Characterizations of (G, N)-implications

Fuzzy implications are one of basic connectives in both theoretical and applied communities of fuzzy set theory. The well known fuzzy implications are usually constructed in a specific way from t-norms, t-conorms and fuzzy negations, and according to construction methods, they can be roughly classified into five classes, namely (S, N)-implication, R-implication, QL-implication, Yager's implication and ordinal sum implication. Recently, a new variant of (S, N)-implication, called (G, N)-implication, was introduced by relaxing the t-conorm in an (S, N)-implication to be a grouping function which plays an important role in many applications such as classification, decision making and image processing, in which the associative property is not necessary. The present paper continues to study some further properties of (G, N)-implications, and the main results are some characterizations of (G, N)-implications.