The best interval representations of t-norms and automorphisms

It is proved that interval t-norms supplied with interval automorphism is also a category, and a functor between these categories is provided that always returns the best interval representation of any t- norm and Automorphism and therefore can be used to deal with optimality of interval fuzzy algorithms.

Abstract

This paper relates an interval generalization for t-norms given by the authors to the interval generalization of automorphism given by M. Gehrke et al. Both interval extensions can be seen as interval representations and therefore satisfy the correctness principle of interval computations. T-norms and automorphisms can be seen as objects and morphisms, respectively, of a category. Analogously, we will prove that interval t-norms supplied with interval automorphism is also a category, and we provide a functor between these categories that always returns the best interval representation of any t-norm and automorphism and therefore can be used to deal with optimality of interval fuzzy algorithms.