A modified interval type-2 Takagi-Sugeno fuzzy neural network and its convergence analysis. (November 2022)

• Record Type: Journal Article
• Authors: Gao, Tao; Bai, Xiao; Wang, Chen; Zhang, Liang; Zheng, Jin; Wang, Jian
• Is Part Of: Pattern recognition. Volume 131(2022)
• Publication Date: 2022-11
• Subjects: IT2 fuzzy model -- Fuzzy neural network -- Takagi-Sugeno -- Conjugate gradient -- Convergence; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2022.108861
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: 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. Abstract: In this paper, to compute the firing strength values of type-2 fuzzy models, a soft version of minimum is presented, which endows the fuzzy model with the ability to solve large dimensional problems. In addition, a conjugate gradient method is borrowed to train the designed interval type-2 Takagi-Sugeno fuzzy model. Compared with the existing gradient-based learning strategy, this scheme can efficiently enhance the fuzzy model performance. Last but not least, convergence analysis for this modified interval type-2 Takagi-Sugeno fuzzy neural network (MIT2TSFNN) is conducted in detail, which proves that the gradient of the error function tends to zero with the iteration increasing (weak convergence) and the sequence of model parameters (weights) convergences to a fixed point (strong convergence). To validate the effectiveness of the proposed MIT2TSFNN and its theoretical results, simulation results of six regression and six classification problems are presented.