Modus Tollens on Fuzzy Implication Functions Derived from Uninorms

The most used inference schemes in approximate reasoning are the so-called Modus Ponens for forward inferences, and Modus Tollens for backward inferences. In this way, finding new fuzzy implication functions satisfying these two properties has become an important topic for researchers. In the framework of fuzzy logic, they can be written as two inequalities involving fuzzy implication functions. In this paper, the property of Modus Tollens with respect to a continuous t-norm and a continuous fuzzy negation is studied for residual implication functions derived from uninorms, that is, for RU-implications. The corresponding inequality is solved in the cases of an RU-implication derived from a uninorm U in the class of \(\mathscr {U}_{\min }\), from an idempotent uninorm or from a representable uninorm.

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