Variable precision (I,SO)-fuzzy rough sets and their applications in image processing and fuzzy decision trees

Fuzzy rough set models based on non-associative aggregation functions (e.g., overlap, semi-overlap functions) lack flexibility. They have not been applied in classification task, and their advantages in image processing are underutilized. To address these issues, this study introduces fuzzy implications, semi-overlap functions, and variable precision parameters into fuzzy rough set theory, constructing a variable precision (I,SO)-fuzzy rough set model (VPISFRS) and innovatively applying it to image edge extraction and fuzzy decision tree construction. Specifically, first, combined with existing semi-overlap function-based rough set models, the VPISFRS model is established, and its basic mathematical properties are explored. Second, a fuzzy mathematical morphology operator (VPISFMM) is designed based on VPISFRS, which is integrated with the fuzzy C-means (FCM) algorithm to develop the VPIS-FCM image edge detection algorithm. Comparative experiments show that the images extracted by the proposed algorithm ensure edge integrity with less noise and superior FoM values. Finally, a VPISFRS-based decision tree generation algorithm (VPIS-FDT) is proposed for classification tasks. Experiments on 18 standard datasets show that the algorithm outperforms the comparison algorithms in all five metrics: classification accuracy, precision, recall, F1-score and AUC.