Equivalence between type-2 TSK fuzzy model and uncertain Gaussian mixture model
二型Takagi-Sugeno-Kang模糊模型和不确定高斯混合模型的等价性

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.