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.
Highlights
In graphical networks, usually pairwise relations are discussed missing some information that more than two objects may satisfy common characteristics
Let R1⊛R2 denote any product of two rough hypergraphs R1 and R2
We introduce the concept of Cartesian product in rough hypergraphs and study its 2-section, L2-section, distance, covering, and coloring of the Cartesian product of rough hypergraphs
Summary
Usually pairwise relations are discussed missing some information that more than two objects may satisfy common characteristics. Hypergraphs cannot study uncertain properties or partial belongingness of objects and their relations Fuzzy hypergraphs and their extensions have been applied successfully to deal with uncertain information in hypergraphical models. All these existing approaches are based on additional suppositions and membership functions to compute the vagueness of objects. Follows: is paper is organized as (1) Section 1 is based on the literature review and motives of the given study (2) Section 2 contains basic ideas, definitions, and terminologies from already existing articles that are used in the paper (3) Section 3 is the main focus of this research paper which contains novel concepts of certain types of rough hypergraphs and their interesting properties Framework of the Paper. follows: is paper is organized as (1) Section 1 is based on the literature review and motives of the given study (2) Section 2 contains basic ideas, definitions, and terminologies from already existing articles that are used in the paper (3) Section 3 is the main focus of this research paper which contains novel concepts of certain types of rough hypergraphs and their interesting properties
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