Residual implications derived from uninorms satisfying Modus Ponens

Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RU implications, satisfy the modus ponens with respect to a continuous t-norm T , or equivalently, when they are T -conditionals. For RU -implications it is proved that T -conditionality only depends on the underlying t-norm TU of the uninorm U used to derive the residual implication and this fact leads to a lot of new solutions of the Modus Ponens property. Along the paper the particular cases when the uninorm lies in any of the most usual classes of uninorms are considered.