Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Correspondence:
[*]
Corresponding author. Muhammad Akram, Department of Mathematics, University of the Punjab, New Campus, Lahore,
Pakistan. E-mail: [email protected].
Abstract: An extraction of granular structures using graphs is a powerful mathematical framework in human reasoning and problem solving. The visual representation of a graph and the merits of multilevel or multiview of granular structures suggest the more effective and advantageous techniques of problem solving. In this research study, we apply the combinative theories of rough fuzzy sets and rough fuzzy digraphs to extract granular structures. We discuss the accuracy measures of rough fuzzy approximations and measure the distance between lower and upper approximations. Moreover, we consider the adjacency matrix of a rough fuzzy digraph as an information table and determine certain indiscernible relations. We also discuss some general geometric properties of these indiscernible relations. Further, we discuss the granulation of certain social network models using rough fuzzy digraphs. Finally, we develop and implement some algorithms of our proposed models to granulate these social networks.
Keywords: Rough fuzzy approximations, rough fuzzy digraphs, information granulation, algorithms
