A study of novel linear Diophantine fuzzy topological numbers and their application to communicable diseases

The idea of linear Diophantine fuzzy sets (LDFs) is a novel tool for analysis, soft computing, and optimization. Recently, the concept of a linear Diophantine fuzzy graph has been proposed in 2022. The aim of this research is to extend topological numbers to LDFSs. A real value assigned to a particular graph is known as a topological graph theoretic parameter. We extend the bound of the crisp graph toward the linear Diophantine fuzzy graph (LDFG), including the edge and vertex deletion operations via LDFG theoretic parameters. We also investigate the interesting bound of the LDFGs via LDFG theoretic parameters. Finally, for decision-making problems, we developed an algorithm by exploiting the relationship between LDFG theoretic parameters and LDFSs. Based on the established approach, we discussed a numerical example of an application of a medical diagnosis using the linear Diophantine fuzzy Sombor graph parameter and the first, fifth, and sixth versions of the linear Diophantine fuzzy Sombor graph parameters.