Fuzzy Implication and Compatibility Modification

The authors examine the separability of several common families of compatibility modification (CM) inference techniques. CM fuzzy inference separates the evaluation of the antecedent of a rule from the generation of the output. The determination of the degree to which the input matches the antecedent is determined by a compatibility measure and an aggregation operator. The order in which these operations occurs changes the set of applicable rules. Separability conditions are introduced to define circumstances in which rule evaluation is independent of the input evaluation strategy. It is shown that compatibility modification inference using fuzzy partial matching and Minkowski dissimilarity satisfies several separability conditions.