Algorithms for training neuro-fuzzy networks and their adaptation for a network based on a bayesian logical-probabilistic model

Abstract

Neuro-fuzzy networks are promising hybrid models that combine the learning capabilities of neural networks with the linguistic interpretability of fuzzy rules base, making them an effective tool for solving tasks involving the approximation of complex nonlinear dependencies, while also providing potential explainability of the results. However, training these networks, including those based on a Bayesian logical-probabilistic fuzzy inference model (hereinafter referred to as the BLP-model), poses challenges due to the heterogeneity of their multi-layer structure, wherein each parametric layer has its own unique characteristics. The goal of this study is to adapt the training algorithms (backpropagation algorithm and a hybrid algorithm) to validate the operability and investigate the efficiency of this network. The scientific novelty of the study lies in the adaptation and application of modern optimization techniques, including normalized gradient descent method, AdaGrad, RMSprop, and Adam, to adjust the learning parameters of the neuro-fuzzy network based on the BLP-model. In the experimental phase, the developed software implementation of the model was compared to ANFIS (Adaptive Neuro-Fuzzy Inference System) from the MATLAB package, using the RMSE metric across several datasets. The results demonstrate that the adapted learning algorithms in combination with optimization methods achieve a level of quality comparable to that of ANFIS and, in some cases, even surpass it in terms of approximation accuracy with fewer epochs for training. The findings confirm the operability of the model’s software implementation and open avenues for the further development and application of neuro-fuzzy networks based on BLP-models in various fields that require approximation of functional dependencies and tools capable of handling uncertainty and imprecision in data. The limited access of Russian consumers to commercial software from foreign manufacturers highlights the practical significance of the developed tool based on the original model, making the solution relevant and beneficial for a wide range of users.