Intuitionistic fuzzy set of $\Gamma$ -submodules and its application in modeling spread of viral diseases, mutated COVID- n, via flights

In this study, we generalize fuzzy $\Gamma$ -module, as intuitionistic fuzzy $\Gamma$ -submodule of $\Gamma$ -module (IF $\Gamma$ M), and utilize it for modeling the spread of coronavirus in air travels. Certain fundamental features of intuitionistic fuzzy $\Gamma$ -submodule are provided, and it is proved that IF $\Gamma$ M can be considered as a complete lattice. Some elucidatory examples are demonstrated to explain the properties of IF $\Gamma$ M. The relevance between the upper and lower $\alpha$ -level cut and intuitionistic fuzzy $\Gamma$ -submodules are presented and the characteristics of upper and lower under image and inverse image of IF $\Gamma$ M are acquired. It is verified that the image and inverse image of intuitionistic fuzzy $\Gamma$ -submodule are preserved under the module homomorphism. The obtained IF $\Gamma$ M is used to model the aerial transition of viral diseases, that is, COVID-n, via flights.