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

• Published in: Fuzzy sets and systems Vol. 150; no. 2; pp. 199 - 209
• Main Authors: Wan, Feng, Shang, Huilan, Wang, Li-Xin, Sun, You-Xian
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2005; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Artificial intelligence; Computational geometric method; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Fuzzy identification; Logic and foundations; Mathematical logic, foundations, set theory; Mathematics; Pattern recognition. Digital image processing. Computational geometry; Piecewise linear approximation; Rule reduction; Sciences and techniques of general use; Set theory; System theory; Theoretical computing; Fuzzy identification; Rule reduction; Piecewise linear approximation; Computational geometric method; Computational geometry; Fuzzy system; Error estimation; Information processing; Approximation error; Fuzzy set; Non linear system; Algorithm
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/j.fss.2004.06.011

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.