Characterization of continuous t-norms compatible with Zadeh's probability of fuzzy events

In this work we study the concept of PZ-compatibility, which holds for those t-norms for which Zadeh's probability of fuzzy events fulfills Kolmogorov's axioms. Whether a probability satisfies Kolmogorov's axioms or not depends almost exclusively on the t-norm and dual t-conorm used to define intersection and union, respectively, of fuzzy sets. In order to better understand fuzzy probability theory, we provide a complete characterization of the PZ-compatible continuous t-norms.