On a class of left-continuous t-norms

摘要

In this paper we study the subclass of left-continuous t-norms *_n which are definable by an arbitrary continuous t-norm and a weak (i.e. non necessarily involutive) negation n by putting x _ny=0 if x≤n(y), x~* _ny=x~*y otherwise, thus generalizing the construction of the so-called nilpotent minimum t-norms. We provide the characterization of weak negations compatible with a given continuous t-norm and conversely which are the continuous t-norms compatible with a given weak negation function.