Despite the importance of link prediction and identification of influencers in dynamic social media systems, the existing methodical theories are not capable of analyzing complex multilayer relations in social media networks which contain uncertainty. In fact, there is no theoretical exploration concurrently focused on multidimensional and interrelated entities in a fuzzy-based social media environment. To cover this gap, a neoteric generalized fuzzy hypergraph (GFH) methodology is designed using developed n-ary fuzzy relation technique that is the extension of convolutional binary fuzzy relation. Characterizing reflexive, symmetric, transitive, composition, t-cut and support techniques is carried out for multidimensional uncertain-based space. Also, a graphical approach is created in the generalized fuzzy hypergraph to assist the derivation of foundational implications and concepts. The GFH framework can be applied for the intelligent management of complex systems for sole or mass users of local and global social media platforms by adopting specific membership degree for each individual. To predict the linkages between elements, a fuzzy-based indicator FLP (fuzzy link prediction) is promoted, along with the indicator of SIR (score of interaction rate) to identify the influencers (strongest communicators) in an uncertain space. Through the FLP evaluation, the extracted data are analyzed as per the highest value of 1 for single, 3 for binary, 3.8 for triplet, and 0.9 for quaternary spaces for their probable links. Through the analysis of SIR data on the individuals’ membership degrees for the usage of social media platforms, the highest interaction value of 0.99 is correlated to a single member, while 5.42 magnitude addresses an influential person. The performance results show that the presented theoretical and structural approach, that is superior to the classical graph theories, is promising to configure intelligent expert systems, predict the likelihood of connections, detect communities, and specify the influencers in real social media platforms that contain uncertainty.

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

In some probabilistic problems, complete information about the probability model may not exist. In this article, we obtain a lower and upper probability for an arbitrary event by using rough set theory and then a measurement for inclusiveness of events is introduced.

Using the concept of triangular norm, we define T-fuzzy subalgebraic hypersystems, we examine a number of extended uncertainty algebraic hypersystems and study a few results in this respect. In fact, we define a probabilistic version of algebraic hypersystems using random sets. We show that fuzzy algebraic hypersystems defined in triangular norms are consequences of probabilistic algebraic hypersystems under certain conditions.