On two properties of the conditional in fuzzy logic

This paper deals with the classical properties of strengthening the antecedent, and weakening the consequent in fuzzy logic. Namely, it is studied in which algebras of fuzzy sets ([0, 1]^X, T, S, N), and with which conditional functions J, these two properties do hold. It should be noticed that the cases in which the first property is not valid are examples of a non-monotonic conditional's behaviour.