Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment

Anam Luqman,Ali N. A. Koam,Muhammad Akram

doi:10.3390/math7060496

Anam Luqman, Ali N. A. Koam + Show 1 more

Open Access

https://doi.org/10.3390/math7060496

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Journal: Mathematics	Publication Date: Jun 1, 2019
Citations: 20	License type: CC BY 4.0

Affiliation: University of the Punjab, Jazan University

Abstract

In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

Highlights

Granular computing (GrC) is defined as an identification of techniques, methodologies, tools, and theories that yield the advantages of clusters, groups, or classes, i.e., the granules
It is worth noting that as we increase the value of parameter q, the space of uncertain data increases, and the bounding constraint is satisfied by more triplets
A q-rung picture fuzzy set is the generalization of the picture of the fuzzy set and the q-rung orthopair fuzzy set

Summary

Introduction

Granular computing (GrC) is defined as an identification of techniques, methodologies, tools, and theories that yield the advantages of clusters, groups, or classes, i.e., the granules. Our proposed model of GrC, based on q-rung picture fuzzy hypergraphs, is much closer to and considerable of human reasoning as compared to earlier concepts. In this model, the range of indication of decision data can be changed by changing the value of parameter q, q ≥ 1. The question of distinct membership degrees of the same object from different scholars has arisen because of various ways of thinking about the interpretation of different functions dealing with the same problem To resolve this issue, FS was structurally defined by Zhang and Zhang [32], which was based on QS theory and FER [33].

Construction of Model

The Construction of Hierarchical Structures

Zooming-in and Zooming-out Operators

A Level Hypergraph Partition Model

Comparison Analysis

Conclusions and Future Directions