Boolean implications are employed in inference schemas like modus ponens, modus tollens, etc., where the reasoning is done with statements or propositions whose truth-values are two-valued. Fuzzy implications play a similar role in the generalizations of the above inference schemas, where reasoning is done with fuzzy statements whose truth-values lie in [0, 1] instead of 0, 1. One of the best known application areas of fuzzy logic is approximate reasoning (AR) (Driankov et al. [84]), wherein from imprecise inputs and fuzzy premises or rules we obtain, often, imprecise conclusions. Approximate reasoning with fuzzy sets encompasses a wide variety of inference schemes and have been readily applied in many fields, among others, decision making, expert systems and fuzzy control. © 2008 Springer-Verlag Berlin Heidelberg.