On the non-monotonicity of fuzzy relations

In any monotonic logic the increase of premises does not lead to erase any conclusion. Nevertheless, this is not the case of common reasoning, in which often one has not all the necessary elements of judgement for obtaining totally valid conclusions. Frequently, one makes inferences with the available information, obtaining plausible results until new data force one to cancel them. This way, while in classic inference the basic concept is "truth", in the inference of common sense it should be "admissibility until new command". The giving up of the monotonicity leads to consider weaker properties getting some different kinds of nonmonotonic logics, according to the desirable properties at each framework. This paper presents a definition of weak monotonicity, and some characterizations through logical states are obtained. The authors' previous characterization of T-preorders is reached in a more general way. In particular, both the finite and the classical cases are studied. The last section is devoted to restricted monotonicity.<>