The need of function approximations arises in many branches of applied mathematics and computer science. Fuzzy system is one of the nonlinear models which have been used in function approximation. Compare with other model, fuzzy system has the advantage of cooperation with human language and understanding....[ Read more ]

The need of function approximations arises in many branches of applied mathematics and computer science. Fuzzy system is one of the nonlinear models which have been used in function approximation. Compare with other model, fuzzy system has the advantage of cooperation with human language and understanding.

To achieve a higher approximation requirement using fuzzy system, the usual method is increasing the rules in the system with existing membership function. However, this reduces the generalization ability. The purpose of this research is to explore a higher-order membership function constructed from normalized B-splines. Fuzzy system adopted such membership function can achieve better approximation accuracy with the same number of fuzzy rules compared with the system using ordinary membership function.

In the thesis, some traditional and fuzzy system models for function approximation are introduced first. Then the ordinary and higher-order membership function are investigated in the second part of the thesis. In the third part, we develop the fuzzy systems using the higher-order membership function to do function approximate in one dimensional case. Finally, we extend the fuzzy systems to two dimensional and multi dimensional function approximation.