Fuzzy Rule Interpolation Methods Based on Sparse Rule Bases

Abstract

Fuzzy rule interpolation algorithms have broad applications in computational fuzzy inference systems. This paper systematically introduces interpolation methods based on α-cuts. It focuses on two classical α-cut-based interpolation methods: the KH fuzzy rule interpolation method and the Lagrange fuzzy rule interpolation method. Through theoretical analysis and comparative studies, the fundamental principles, performance characteristics, and limitations of these two interpolation algorithms are explored in depth. Based on this, a fuzzy inference system for the "tip calculation problem" was constructed using the MATLAB Fuzzy Toolbox. Empirical studies were conducted to verify the necessity and feasibility of applying fuzzy rule interpolation techniques in sparse rule bases. The results indicate that fuzzy rule interpolation methods effectively enhance inference performance in sparse rule bases, providing essential theoretical foundations and practical support for the application of fuzzy inference systems.