Forecasting Higher-Order Fuzzy Time Series Using an Improved FCMeans Method

Abstract

Fuzzy time series models are extensively applied to forecast uncertain and nonlinear data. Although higher-order FTS frameworks capture richer temporal dependencies, their predictive accuracy critically depends on the partitioning of the data universe. Conventional techniques frequently rely on subjective judgments or heuristic adjustments, which compromise consistency and overall forecasting performance. To address this, we introduce an Improved Fuzzy C-Means partitioning approach for higher-order FTS, designed as a more principled and data-responsive mechanism. The proposed method enhances standard fuzzy C-means clustering by integrating variance-aware centroid initialization and an adaptive fuzziness strategy, thereby more accurately representing underlying data dynamics. When evaluated on the well-established benchmark of the University of Alabama enrollment series, the approach generates more coherent and stable fuzzy partitions, allowing higher-order logical relationships to be modeled with greater precision. Beyond demonstrated empirical improvements, the framework offers a generalizable solution for diverse forecasting contexts, including financial markets and resource management. By providing a more robust and scalable foundation for high-order fuzzy modeling, this Improved FCM method contributes meaningfully to both methodological advancement and practical forecasting applications across various domains.