Simplified fuzzy model based on grey relation and data transformation techniques

Unlike the previous methods which relied on the given data, this paper depends on the preprocessed patterns to construct a satisfactory fuzzy model. The grey relational method is exploited to help determine the most appropriate premise variables for the fuzzy rules such that a simplified modeling procedure can be achieved. There is no need to refine the membership functions used in the fuzzy rules. Only the transformation functions and the consequent real numbers are required to be adjusted to satisfy the identification purpose. To validate how well the consequent singletons are adjusted, the refined parameters are compared with the desired values calculated by the least squared method. The results show that the adjusted parameters from the proposed model conform to the desired ones. Simulation results from different examples are presented to demonstrate the superiority of the proposed model to the conventional methodologies.