2026-05-17T00:18:39Zhttps://repisalud.isciii.es/rest/oai/requestoai:repisalud.isciii.es:20.500.12105/229022024-11-28T20:03:55Zcom_20.500.12105_15322com_20.500.12105_2051col_20.500.12105_16967
Repisalud
author
Aguilo, Isabel
author
Riera, Juan Vicente
author
Suner, Jaume
author
Torrens, Joan
2024-09-13T09:13:26Z
2024-09-13T09:13:26Z
2020-12
Aguilo I, Vicente Riera J, Suner J, Torrens J. Modus tollens with respect to uninorms: U-Modus Tollens. Int J Approx Reasoning. 2020 Dec;127:54-69.
10.1016/j.ijar.2020.10.003
1873-4731
0888-613X
International Journal of Approximate Reasoning
http://hdl.handle.net/20.500.13003/17230
2-s2.0-85093646670
https://hdl.handle.net/20.500.12105/22902
591502900004
In fuzzy logic and approximate reasoning the inference rule given by the Modus Tollens usually derives into an inequality involving three logical operators: a conjunction, an implication function and a negation. Until now, in this scenario the conjunction has been commonly modeled by a t-norm, but recently the possibility of using a more general conjunction has been pointed out. In this work, we want to generalize the Modus Tollens inequality by using a conjunctive uninorm instead of a t-norm, leading to the so-called U-Modus Tollens. First, we give a study of this new property for implication functions in general and then we specially focus on residual implications derived from uninorms. In all cases, we prove that there are a lot of solutions of the U-Modus Tollens and we give a characterization of all the solutions in some particular cases. (c) 2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
eng
Modus Tollens
Uninorm
Implication function
RU-implication
Modus tollens with respect to uninorms: U-Modus Tollens
research article