How to determine the minimum number of fuzzy rules to achieve given accuracy: a computational geometric approach to SISO case

How to construct fuzzy systems using as less as possible rules with guaranteed performance is a difficult but important problem. In this paper, a computational geometry approach is introduced to determine the minimum number of rules required in building a fuzzy model to achieve a given approximation accuracy, from the input-output data of an unknown nonlinear system with single input and single output. The basic idea is to partition system input domain in a non-uniform manner according to the sampling data distribution and the approximation error tolerance. By borrowing concepts and tools from computational geometry, the problem is formulated and transformed into an edge-visibility problem and a tunnel algorithm is used to find the minimum rule number. Numerical examples are given to illustrate the ideas. Difficulties and potentials are discussed in extending to the multi-input case.