Interval t-norms as Interval Representations of t-norms

In this paper a new interval generalization for t-norms is proposed. The main property of our generalization is that each interval t-norm can be seen as an interval representation of a t-norm and, therefore, can be used to deal with correctness of interval fuzzy algorithms. Moreover, how to obtain in a canonical way the best interval representation (interval t-norm) for a t-norm will be shown. Also it will be proved that the main classes of t-norms, such as continuous, Archimedean, without zero divisors, and idempotent, are preserved by these constructions