On least coherence-preserving negations

We focus on the notion of coherent L-interpretations with respect to a negation operator, as a convenient generalization to a fuzzy or multiple-valued environment of the classical notion of consistent interpretation. We show that, given an L-interpretation I, the set of negation operators n satisfying that I is coherent w.r.t. n has a structure of complete lattice; so there exists the greatest and the least negation operators satisfying such property; moreover, the expression of the least negation operator n satisfying that I is coherent w.r.t. n is presented. Finally, for the case in which the underlying set of truth-values is the real unit interval [0, 1], we describe a method to achieve a practical expression for the least coherence-preserving negation.