| Function approximation is a common task or problem in the research and application of science and technology. This problem can be solved by several kinds of models, such as the artificial neural network (ANN), the fuzzy inference system (FIS), etc. By unifying the ANN and FIS, an adaptive-network-based fuzzy inference system (ANFIS), can not only solve the problem of function approximation in high precision, but also convey the human knowledge related to the problem at hand. Hence, the ANFIS has been widely used in many disciplines and applications.; However, the capability of ANFIS is still limited by the dilemma between the approximation precision and the fuzzy interpretability and the dilemma between the approximation precision and the learning speed. To solve these issues, this thesis advocates the idea of flexible fuzzy interpretability, and suggests a new membership function based on the flexible fuzzy interpretability; in order to fully exploit the capability of ANFIS, a random parallel gradient decent (GD) algorithm has been selected and customized as part of the learning algorithms. The new model is called: flexible ANFIS (FANFIS). The frequently used 2-D sinc and a newly developed 2-D ragged benchmark functions have been used in extensive computer simulations organized by design of experiments and analyzed by analysis of variance techniques. The simulation results show the effectiveness and superiority of FANFIS over the original ANFIS. Furthermore, the ideas of flexible interpretability and random parallel GD not only can be used for other types of FIS, but also implies new perspectives of human-computer interaction on knowledge engineering. |
