2026-07-22T03:36:38Zhttps://repisalud.isciii.es/rest/oai/requestoai:repisalud.isciii.es:20.500.12105/233642024-10-04T13:16:19Zcom_20.500.12105_15322com_20.500.12105_2051col_20.500.12105_16967
Repisalud
author
Fernandez-Peralta, Raquel
author
Massanet, Sebastia
author
Mesiarová-Zemánková, Andrea
author
Mir, Arnau
2024-10-04T13:16:19Z
2024-10-04T13:16:19Z
2022
Fernandez-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.
10.1016/j.fss.2021.06.009
0165-0114
Fuzzy Sets and Systems
http://hdl.handle.net/20.500.13003/18520
2-s2.0-85109832835
https://hdl.handle.net/20.500.12105/23364
The 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.
eng
A general framework for the characterization of (S,N)-implications with a non-continuous negation based on completions of t-conorms
research article