Adjoint negations, more than residuated negations

Negation operators are useful operators, which have extensively been studied and used in different fuzzy settings, such as in fuzzy logic. This paper introduces a new and flexible kind of negation operator, based on adjoint triples, and which is called adjoint negation relative to a fixed element.Besides proving several interesting properties, the comparison with weak negations, studied by Trillas, Esteva et al., and pairs of weak negations introduced by Georgescu and Popescu, is presented. Furthermore, adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor.