An improved Takagi-Sugeno fuzzy model with multidimensional fuzzy sets

Abstract

In this study, we propose fuzzy modeling algorithm to improve Takagi-Sugeno fuzzy model. This algorithm initially finds desirable number of rules at once, in advance, and then identifies the premise and consequent parameters separately by fixing number determined. The proposed algorithm consists of three stages: determination of the optimal number of fuzzy rules, coarse tuning of parameters and fine tuning of these parameters. To find the optimal number of rules, the new cluster validity algorithm that is based on the validity criterion V-sv adapted to the usage of FCRM-like clustering, is proposed. In coarse tuning, by using the mentioned clustering algorithm for input-output data and the projection scheme, the consequent and premise parameters are coarsely defined. In fine tuning, the gradient descent (GD) method is used to precisely adjust parameters of fuzzy model but unlike other similar modeling algorithms, the premise parameters are adjusted with respect to multidimensional membership function in premise part of rule. Finally, two examples are given to demonstrate the validity of suggested modeling algorithm and show its excellent predictive performance.