Equivalence between type-2 TSK fuzzy model and uncertain Gaussian mixture model
Qinli Zhang, Shitong Wang · Control theory & applications · 2009
This work explores how the uncertain Gaussian mixture model(UGMM)can be translated to an additive type-2 TSK(Takagi-Sugeno-Kang)fuzzy logic system.The mathematical equivalence between the conditional mean of a UGMM and the defuzzified output of a type-2 TSK fuzzy model(T2-TSK-FM)is proved.The relationship between a UGMM and a T2-TSK-FM,and the conditions for UGMM to T2-TSK-FM translation is made explicit in the form of a theorem.The proposed results provide a new method for constructing a T2-TSK-FM by interpreting a fuzzy system from a probabilistic viewpoint.Instead of estimating the parameters of the fuzzy rules directly,the parameters of a UGMM are estimated using any popular density estimation algorithm,such as expectation maximization.The proposed approach is also applied to Mackey-Glass chaotic time series.After comparing the simulation results with those obtained with other system modeling tools,it can be claimed that successful results are achieved.