On the Suitability of the Bandler-Kohout Subproduct as an Inference Mechanism

Fuzzy Relational Inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. Especially, the compositional rule of inference (CRI) introduced by Zadeh has attracted the most attention so far. In this work we show that the FRI scheme based on the BandlerKohout subproduct along with a suitable realisation of the fuzzy rules, does possess all the important properties cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions the equivalence of First Infer Then Aggregate and First Aggregate Then Infer (FITA and FATI) inference strategies can be shown for the Bandler-Kohout subproduct (BK-Subproduct), much like in the case of CRI. Finally, by way of addressing the computational complexity that may exist in the Bandler-Kohout subproduct we suggest a hierarchical inferencing scheme. Thus this work shows that the BK-subproduct based FRI is as effective and efficient as the CRI itself.