Fuzzy-UCS Revisited: Self-Adaptation of Rule Representations in Michigan-Style Learning Fuzzy-Classifier Systems

TL;DR

This work investigates how rule representation shapes classification performance in Michigan-style LFCSs and introduces Adaptive-UCS, a self-adaptive variant of Fuzzy-UCS that uses a fuzzy indicator to switch between crisp (rectangular) and fuzzy (triangular) rule conditions. By evolving the representation alongside traditional rule parameters, Adaptive-UCS achieves superior classification accuracy and robustness to noise and missing values on both benchmark and real-world datasets, particularly excelling at oblique decision boundaries. The approach unifies crisp and fuzzy rule representations under a single evolving framework and demonstrates potential for extending to other LCS families (e.g., XCSF) and evidential reasoning paradigms. Overall, the self-adaptive rule representation mechanism offers a practical path to more robust, adaptable fuzzy classifiers in uncertain data environments.

Abstract

This paper focuses on the impact of rule representation in Michigan-style Learning Fuzzy-Classifier Systems (LFCSs) on its classification performance. A well-representation of the rules in an LFCS is crucial for improving its performance. However, conventional rule representations frequently need help addressing problems with unknown data characteristics. To address this issue, this paper proposes a supervised LFCS (i.e., Fuzzy-UCS) with a self-adaptive rule representation mechanism, entitled Adaptive-UCS. Adaptive-UCS incorporates a fuzzy indicator as a new rule parameter that sets the membership function of a rule as either rectangular (i.e., crisp) or triangular (i.e., fuzzy) shapes. The fuzzy indicator is optimized with evolutionary operators, allowing the system to search for an optimal rule representation. Results from extensive experiments conducted on continuous space problems demonstrate that Adaptive-UCS outperforms other UCSs with conventional crisp-hyperrectangular and fuzzy-hypertrapezoidal rule representations in classification accuracy. Additionally, Adaptive-UCS exhibits robustness in the case of noisy inputs and real-world problems with inherent uncertainty, such as missing values, leading to stable classification performance.

Figures (19)

• Figure 1: The illustration on the left depicts a fuzzy set $A_i=(a_i,b_i,c_i,d_i)$ that is characterized by a trapezoidal membership function. On the right is the illustration of the matching degree landscape of a 2-dimensional rule $k$ where $A_1^k=A_2^k=(0.1, 0.3, 0.7, 0.9)$, with white indicates $\mu_{{\bm A}^k}(\cdot)=0$, black indicates $\mu_{{\bm A}^k}(\cdot)=1$ (i.e., a certain region), and the shades of gray indicate $\mu_{{\bm A}^k}(\cdot)\in (0,1)$ (i.e., a vague region).
• Figure 2: A fuzzy set $A_i=(c_i,s_i)$ in Adaptive-UCS. The membership function of $A_i$ is self-adapted based on the fuzzy indicator $\mathcal{F}_i\in\mathbb{B}$.
• Figure 3: $\bm{\mathcal{F}}=(0, 0)$
• Figure 4: $\bm{\mathcal{F}}=(0, 1)$
• Figure 5: $\bm{\mathcal{F}}=(1, 0)$