Details

Autor(en) / Beteiligte

• Aguiló, Isabel
• Riera, Juan Vicente
• Suñer, Jaume
• Torrens, Joan

Titel

Modus tollens with respect to uninorms: U-Modus Tollens

Ist Teil von

• International journal of approximate reasoning, 2020-12, Vol.127, p.54-69

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Elsevier ScienceDirect Journals

Beschreibungen/Notizen

• 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.