A new extension of fuzzy C-Means algorithm using non Euclidean distance and kernel methods

Most of processes in industry are characterized by nonlinear and time-varying behavior. Nonlinear system identification is becoming an important tool which can be used to improve control performance [9]. Among the different nonlinear identification techniques, the Takagi Sugeno fuzzy model has attracted most attention of several researches. In literature, several fuzzy clustering algorithms have been proposed to identify the parameters involved in the Takagi-Sugeno fuzzy model, as the Fuzzy C-Means algorithm (FCM) and Fuzzy C-Means algorithm using non-Euclidean distance (NFCM). This paper presents a new Clustering algorithm for Takagi-Sugeno fuzzy model identification. The proposed algorithm is an extension of the NFCM algorithm called New Extension of Fuzzy C-Means algorithm based on kernel method (KNFCM) and non-Euclidean distance, where the non-Euclidean distance using the Gaussian kernel function. The proposed algorithm (KNFCM) can solve the nonlinear separable problems found by FCM and NFCM. So the KNFCM algorithm is more robust than FCM and NFCM.