A method of converting a fuzzy system to a two-layered hierarchical fuzzy system and its run-time efficiency

Abstract—In classical single-layer fuzzy systems (FSs), the num-ber of rules and the run-time computational requirements increase exponentially with the number of input domains. In this paper, we present a method for converting a multidimensional FS to a two-layer hierarchical FS that reduces the number of rules and improves the run-time efficiency. The first layer of the two-layer system consists of FSs whose rule bases can be represented as linearly independent vectors. The second layer constructs linear combinations of the rule base vectors. The effectiveness of the hier-archical conversion in reducing the number of rules and improving efficiency is demonstrated on a classic control problem and a sim-ulated higher dimensional FS. Index Terms—Hierarchical fuzzy system (HFS), rule reduction, run-time efficiency. I