Multi-Adjoint Algebras Versus Extended-Order Algebras

Adjoint triples are an interesting generalization of t-norms and their residuated implications, since they increase the flexibility in the framework where they are used. Following the same motivation of adjoint triples, in order to reduce the mathematical requirements for the computation, extended-order algebras are studied. Extended-order algebras are implicative algebras that generalize the integral residuated structures. In this paper, adjoint triples will be related to the operators considered in extended-order algebras. Furthermore, a comparison between adjoint negations and the negations introduced in extended-order algebras is presented.