A modified interval type-2 Takagi-Sugeno fuzzy neural network and its convergence analysis

Highlights：

• To tune the fuzzy rule parameters, the conjugate gradient method is employed to realize the backpropagation task and the iterative updating formulas are deduced. Using simulation results, the performance enhancement of the conjugate method based fuzzy model is proved.

• Convergence analysis of the MIT2TSFNN is presented, which provides the theoretical foundation for the application of IT2 fuzzy model. Weak convergence illustrates that the real data structure can be approximated using IT2 fuzzy model. Strong convergence shows that the conjugate gradient method can help the fuzzy model get the optimal structure.

摘要

•For the forward process, the clustering algorithm is employed to generate the initial interval type-2 fuzzy rules, and we illustrate the interpretable mathematical process. In addition, a soft version minimum is used as the T-norm operation of IT2TSFNN to realize fuzzy reasoning, and it can be applied to any other fuzzy models to solve the problem of vanishing firing strength due to a lot of input features.•To tune the fuzzy rule parameters, the conjugate gradient method is employed to realize the backpropagation task and the iterative updating formulas are deduced. Using simulation results, the performance enhancement of the conjugate method based fuzzy model is proved.•Convergence analysis of the MIT2TSFNN is presented, which provides the theoretical foundation for the application of IT2 fuzzy model. Weak convergence illustrates that the real data structure can be approximated using IT2 fuzzy model. Strong convergence shows that the conjugate gradient method can help the fuzzy model get the optimal structure.