A unified deep learning framework for scalable learning and uncertainty quantification in interval Type-2 fuzzy logic systems

Abstract

Fuzzy Logic Systems are widely used in control, prediction, and modeling problems where uncertainty, nonlinearity, and complex input–output relationships are present. Their rule-based structure provides high interpretability, which makes them attractive for engineering applications. Type-1 Fuzzy Logic Systems have been successfully applied to many practical problems due to their simple and fixed structure. However, real-world data often include measurement noise, model uncertainty, and environmental variability. Because Type-1 Fuzzy Logic Systems use fixed membership functions, they cannot represent such uncertainties adequately, which limits their performance and applicability. To address these limitations, Interval Type-2 Fuzzy Logic Systems were introduced. In these systems, membership degrees are defined as intervals rather than single values through the use of the footprint of uncertainty. This structure allows uncertainty to be modeled in a more flexible and realistic manner. In regression problems, generating prediction intervals instead of only point predictions is especially important for safety-critical and high-risk applications. Interval Type-2 Fuzzy Logic Systems naturally support the generation of prediction intervals while preserving model interpretability. Despite these advantages, the practical use of Interval Type-2 Fuzzy Logic Systems is limited by high computational cost and poor scalability. Uncertainty processing relies on center of sets calculation methods, which are often iterative and require sorting operations. Methods such as the Karnik–Mendel Algorithm are computationally expensive and not suitable for parallel computation. As a result, training and inference become slow, particularly for large data sets and high-dimensional input spaces. Many existing learning methods for Interval Type-2 Fuzzy Logic Systems are direct extensions of methods developed for Type-1 Fuzzy Logic Systems. In these approaches, uncertainty-related parameters are treated as additional trainable variables, and learning mainly focuses on improving point prediction accuracy. Consequently, uncertainty quantification quality is not directly optimized, and prediction intervals may be unreliable. In addition, these methods do not effectively utilize modern machine learning tools such as mini-batch training, automatic differentiation, and graphics processing unit acceleration. The main objective of this thesis is to develop a unified learning framework that embeds Type-1 and Interval Type-2 Fuzzy Logic Systems into modern deep learning environments. The proposed framework aims to reduce computational cost, address high-dimensional input spaces, and directly optimize uncertainty information during learning. To achieve this, fuzzy system structures are reformulated using appropriate parameterization strategies, allowing unconstrained optimization and efficient mini-batch training. New inference formulations are proposed to remove the iterative structure of traditional center of sets calculation methods. All inference and learning operations are expressed in a fully vectorized and parallelizable form, enabling efficient execution on graphics processing units. Experimental results show that the proposed framework significantly reduces training and inference time while maintaining prediction accuracy and improving uncertainty estimation. In conclusion, this thesis presents an efficient and scalable learning framework that integrates fuzzy logic systems with modern deep learning tools. The proposed methods preserve the interpretability of fuzzy rule-based models while enabling reliable uncertainty modeling and practical applicability in large-scale and high-dimensional problems.