Characterizing non-monotonic fuzzy relations

Abstract

 This paper is on &-T-monotonic Fuzzy Relations and on the particular case of &-Monotonic Fuzzy Relations (in the crisp case &-Weakly-monotonic and &-Strongly-monotonic Relations, respectively). It goes a little further of the previous work the authors did on this kind of Fuzzy and Crisp Relations by proving a Characterization Theorem of &-T-monotonicity for Reflexive Fuzzy Relations that contains all the former results. This theorem is not only particularized to the crisp case but it is shown that then only crisp Logical States are needed. Of course, also Non-&-T-monotonic Fuzzy Relations and Non-Weak-&-monotonic crisp Relations became characterized.