Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part II

The continuous completions of conditionally cancellative pre-t-norms defined in the regions linked to the characterization of (S,N)-implications when S is a continuous t-conorm and N is a fuzzy negation with one point of discontinuity are determined. The results have been divided in two parts. In this second part, we use the results of the first part for providing the continuous completions of a conditionally cancellative pre-t-norm defined in the four remaining regions. The most significant contribution in this second part is the study of the case that corresponds to a region of the type B=([0,1]2∖(a,1)2)∪({c}×[0,1])∪([0,1]×{c}) with 0<a<c<1, which has to be separated in six different cases. © 2023 The Author(s)