Minimal fuzzy memberships and rules using hierarchical genetic algorithms

A new scheme to obtain optimal fuzzy subsets and rules is proposed. The method is derived from the use of genetic algorithms, where the genes of the chromosome are classified into two different types. These genes can be arranged in a hierarchical form, where one type of gene controls the other. The effectiveness of this genetic formulation enables the fuzzy subsets and rules to be optimally reduced and, yet, the system performance is well maintained. In this paper, the details of formulation of the genetic structure are given. The required procedures for coding the fuzzy membership function and rules into the chromosome are also described. To justify this approach to fuzzy logic design, the proposed scheme is applied to control a constant water pressure pumping system. The obtained results, as well as the associated final fuzzy subsets, are included in this paper. Because of its simplicity, the method could lead to a potentially low-cost fuzzy logic implementation.