A type-2 fuzzy c-regression clustering algorithm for Takagi–Sugeno system identification and its application in the steel industry

• Published in: Information sciences Vol. 187; pp. 179 - 203
• Main Authors: Fazel Zarandi, M.H., Gamasaee, R., Turksen, I.B.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.03.2012
• Subjects: Algorithms; Clustering; Fuzzy; Fuzzy logic; Fuzzy set theory; Gaussian mixture; Intervals; Iron and steel industry; IT2F c-regression clustering; Mathematical models; Multiple-regression; Steel industry; Structure identification; Weighted least square; Structure identification; Gaussian mixture; Multiple-regression; IT2F c-regression clustering; Steel industry; Weighted least square
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2011.10.015

This paper proposes a new type-2 fuzzy c-regression clustering algorithm for the structure identification phase of Takagi–Sugeno (T–S) systems. We present uncertainties with fuzzifier parameter “ m”. In order to identify the parameters of interval type-2 fuzzy sets, two fuzzifiers “ m 1 ” and “ m 2 ” are used. Then, by utilizing these two fuzzifiers in a fuzzy c-regression clustering algorithm, the interval type-2 fuzzy membership functions are generated. The proposed model in this paper is an extended version of a type-1 FCRM algorithm [25], which is extended to an interval type-2 fuzzy model. The Gaussian Mixture model is used to create the partition matrix of the fuzzy c-regression clustering algorithm. Finally, in order to validate the proposed model, several numerical examples are presented. The model is tested on a real data set from a steel company in Canada. Our computational results show that our model is more effective for robustness and error reduction than type-1 NFCRM and the multiple-regression.