Fuzzy inferences using geometric compatibility or using graduality and ambiguity constraints
Valerie V. Cross, Marie‐Jeanne Lesot · 2017
In classical logic, Modus Ponens allows to infer new knowledge in the case where the antecedent of a given rule is observed, establishing that the rule conclusion then holds. Approximate reasoning extends the principle to the case where the observation does not totally match the rule antecedent. Several approaches have been proposed to deal with the extreme case where the observation is actually disjoint from the rule antecedent, using different principles to guide inference and avoid producing total uncertainty. This paper studies two of them, namely Geometric Compatibility Modification (GCM) and the Transformation-based Constraint-Guided Generalised Modus Ponens (T-CGMP), that respectively perform a type of approximate analogical reasoning and extend the GMP: it provides an indepth comparison, to determine their relationships, common points and distinct features. It thus provides guidelines for the definition of fuzzy inference schemes.