Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup-based graph (SBG) of G=H,E is constructed through the fundamental relation γn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xγny. The connectivity of graph G is characterized by xγ*y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/γ*. Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
In this study, we generalize fuzzy
‐module, as intuitionistic fuzzy
‐submodule of
‐module (IF
M), and utilize it for modeling the spread of coronavirus in air travels. Certain fundamental features of intuitionistic fuzzy
‐submodule are provided, and it is proved that IF
M can be considered as a complete lattice. Some elucidatory examples are demonstrated to explain the properties of IF
M. The relevance between the upper and lower
‐level cut and intuitionistic fuzzy
‐submodules are presented and the characteristics of upper and lower under image and inverse image of IF
M are acquired. It is verified that the image and inverse image of intuitionistic fuzzy
‐submodule are preserved under the module homomorphism. The obtained IF
M is used to model the aerial transition of viral diseases, that is, COVID‐
n
, via flights.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.