# Backpropagation-Free Learning Method for Correlated Fuzzy Neural Networks

arXiv: https://arxiv.org/abs/2012.01935 · HTML: https://mlsanity.com/paper/2012.01935/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [IT2CFNN: An Interval Type-2 Correlation-Aware Fuzzy Neural Network to Construct Non-Separable Fuzzy Rules with Uncertain and Adaptive Shapes for Nonlinear Function Approximation](https://mlsanity.com/paper/2108.08704/) (2021)
- [Parkinson's Disease Diagnosis based on Gait Cycle Analysis Through an Interpretable Interval Type-2 Neuro-Fuzzy System](https://mlsanity.com/paper/2109.02442/) (2021)
- [Multi-step-ahead Stock Price Prediction Using Recurrent Fuzzy Neural Network and Variational Mode Decomposition](https://mlsanity.com/paper/2212.14687/) (2022)
- [Crisp complexity of fuzzy classifiers](https://mlsanity.com/paper/2504.15791/) (2025)
- [UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification](https://mlsanity.com/paper/2211.00599/) (2022)
- [A fuzzy adaptive evolutionary-based feature selection and machine learning framework for single and multi-objective body fat prediction](https://mlsanity.com/paper/2303.11949/) (2023)

## Abstract (arXiv)

In this paper, a novel stepwise learning approach based on estimating desired premise parts' outputs by solving a constrained optimization problem is proposed. This learning approach does not require backpropagating the output error to learn the premise parts' parameters. Instead, the near best output values of the rules premise parts are estimated and their parameters are changed to reduce the error between current premise parts' outputs and the estimated desired ones. Therefore, the proposed learning method avoids error backpropagation, which lead to vanishing gradient and consequently getting stuck in a local optimum. The proposed method does not need any initialization method. This learning method is utilized to train a new Takagi-Sugeno-Kang (TSK) Fuzzy Neural Network with correlated fuzzy rules including many parameters in both premise and consequent parts, avoiding getting stuck in a local optimum due to vanishing gradient. To learn the proposed network parameters, first, a constrained optimization problem is introduced and solved to estimate the desired values of premise parts' output values. Next, the error between these values and the current ones is utilized to adapt the premise parts' parameters based on the gradient-descent (GD) approach. Afterward, the error between the desired and network's outputs is used to learn consequent parts' parameters by the GD method. The proposed paradigm is successfully applied to real-world time-series prediction and regression problems. According to experimental results, its performance outperforms other methods with a more parsimonious structure.