On a class of left-continuous t-norms

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Authors:
Roberto Cignoli
Francesc Esteva
Lluís Godo
Franco Montagna
Title: On a class of left-continuous t-norms
Journal: Fuzzy Sets and Systems
Volume 131
Number 3
Pages: 283-296
Year: 2002




Abstract

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.