Simplifying fuzzy modeling by both gray relational analysis and data transformation methods

Instead of following the traditional approaches which utilize original data patterns to construct the fuzzy model, this paper proposes to exploit both gray relational analysis and data transformation techniques to simplify the modeling procedures. The transformation method allows us to map the original data to other domains such that there is no need to adjust the membership functions and the fuzzification process is simply taking place on the fixed ones. Since too many system variables involved may complicate the fuzzy modeling, the gray relational method is exploited to select the crucial variables from a finite set of candidates. Based on the calculated relational degrees between the output and the prospective input variables, we can decide which are the important premise variables. The proposed methods have definite effects on the model's performance; therefore, the way to systematically adjust the transformation functions is also investigated. Ease in selecting the premise variables and minimal effort needed to adjust system parameters are the merits of the proposed work. Simulation results from two different examples are presented to demonstrate the superiority of the proposed model to the conventional methodologies. (C) 1999 Elsevier Science B.V. All rights reserved.