New Concepts in the Vague Graph Structure with an Application in Transportation

Abstract

Fuzzy graph (FG) models take on the presence being ubiquitous in environmental and fabricated structures by humans, specifically the vibrant processes in physical, biological, and social systems. Owing to the unpredictable and indiscriminate data which are intrinsic in real life and problems being often ambiguous, it is very challenging for an expert to exemplify these problems through applying an FG. Vague graph structure (VGS), belonging to the FG family, has good capabilities when facing with problems that cannot be expressed by FGs. VGS can handle the vagueness connected with the incompatible and determinate information of any real-world problem, where FGs may not succeed to bear satisfactory results. The previous definitions’ restrictions in FGs have led us to propose new definitions in the VGS. Domination is one of the key issues that has many applications in computer science and social networks. Today, many researchers are trying to prove its application in medical sciences and psychology. Therefore, in this paper, different concepts related to domination in VGSs such as Ni-dominating set, vague full dominating set, minimal $N_i$ -DS, and strong capacity Ni-dominating set are defined using some examples. Finally, an application of domination in medical sciences has been presented.