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Modus tollens with respect to uninorms: U-Modus Tollens.
- Source :
-
International Journal of Approximate Reasoning . Dec2020, Vol. 127, p54-69. 16p. - Publication Year :
- 2020
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *APPROXIMATE reasoning
*FUZZY logic
Subjects
Details
- Language :
- English
- ISSN :
- 0888613X
- Volume :
- 127
- Database :
- Academic Search Index
- Journal :
- International Journal of Approximate Reasoning
- Publication Type :
- Periodical
- Accession number :
- 147019824
- Full Text :
- https://doi.org/10.1016/j.ijar.2020.10.003