Zadeh–MacFarlane–Jamshidi theorems on decoupling of a fuzzy rule base

This paper outlines the inspiration received by the author from the Zadeh–MacFarlane–Jamshidi trio in his pursuit concerning the theory and Application of fuzzy logic. Beginning with Zadeh’s pioneering work, a hierarchical control system was developed, in collaboration with MacFarlane, for application in robotic manipulators. Subsequently, the work was extended to an analytical basis for controller tuning using fuzzy decision making. On the prompting of Jamshidi to address the issue of knowledge-base simplification, theorems were developed related to decoupling a fuzzy rule base. These developments provided a theoretical basis for applying single-context decision making to a problem governed by the knowledge base of coupled fuzzy rules. The developed theorems establish an analytical equivalence between the decisions made from a coupled set of fuzzy rules and an uncoupled set of fuzzy rules concerning the same problem domain. These developments have been applied to supervisory control of an industrial fish cutting machine. The paper presents the pertinent theory and illustrative examples.