Optimal set placement and multidimensional fuzzy sets for fuzzy logic controllers

This paper describes knowledge representation in a fuzzy logic controller (FLC) with respect to the placement of an optimal number of linguistic descriptive sets. The number of sets is shown to be optimal, any less and the information in an expert scheme is not conveyed, and any more introducing redundancy. The basic theory of optimal set placement is described for a SISO controller. The extension of this theory for MIMO controllers is achieved with the introduction of n-dimensional fuzzy sets. That is, sets that contain more than one input space within their defined domain. The advantage of this approach is a reduction in the number of rules required to represent a nonlinear multi-input control scheme. A deterministic FLC is then presented using the theories of optimal set placement and n-dimensional set theory.