Linear Diophantine Fuzzy Sets: Image Edge Detection Techniques based on Similarity Measures

In the digital imaging process, fuzzy logic provides many advantages, including uncertainty management, adaptability to variations, noise tolerance, and adaptive classification. One of the techniques of digital image processing is the edge detection. The edge detection process is an essential tool to segment the foreground objects from the image background. So, it facilitates subsequent analysis and comprehension of the image’s underlying structural properties. This process can be moved on with the notion of fuzzy sets and their generalizations. The concept of Linear Diophantine fuzzy sets is a generalization of fuzzy sets where reference parameters correspond to membership and non-membership grades. This study aims to apply linear Diophantine fuzzy sets (LDFSs) to edge detection of images. The novelty of this paper is twofold. The first one is that we conduct a comprehensive evaluation to ascertain the similarity values using the linear Diophantine fuzzy similarity measure by leveraging the gray normalized membership values associated with fundamental edge detection techniques. The other is to modify the image pixels into the LDFSs and then filter the images by using the presented similarity measure operators given in the LDFS environment.