Erratum to 'On the characterizations of (S, N)-implications' [Fuzzy Sets and Systems 158 (2007) 1713-1727]

摘要

We would like to bring to the notice of the readers, that point (i) of Theorem 5.2 on p. 1725 correctly should read (ⅰ) I is an (S, N)-implication generated from some t-conorm S and some strict negation N. Also the last two examples in Table 1 on p. 1717 are not correct. The function I(x,y) ={1-x if y= 0, y if x=1, 1 otherwise satisfies (EP), since it is an (S, N)-implication generated from the drastic t-conorm and the classical negation. The function I(x,y)=1-x if y=0, y if x = l, 0 otherwise does not satisfy (EP), because for x = 0.3, y = 0.5 and z = 0.5 we get I(x, I(y, z)) = 0.7 ≠ 0.5 = I(y, I(x, z)). The corrected last two rows are provided in Table 1 here.