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- Title
Transformation between type-2 TSK fuzzy systems and an uncertain Gaussian mixture model.
- Authors
Qinli Zhang; Fu-lai Chung; Shitong Wang
- 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.
- Subjects
FUZZY systems; GAUSSIAN measures; MATHEMATICAL models; MATHEMATICAL formulas; FREE probability theory
- Publication
Soft Computing - A Fusion of Foundations, Methodologies & Applications, 2010, Vol 14, Issue 7, p701
- ISSN
1432-7643
- Publication type
Article
- DOI
10.1007/s00500-009-0459-4