Boosting fuzzy classification rules under footprint of uncertainty of type-2 fuzzy sets

This paper presents a novel approach to improving classification accuracy in fuzzy rule-based systems by selecting Embedded Type-1 Fuzzy Sets (ET1 FSs) from Footprint of Uncertainty (FOU) areas. The method consists of three stages: (1) learning Type-1 fuzzy rules from predefined linguistic variables, (2) generating FOU areas with Interval Type-2 Fuzzy Sets (IT2 FSs), and (3) using the adaboost ensemble method, where multi-class problems are decomposed into binary classification tasks, and ET1 FSs are iteratively selected via genetic algorithms. By relying on IT2 FSs for the flexible partitioning of classification boundaries, the method enhances accuracy while addressing challenges in high-dimensional and multi-class problems. Experiments were performed on 12 UCI datasets and three image classification tasks using features from pre-trained convolutional neural networks. These datasets were selected to ensure diversity in dimensionality and class distribution. Comparative analyses with several state-of-the-art classification methods demonstrate that IT2 FSs can be effectively used to develop accurate classification systems. Additionally, this work analyzes trade-offs between complexity and interpretability by tuning FOU size (distinguishability) and adjusting the number of rules. The results show that a balanced FOU size and rule count yield better accuracy gains than either alone. Furthermore, several suitable trade-off regions with their parameters are presented.