Distances from Fuzzy Implications

In the literature, there have been a few works studying distance functions from fuzzy logic connectives (FLCs), such as t-norms, t-conorms, copulas, and quasi-copulas. Recently, Nanavati et al. defined a distance function $$d_I$$ using a fuzzy implication I. They characterised fuzzy implications that would yield a metric and showed that $$ d_I$$ is a pseudo-monometric w.r.t. the usual order on [0, 1]. In this work, we generalise the definition of $$d_I$$ with the aid of any t-conorm S. Denoting it by $$d_{I,S}$$ , we investigate the conditions under which $$d_{I,S}$$ yields metrics and pseudo-monometrics for the major t-conorms. We thus expand our armoury of practical distance functions using FLCs such as t-conorms and fuzzy implications.