Comparison of Two Approaches to Approximated Reasoning

A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-complexity, provided the minimum operator is chosen as t-norm. Otherwise, the time-complexity of both methods is the same. It is more efficient to first compile a set of fuzzy rules into a fuzzy relation, instead of aggregating inference results for each fuzzy rule separately