General fuzzy difference operator and its application in edge detector

This paper gives a more general definition of fuzzy difference operator by relaxing existing constraints, enabling a broader range of operator constructions. The characteristics and attributes of general fuzzy difference operator are thoroughly examined. Then, these novel constructions of general fuzzy difference operator are applied as fuzzy morphological gradient operators in edge detection. Experiments and analyses compare the proposed edge detection algorithm's performance with alternative methods, evaluating various configurations (t-norms, implications, and general fuzzy difference operators). The main findings of this study are: (1) By relaxing the condition, the generalized fuzzy difference operator can be constructed using various t-norms, implications, and fuzzy difference operators, offering greater flexibility in edge detector. (2) The experimental results show that novel fuzzy difference operators applied as fuzzy morphological gradient operators for edge detection in image processing perform better than those existing. • A more general definition of fuzzy difference operator is obtained. • Some tautologies in fuzzy setting corresponding to fuzzy difference operators are discussed. • Novel construction of fuzzy difference operators are utilized in edge detection.