From fuzzy center average defuzzifier (CAD) to fuzzy lookup table controller (FLTC) with an efficient Heaviside search algorithm (HSA)

Abstract

This paper proposes an alternate interpretation of the traditional lookup table controller via the center average defuzzifier (CAD) in fuzzy set theory with a set of disjoint block pulse membership functions (DBPMFs). The DBPMFs with CAD can be proved to be equivalent to the traditional fuzzy lookup table controller (FLTC). Further, a new Heaviside search algorithm (HSA) is also proposed to implement the FLTC in a more efficient way. The HSA is to find the indices for every fuzzy input variable independently, in order to speed up the table-searching process. The computational complexity of our new HSA is far less than the complexity of the traditional linear search algorithm (LSA), where HSA is the sum of Ri, where Ri is the number of membership functions for ith input variable in FLTC. The average computational complexity in LSA is the product of Ri divided by 2. The HSA also reduces the complexity of coding significantly in the same order as the comparison of computation complexities between HSA and LSA. The balancing of the inverted pendulum system is adopted as the benchmark to show the feasibility and efficiency of this new FLTC and HSA.