Abstract
Graphs are among the more ubiquitous models of natural and human-made structures. They are used to model with various categories of relations and process dynamics in biological and social systems. A vague graph has numerous applications in the fields of geometry and operational research. It has been a useful scope in various fields of computer science. In this paper, our important purpose of the study is to describe properties rejection, maximal product, symmetric difference and residue product of vague graphs which have been deeply discussion with different examples and moreover, we investigate some of their other related properties. We also presented the applications of vague set in medical diagnosis.
Highlights
Graph theory is an extremely useful tool for solving combinatorial problems in a wide range of fields, including geometry, algebra, number theory, topology, operations research, biology, and social systems
Rashmanlou and Borzooei [9] studied new concepts relating to vague graphs, product vague graphs [10], regularity of vague graphs [11], and vague competition graphs [12]
Besides the Certain Concepts of Vague Graphs membership degree, the non-membership degree has been introduced as well, which is presented by Atanassove [14] in an intuitionistic fuzzy set, a type of extension of a fuzzy set
Summary
Graph theory is an extremely useful tool for solving combinatorial problems in a wide range of fields, including geometry, algebra, number theory, topology, operations research, biology, and social systems. Descriptions of realworld problems can be improved by using the theory of vague sets Researchers have applied this theory to several real-world situations, such as decision-making and fuzzy control. Ramakrishna [8] introduced the concept of vague graph and studied related properties. In this study we outline and explore the key properties of some new operations on vague graphs, including rejection, maximal product, symmetric difference, and residue product. We outline specific conditions for obtaining the degrees of vertices in vague graphs under the operations of maximal product, symmetric difference, and rejection. We explore applications of vague sets in medical diagnosis
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