Hierarchical fuzzy inference based on Bandler-Kohout subproduct

Fuzzy inference with the Bandler-Kohout subproduct (BKS) has been successfully applied in many fields such as fuzzy control, artificial intelligence, image processing, data mining, decisionmaking, prediction, classification and so on. However, one has to face with the rule explosion in these applications. To deal with this problem, hierarchical fuzzy systems with the compositional rule of inference (CRI) method have been constructed by a series of low-dimensional sub fuzzy systems. And it has been proved that hierarchical fuzzy inference method can efficiently restrain the explosion of fuzzy rules. Therefore, in order to increase the computational efficiency of the fuzzy inference based on the BKS when multi -input -single -output (MISO) fuzzy rules are involved, this paper mainly constructs two hierarchical fuzzy inference methods based on the BKS in which the if-then rules are respectively interpreted by fuzzy implications and ML-implications. Moreover, the validity of the two BKS hierarchical fuzzy inferences is studied with the GMP rules. Finally, two examples are employed to illustrate the computational efficiency of our proposed BKS hierarchical inference methods.