Transformation between type-2 TSK fuzzy systems and an uncertain Gaussian mixture model

Authors:
Qinli Zhang;Fu-lai Chung;Shitong Wang
Affiliations:
Southern Yangtze University, School of Information Technology, Wuxi, Jiangsu, China;Hong Kong Polytechnic University, Department of Computing, Hong Kong, China;Southern Yangtze University, School of Information Technology, Wuxi, Jiangsu, China
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2010

Citing 0
Cited 1

Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems

Information Sciences: an International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, an interval extension of the Gaussian mixture model called uncertain Gaussian mixture model (UGMM) is proposed and its transformation into the additive type-2 TSK fuzzy systems is presented. The conditions under which a UGMM becomes a corresponding type-2 TSK fuzzy system are derived theoretically. Furthermore, the mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy system is proved. Our results provide a new perspective for type-2 TSK fuzzy systems, i.e., interpreting them from a probabilistic viewpoint. Thus, instead of directly estimating the parameters of the fuzzy rules in a type-2 TSK fuzzy system, we can first estimate the parameters of the corresponding UGMM using any popular density estimation algorithm like the expectation maximization (EM) algorithm. Our experimental results clearly indicate that a type-2 fuzzy system trained in such a new way has higher approximation accuracy and stronger robustness than current type-2 fuzzy systems.