On the characterizations of (S,N)-implications

The characterization of S-implications generated from strong negations presented firstly by Trillas and Valverde in 1985 is well-known in the literature. In this paper we show that some assumptions are needless and present two characterizations of S-implications with mutually independent requirements. We also present characterizations of (S,N)-implications obtained from continuous fuzzy negations or strict negations. Besides these main results some new facts concerning fuzzy implications, fuzzy negations and laws of contraposition are proved.