Sensitivity analysis of Takagi-Sugeno fuzzy neural network

In this paper, we first define a measure of statistical sensitivity of a zero-order Takagi- Sugeno (TS) fuzzy neural network (FNN) with respect to perturbation of weights and parameters of the system. Then we derive measures of sensitivity of the system with respect to additive and multiplicative noises to the consequent parameters. For this we consider a multiple-input multiple-output (MIMO) FNN. The derivation can be easily extended to sensitivity with respect to other parameters as well. These measures of sensi-tivity are then used as regularizers to the loss function while training the system. Finally, to validate the sensitivity-based learning method, another definition of statistical sensitivity measure, based on absolute output error, is proposed, and its corresponding expression for additive/multiplicative perturbations of the consequent parameters is derived as well. Using simulation results on one classification problem and two regression problems, the effectiveness of the sensitivity measures is demonstrated. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper defines a measure of statistical sensitivity of a zero-order Takagi-Sugeno (TS) fuzzy neural network (FNN) with respect to perturbation of weights and parameters, as well as derive measures of sensitivity of the system to additive and multiplicative noises to the consequent parameters. These sensitivity measures are used as regularizers to the loss function during training, and their effectiveness is demonstrated through simulation results on classification and regression problems.