Fernandez-Peralta, RaquelMassanet, SebastiaMesiarová-Zemánková, AndreaMir, Arnau2024-10-042024-10-042022Fernandez-Peralta R, Massanet S, Mesiarová-Zemánková A, Mir A. A general framework for the characterization of (S,N)-implications with a non-continuous negation based on completions of t-conorms. Fuzzy Sets Syst. 2022 Aug;441:1-32.0165-0114http://hdl.handle.net/20.500.13003/18520https://hdl.handle.net/20.500.12105/23364The characterization of (S, N)-implications when Nis a non-continuous negation has remained one of the most significant open problems in fuzzy logic for the last decades. This paper constitutes the first progress in this topic. Namely, a general characterization of this family of fuzzy implication functions is presented, in which the central property is the existence of a completion of a binary function defined on a certain subregion of [0, 1]2 to a t-conorm. In this paper, the dual problem of finding a completion of a binary function defined on a subregion of [0, 1]2 to a continuous t-norm is studied and solved for the minimum and a cancellative function. These results are the basis for the novel axiomatic characterizations of (S, N)-implications in the case when Nhas one point of discontinuity and Sis equal to the maximum t-conorm in a certain subregion of [0, 1]2 or a strict t-conorm.enghttp://creativecommons.org/licenses/by-nc-nd/4.0/research articleAttribution-NonCommercial-NoDerivatives 4.0 Internacional441110.1016/j.fss.2021.06.009Fuzzy Sets and Systemsopen access2-s2.0-85109832835