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

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