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VRF: Variance-Redistribution-Driven Fuzzy Rule Interpolation for TSK Models
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DOI：10.1109/TFUZZ.2026.3675847.png)
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Abstract
En 中文
Fuzzy rule interpolation (FRI) supports inference with sparse rule bases and plays a key role in Takagi–Sugeno–Kang (TSK) fuzzy model-based reasoning, such as regression and real-time prediction. Current TSK-based FRI methods mainly employ distance-driven or rule-level optimization strategies, implicitly assuming an unchanged geometric structure of the rule base. Recent findings, however, show that uneven variance allocation and directional imbalance in input data can induce rule selection bias, materially affecting interpolation behavior. This article introduces a variance-redistribution-driven mechanism for TSK-based FRI algorithms. With a one-to-one orthogonal transformation in the input data supported by principal component analysis, the method redistributes variance across data dimensions while strictly preserving the original geometric and topological relationships of the data. The transformed variance structure propagates to the generated fuzzy rule base, yielding more directionally balanced rule selection and improved interpolation stability. The VRF mechanism functions as a preprocessing step and can be directly coupled with existing TSK-based FRI algorithms without increasing online computational complexity. This work not only delivers a simple and general optimization method for a class of TSK-based FRI methods, but also extends the foundational theory of direction-aware FRI optimization by clarifying how input-space variance reshaping influences rule induction and interpolation bias. Experiments on benchmark datasets confirm that VRF reliably enhances accuracy and robustness, while also exposing directional-sensitivity-dependent limitations that motivate further parameter-specific analysis for the future.
Keywords:
Fuzzy rule interpolation (FRI)
principal component analysis (PCA)
Takagi–Sugeno–Kang (TSK) model
variance redistribution
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