Positive definite indistinguishability operators

摘要

Two geometric characterizations of positive definite reflexive and symmetric fuzzy relations are provided based on the embeddability of their naturally associated pseudodistances with respect to the continuous Archimedean t-norms with additive generators t(x) = arccos x and t(x) = root 1 - x.Due to the important role of the t-norm T-arccos (x) with additive generator t(x) = arccos x in these characterizations, different characterizations of it are given. In particular, a left-continuous t-norm T is T-arccos (x) if and only if the rank of the matrices of all one-dimensional indistinguishability operators with respect to T are less than or equal to 2. (C) 2018 Elsevier B.V. All rights reserved.