Modus tollens with respect to uninorms: U-Modus Tollens
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 r...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Instituto de Salud Carlos III (ISCIII) |
| Repository: | Repisalud |
| Language: | English |
| OAI Identifier: | oai:repisalud.isciii.es:20.500.12105/22902 |
| Online Access: | https://hdl.handle.net/20.500.12105/22902 |
| Access Level: | Open access |
| Keyword: | Modus Tollens Uninorm Implication function RU-implication |
| Summary: | 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/). |
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