# 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

arXiv: https://arxiv.org/abs/2108.08704 · HTML: https://mlsanity.com/paper/2108.08704/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 93 references that are in the map.
- First posted on arXiv 11 Aug 2021.

## Builds on (most cited first, 2 of 2)

- [Backpropagation-Free Learning Method for Correlated Fuzzy Neural Networks](https://mlsanity.com/paper/2012.01935/) (2020)
- [A self-organizing fuzzy neural network for sequence learning](https://mlsanity.com/paper/1908.00617/) (2019)

## Built on by (most cited first, 4 of 4)

- [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)
- [A Self-organizing Interval Type-2 Fuzzy Neural Network for Multi-Step Time Series Prediction](https://mlsanity.com/paper/2407.08010/) (2024)
- [A novel evolutionary-based neuro-fuzzy task scheduling approach to jointly optimize the main design challenges of heterogeneous MPSoCs](https://mlsanity.com/paper/2203.14717/) (2022)
- [UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification](https://mlsanity.com/paper/2211.00599/) (2022)

## Abstract (arXiv)

In this paper, a new interval type-2 fuzzy neural network able to construct non-separable fuzzy rules with adaptive shapes is introduced. To reflect the uncertainty, the shape of fuzzy sets considered to be uncertain. Therefore, a new form of interval type-2 fuzzy sets based on a general Gaussian model able to construct different shapes (including triangular, bell-shaped, trapezoidal) is proposed. To consider the interactions among input variables, input vectors are transformed to new feature spaces with uncorrelated variables proper for defining each fuzzy rule. Next, the new features are fed to a fuzzification layer using proposed interval type-2 fuzzy sets with adaptive shape. Consequently, interval type-2 non-separable fuzzy rules with proper shapes, considering the local interactions of variables and the uncertainty are formed. For type reduction the contribution of the upper and lower firing strengths of each fuzzy rule are adaptively selected separately. To train different parameters of the network, the Levenberg-Marquadt optimization method is utilized. The performance of the proposed method is investigated on clean and noisy datasets to show the ability to consider the uncertainty. Moreover, the proposed paradigm, is successfully applied to real-world time-series predictions, regression problems, and nonlinear system identification. According to the experimental results, the performance of our proposed model outperforms other methods with a more parsimonious structure.