An Application of Linear Diophantine Fuzzy Sets to the Edge Detection Techniques

The utilization of fuzzy set theory within the domain of image processing provides a lot of advantages such as encompassing the management of uncertainty, adaptability to variations, noise tolerance and adaptive classification compared to the other techniques. These advantages contribute to heightened precision and adaptability in the realm of image processing, enabling more precise and versatile handling of visual data. The process of edge detection performs a pivotal role in the segmentation of foreground objects from the image background. So, it facilitates subsequent analysis and comprehension of the image’s underlying structural properties through complex computational procedures. This complex process can be handled with the notion of fuzzy sets and their generalizations. The concept of linear Diophantine fuzzy sets is a generalization of fuzzy sets where the use of reference parameters corresponds to membership and non-membership grades. The aim of this study is to give an application of linear Diophantine fuzzy sets to edge detection of images. For this aim, we conduct a comprehensive evaluation to ascertain the similarity values using the linear Diophantine fuzzy similarity measure by leveraging the normalized membership values of the gray level associated with fundamental edge detection techniques.