Novel concepts in vague incidence graphs with application

Abstract

Fuzzy graph (FG) models enjoy the ubiquity of being in natural and humanmade structures, namely dynamic process in physical, biological, and social systems. As a result of inconsistent and indeterminate information inherent in real-life problems, which are often uncertain, it is highly difficult for an expert to model those problems based on an FG. Vague incidence graph (VIG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem, where FGs may fail to reveal satisfactory results. Also, VIGs are outstandingly practical tools for analyzing different computer science domains such as networking, clustering, capturing the image, and also other issues such as medical sciences, and traffic planning. Hence, in this research, we introduce new operations on VIGs, namely, maximal product, rejection, and residue product with several examples. Likewise, some results related to operations have been described.