An application of the proportional spherical fuzzy sets to color edge detection

Fuzzy set theory is a powerful mathematical framework for modeling uncertain and imprecise information and has been extended through various generalizations, including intuitionistic, Pythagorean, picture, and spherical fuzzy sets. Proportional spherical fuzzy sets, proposed in recent years, provide a more flexible modeling framework by establishing proportional relationships among membership, uncertainty, and non-membership degrees. However, their applications in image processing remain insufficiently explored. This study proposes a novel edge detection method for color images based on proportional spherical fuzzy sets. In the proposed approach, the relationships between neighboring pixels are evaluated using a proportional spherical fuzzy distance measure to identify edge regions. Unlike conventional approaches, the proposed method does not require the pixel values in the RGB channels to satisfy additional conditions, thereby reducing potential color and information loss. It also eliminates unnecessary processing steps, resulting in a simpler and more efficient edge detection process. The performance of the proposed method is evaluated against the classical Canny edge detection method using Precision, Recall, and Dice/F1 metrics. The experimental results show that the proposed method achieves Precision, Recall, and Dice/F1 values of 0.5422, 0.8845, and 0.6658, respectively, whereas the Canny method achieves 0.2445, 0.9871, and 0.3868. Although Canny provides a higher Recall, its considerably lower Precision indicates a high number of false-positive detections, which substantially reduces its overall F1/Dice performance. In contrast, the proposed method achieves a more balanced performance by significantly improving Precision while accepting a relatively small decrease in Recall. Consequently, the proposed method obtains an F1 score approximately 72% higher than that of the Canny method. These results demonstrate that proportional spherical fuzzy sets provide an effective and flexible framework for edge detection and have strong potential for real-world color image processing applications.