A decomposition theorem for T-indistinguishability operators. The continuous strict Archimedean case

In this paper we study the relationship between the cuts of a T-indistinguishability operator and the t-norm T chosen to define fuzzy transitivity. The key result is, strict Archimedean t-norms provide equivalence relations as their zero cuts, and that property characterizes such t-norms. As a consequence, a decomposition theorem for such T-indistinguishabilities is proved.