Topological Indices on Linguistic Generalized Z Graphs

When making decisions in real life, one of the most crucial and worrisome factors is information reliability. Information is not perfect in reality. It is common to present this information in a number of languages. This data is not entirely trustworthy. In order to prevent inconsistent information when making decisions, Lotfi Zadeh has introduced the notion of the \(Z\) -number. \(Z\) number is crucial for verifying the accuracy of the information. A \(Z\) -number is a combination of two parts; the first of which restricts the value of an associated random variable, and the second of which estimates the first fuzzy number’s reliability. If a number remains unchanged across graph isomorphisms, it is referred to as a graphical invariant. Topological indices are graphical invariants in molecular graph theory that are important in detecting molecular irregularities, molecular structure, and molecular complexity. The wide range of applications for topological indices attracts the interest of researchers in this field. In this chapter, we constructed two generalized fuzzy graphs using the idea of linguistic \(Z\) numbers and linguistic hedges. Next, we discussed a few topological indices and proved some theorems. Finally, we have included some future works.