On Some Classes of RU-Implications Satisfying U-Modus Ponens.

The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.