A survey on cubic fuzzy graph structure with an application in the diagnosis of brain lesions

Abstract

A cubic fuzzy graph is a fuzzy graph that simultaneously supports fuzzy membership and interval-valued fuzzy membership. This simultaneity leads to a better flexibility in modeling problems regarding uncertain variables. The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and graph structures, shows better capabilities in solving complex problems, especially where there are multiple relationships. Since many problems are a combination of different relationships, as well, applying some operations on them creates new problems; therefore, in this article, some of the most important product operations on cubic fuzzy graph structure have been investigated and some of their properties have been described. Studies have shown that the product of two strong cubic fuzzy graph structures is not always strong and sometimes special conditions are needed to be met. By calculating the vertex degree in each of the products, a clear image of the comparison between the vertex degrees in the products has been obtained. Also, the relationships between the products have been examined and the investigations have shown that the combination of some product operations with each other leads to other products. At the end, the cubic fuzzy graph structure application in the diagnosis of brain lesions is presented.