On distances derived from t-norms

The construction of distances from t-norms is studied. The generation of distances from a t-norm and its dual t-conorm is extended to the more general case of any t-norm and t-conorm. The open problem of characterizing those t-norms that define distances is solved in the case that the t-norms have the same zero region as the Lukasiewicz one. (C) 2014 Elsevier B.V. All rights reserved.