A Theoretical Investigation Based on the Rough Approximations of Hypergraphs. (7th March 2022) - Sarwar, Musavarah
Abstract : Rough sets are a key tool to model uncertainty and vagueness using upper and lower approximations without predefined functions and additional suppositions. Rough graphs cannot be studied more effectively when the inexact and approximate relations among more than two objects are to be discussed. In this research paper, the notion of a rough set is applied to hypergraphs to introduce the novel concept of rough hypergraphs based on rough relations. The notions of isomorphism, conformality, linearity, duality, associativity, commutativity, distributivity, Helly property, and intersecting families are illustrated in rough hypergraphs. The formulae of 2-section, L2-section, covering, coloring, rank, and antirank are established for certain types of rough hypergraphs. The relations among certain types of products of rough hypergraphs are studied in detail.