On a class of left-continuous t-norms
|Title:||On a class of left-continuous t-norms|
|Journal:||Fuzzy Sets and Systems|
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*n y =0 if x<=n(y), x*n y=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.