On interval fuzzy negations

There exist infinitely many ways to extend the classical propositional connectives to the set [0,1], preserving their behaviors in the extremes 0 and 1 exactly as in the classical logic. However, it is a consensus that this issue is not sufficient, and, therefore, these extensions must also preserve some minimal logical properties of the classical connectives. The notions of t-norms, t-conorms, fuzzy negations and fuzzy implications taking these considerations into account. In previous works, the author, joint with other colleagues, generalizes these notions to the set U={[a,b]|0≤a≤b≤1}, providing canonical constructions to obtain, for example, interval t-norms that are the best interval representations of t-norms. In this paper, we consider the notion of interval fuzzy negation and generalize, in a natural way, several notions related with fuzzy negations, such as the ones of equilibrium point and negation-preserving automorphism. We show that the main properties of these notions are preserved in those generalizations.