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

中文翻译：

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直观模糊的 Γ 子模块集及其在模拟病毒性疾病（突变的 COVID-n）通过航班传播的应用


在本研究中，我们将模糊Γ$\mathrm{\Gamma }$
- 模块，作为直觉模糊Γ$\mathrm{\Gamma }$ -子模块Γ$\mathrm{\Gamma }$ -模块（如果Γ$\mathrm{\Gamma }$
M），并利用它来模拟冠状病毒在航空旅行中的传播。直觉模糊的某些基本特征Γ$\mathrm{\Gamma }$
-提供了子模块，并且证明了 IFΓ$\mathrm{\Gamma }$
M可以被认为是一个完全格子。一些说明性的例子来解释 IF 的属性Γ$\mathrm{\Gamma }$
M.上下关联性α$\alpha$
-水平切割和直观模糊Γ$\mathrm{\Gamma }$
-给出了子模块以及IF的上、下下像和逆像的特性Γ$\mathrm{\Gamma }$
M 是后天获得的。验证了直觉模糊的像和逆像Γ$\mathrm{\Gamma }$
-submodule 保留在模块同态下。得到的中频Γ$\mathrm{\Gamma }$
M 用于模拟病毒性疾病（即 COVID -n ）通过航班在空中传播的模型。