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

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