Consistency of models for approximate reasoning and systems of fuzzy relational equations

Necessary and sufficient conditions for validity of the Generalized Modus Ponens scheme of inference are suggested in the general case where t-norm is arbitrary. The special cases of t-norms (min and Lukasiewicz t-norm) are considered separately with examples. The used techniques is based on solving the system of fuzzy relation equations. Thus the obtained results can also be interpreted as necessary and sufficient conditions for consistency of fuzzy relational equation systems