RU and (U,N)-implications satisfying Modus Ponens

In this paper it is investigated when some kinds of fuzzy implication functions derived from uninorms satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. The study is done for RU-implications and ( U , N ) -implications with N a continuous fuzzy negation leading to a lot of solutions in both cases. For RU-implications T-conditionality only depends on the underlying t-norm of the uninorm used to derive the residual implication. On the contrary, for ( U , N ) -implications the underlying t-norm is never relevant and only the region out of the t-norm is so. Even the t-conorm can be not relevant also in some cases. Characterization of all residual implications for uninorms satisfying Modus Ponens.Study of Modus Ponens for ( U , N ) -implications.Modus Ponens (T-conditionality) for implications generated from uninorms.