Algebra-based Fuzzy Rule Interpolation

: Through Exploitation of Rule Base Structure

Abstract

Fuzzy logic plays a crucial role in handling uncertainty, particularly in artificial intelligence systems. A key challenge in fuzzy rule-based systems is the issue of sparsity in rule bases, where gaps in the rule coverage can hinder inference accuracy. This thesis focuses on addressing these challenges by introducing a "location view" framework, particularly regarding the Takagi-Sugeno-Kang (TSK) and Mamdani models. The "location view" framework offers a novel geometric interpretation of fuzzy rule bases that enhances traditional fuzzy rule interpolation (FRI) algorithms. By incorporating directional parameters into rule selection, the location view enables more precise and contextaware comparisons of rules, leading to improved inference accuracy. This framework also provides insights into the limitations existing Transformation-based Fuzzy Rule Interpolation (T-FRI) algorithms, showing that using only two of the closest rules often yields better results than involving more rules, contrary to previous assumptions. Another contribution of this thesis is the enhancement of TSK model interpolation through a rule weight adjustment mechanism. This method, again based on the location view, refines the interpolation process by considering both the distance and direction between rules, significantly improving the accuracy of recently proposed K-Closest Rules (KCR) and K-Closest Rule Clusters (CRC) algorithms. Additionally, a new vector-based rule screening method is introduced, offering a more flexible approach to rule selection than traditional scalar distance metrics like Euclidean distance. This vector-based method allows for the consideration of both distance and direction, enhancing the accuracy of rule-based inferences. The proposed methods are validated through a series of experiments, demonstrating their effectiveness in improving FRI system performance when dealing with sparse rule bases. The contributions of this research offer valuable insights into the future development of fuzzy logic systems, with practical applications in decision-making, control systems, and pattern recognition.

Date of Award	2025
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Changjing Shang (Supervisor) & Qiang Shen (Supervisor)