Towards More Flexible Fuzzy Membership Functions: Learning from Data

Fakhri Abbasov, Chao Chen, Jonathan M. Garibaldi

Abstract: Fuzzy systems are widely recognised for their ability to model uncertainty and linguistic knowledge, but their effectiveness often depends on the choice of membership functions. Traditional approaches have relied on membership functions with predefined, convex shapes to facilitate interpretability and computational efficiency. However, such constraints can limit the expressive power of fuzzy systems. This paper advocates for a more flexible and data-driven approach to fuzzy membership function design, using B-splines as a powerful example of adaptable, learnable shapes. Unlike previous approaches that impose boundary conditions, the learned B-splines are allowed to assume any shape required by the application domain. To optimise these flexible membership functions, an Adaptive Network-based Fuzzy Inference System (ANFIS) is integrated with gradient-based techniques enabled by PyTorch’s automatic differentiation engine. This integration eliminates the need for manually derived gradients for each B-spline control point, thereby enhancing both the efficiency and reliability of the training process. Experimental evaluations on real-world datasets demonstrate that this flexible, data-driven approach captures complex, non-convex relationships effectively, leading to improved predictive performance and robustness.

External IDs:dblp:conf/fuzzIEEE/AbbasovCG25