Construction of an Analytical Method for Limiting the Complexity of Neural-fuzzy Models with Guaranteed Accuracy

We have proposed an analytical method for limiting the complexity of neural-fuzzy models that provide for the guaranteed accuracy of their implementation when approximating functions with two or more derivatives. The method makes it possible to determine the required minimal number of parameters for systems that employ fuzzy logic, as well as neural models.We have estimated the required number of neurons (terms) in a model, which ensure the accuracy required for the area of a model curve to approach the system one along the sections of function approximation. The estimate for an approximation error was obtained based on the residual members of decomposition, in the Lagrangian form, of areas of the approximated system function into a Maclaurin series. The results received make it possible to determine the required number of approximation sections and the number of neurons (terms) in order to ensure the assigned relative and absolute error of approximation.We have estimated the required number of neurons (terms) that provide for the necessary accuracy of model implementation based on the maximum deviation between the system and model curves along the section of approximation. This makes it possible to select, depending on the assigned required accuracy, the number of terms of fuzzy variables, input and output variables, linguistic rules, coordinates of modal values along the axes of input and output variables.To verify validity of the proposed solutions, we modeled the system curves in the Matlab/Simulink environment, which confirmed the guaranteed accuracy of their implementation in accordance with the analytical calculations reported earlier.The results obtained could be applied in modern intelligent technical systems of management, control, diagnosis, and decision-making. Using the proposed methods for selecting and applying the minimal number of terms (neurons) would help reduce the required computing power in nonlinear system

Construction of an Analytical Method for Limiting the Complexity of Neural-fuzzy Models with Guaranteed Accuracy

We have proposed an analytical method for limiting the complexity of neural-fuzzy models that provide for the guaranteed accuracy of their implementation when approximating functions with two or more derivatives. The method makes it possible to determine the required minimal number of parameters for systems that employ fuzzy logic, as well as neural models.We have estimated the required number of neurons (terms) in a model, which ensure the accuracy required for the area of a model curve to approach the system one along the sections of function approximation. The estimate for an approximation error was obtained based on the residual members of decomposition, in the Lagrangian form, of areas of the approximated system function into a Maclaurin series. The results received make it possible to determine the required number of approximation sections and the number of neurons (terms) in order to ensure the assigned relative and absolute error of approximation.We have estimated the required number of neurons (terms) that provide for the necessary accuracy of model implementation based on the maximum deviation between the system and model curves along the section of approximation. This makes it possible to select, depending on the assigned required accuracy, the number of terms of fuzzy variables, input and output variables, linguistic rules, coordinates of modal values along the axes of input and output variables.To verify validity of the proposed solutions, we modeled the system curves in the Matlab/Simulink environment, which confirmed the guaranteed accuracy of their implementation in accordance with the analytical calculations reported earlier.The results obtained could be applied in modern intelligent technical systems of management, control, diagnosis, and decision-making. Using the proposed methods for selecting and applying the minimal number of terms (neurons) would help reduce the required computing power in nonlinear system