach some questions related to the continuous triangular norms from which such fuzzy metrics are defined. Morever, we show the applicability of the new fuzzy metrics to an engineering problem. More specifically, we address successfully robust model estimation through a variant of the well-known estimator RANSAC. By way of illustration of the performance of the approach, we report on the accuracy achieved by the new estimator and other RANSAC variants for a benchmark involving a specific model estimation problem and a large number of datasets with varying proportion of outliers and different levels of noise. The resulting estimator is shown able to outperform the classical counterparts considered.

This work is also supported by project PGC2018-095709-B-C21 (MCIU/AEI/FEDER, UE), and PROCOE/4/2017 (Govern Balear, 50% P.O. FEDER 2014-2020 Illes Balears).