Abstract
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)=arccosx and t(x)=1−x.Due to the important role of the t-norm Tarccosx with additive generator t(x)=arccosx in these characterizations, different characterizations of it are given. In particular, a left-continuous t-norm T is Tarccosx 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.
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