Reasonable conclusions in fuzzy reasoning

We consider fuzzy implication operators which are extensions of the two valued logic implication operator and are non decreasing with respect to their second argument. Firstly, we analyze some features of these operators with regard to fuzzy reasoning with one rule. Then, as regards approximate reasoning with multiple rules, we demonstrate that, for an inference process using Sup-T composition in the context of Compositional Rule of Inference (CRI), a necessary condition to infer a reasonable conclusion is that the minimum be used as an aggregation operator. Finally, when the minimum is used as an aggregation operator we provide a sufficient condition to obtain a reasonable inference result.