t-norms induced by metrics on Boolean algebras

Let d _ν be the metric associated with a strictly positive submeasure ν on some Boolean algebra . If d _ν is bounded from above by 1, E _ν=1−d _ν is a (fuzzy) similarity relation on at least w.r.t. the Lstrok ukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms.In this paper, we show that under certain assumptions on and ν, we may associate with ν in a natural way a continuous t-norm w.r.t. which E _ν is a similarity relation and which, in a certain sense, is the weakest such t-norm. Up to isomorphism, every continuous t-norm arises in this way