Approximation Forms of Soft Subgraph and Its Application on the Cardiovascular System

Abstract

The incorporation of many various and modern mathematical tools provides efficient and successful methods to model problems with uncertainty such as graph theory, Fuzzy sets, rough sets and soft sets. This powerful incorporation of the three different concepts rough sets, soft sets and graphs is known as soft rough graphs that is introduced previously by Noor et al. The aim of this paper is to propose new concepts of linking soft set, rough set and graph theory in order to create new types of sub-graphs according to properties on the original graph by using generalized relationship through the out-link vertices or directed cycle. Our approach is based on introducing new structure for the roughness of the soft graphs by defining new types of operators by using closed paths. Then, it applies all of these concepts to the cardiovascular system in the human body in order to explain some phenomena and medical facts in a mathematical style. Finally, it discusses the comparison properties and containment relationships between various kinds of new approximation soft subgraph.