Fuzzy Hypergraphs and Related Extensions (Studies in Fuzziness and Soft Computing, 390)

✍ Scribed by Muhammad Akram, Anam Luqman

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 522
• Category: Library

✦ Synopsis

This book presents the fundamental and technical concepts of fuzzy hypergraphs and explains their extensions and applications. It discusses applied generalized mathematical models of hypergraphs, including complex, intuitionistic, bipolar, m-polar fuzzy, Pythagorean, complex Pythagorean, and q-rung orthopair hypergraphs, as well as single-valued neutrosophic, complex neutrosophic and bipolar neutrosophic hypergraphs. In addition, the book also sheds light on real-world applications of these hypergraphs, making it a valuable resource for students and researchers in the field of mathematics, as well as computer and social scientists.

✦ Table of Contents

Foreword
Preface
Contents
About the Authors
List of Figures
List of Tables
1 Fuzzy Hypergraphs
1.1 Introduction
1.2 Fuzzy Hypergraphs
1.3 Fuzzy Competition Hypergraphs
1.4 Fuzzy Neighborhood Hypergraphs
1.5 Applications of Fuzzy Competition Hypergraphs
1.5.1 Identifying Predator–Prey Relations in Ecosystem
1.5.2 Identifying Competitors in Business Market
1.5.3 Finding Influential Communities in a Social Network
1.6 mathcalN-Hypergraphs
1.7 Application of mathcalN-Hypergraphs
1.8 Complex Fuzzy Hypergraphs
1.8.1 Homomorphisms and Covering Constructions of Complex Fuzzy Hypergraphs
1.8.2 Products on Complex Fuzzy Hypergraphs
1.9 A Complex Fuzzy Hypergraph Model of Co-authorship Network
1.9.1 Flow Chart of Proposed Model
1.9.2 Comparative Analysis
References
2 Hypergraphs in Intuitionistic Fuzzy Environment
2.1 Introduction
2.2 Intuitionistic Fuzzy Hypergraphs
2.3 Applications of Intuitionistic Fuzzy Hypergraphs
2.3.1 The Intersecting Communities in Social Network
2.3.2 Planet Surface Networks
2.3.3 Grouping of Incompatible Chemical Substances
2.3.4 Radio Coverage Network
2.3.5 Clustering Problem
2.4 Intuitionistic Fuzzy Directed Hypergraphs
2.5 Complex Intuitionistic Fuzzy Hypergraphs
References
3 Hypergraphs for Interval-Valued Structures
3.1 Introduction
3.2 Interval-Valued Fuzzy Hypergraphs
3.3 Vague Hypergraphs
3.4 Interval-Valued Intuitionistic Fuzzy Hypergraphs
References
4 Bipolar Fuzzy (Directed) Hypergraphs
4.1 Introduction
4.2 Bipolar Fuzzy Hypergraphs
4.3 Bipolar Fuzzy Directed Hypergraphs
4.4 Algorithm for Computing Minimum Arc Length and Shortest Hyperpath
4.5 Application
References
5 Extended Bipolar Fuzzy (Directed) Hypergraphs to m-Polar Information
5.1 Introduction
5.2 m-Polar Fuzzy Hypergraphs
5.3 Applications of m-Polar Fuzzy Hypergraphs
5.3.1 Super-Dyadic Managements in Marketing Channels
5.3.2 m-Polar Fuzzy Hypergraphs in Work Allotment Problem
5.3.3 Availability of Books in Library
5.3.4 Selection of a Pair of Good Team for Competition
5.4 m-Polar Fuzzy Directed Hypergraphs
5.5 Application of m-Polar Fuzzy Directed Hypergraphs
5.5.1 Business Strategy Company
References
6 (Directed) Hypergraphs: q-Rung Orthopair Fuzzy Models and Beyond
6.1 Introduction
6.2 q-Rung Orthopair Fuzzy Hypergraphs
6.3 Transversals of q-Rung Orthopair Fuzzy Hypergraphs
6.4 Applications to Decision-Making
6.4.1 Selection of Most Desirable Appliance
6.4.2 Adaptation of Most Alluring Residential Scheme
6.5 q-Rung Orthopair Fuzzy Directed Hypergraphs
6.6 Coloring of q-Rung Orthopair Fuzzy Directed Hypergraphs
6.7 Applications
6.7.1 The Most Proficient Arrangement for Hazardous Chemicals
6.7.2 Assessment of Collaborative Enterprise to Achieve a Particular Objective
6.8 Comparative Analysis
6.9 Complex Pythagorean Fuzzy Hypergraphs
6.10 Complex q-Rung Orthopair Fuzzy Hypergraphs
6.11 Transversals of Complex q-Rung Orthopair Fuzzy Hypergraphs
6.12 Application of Complex q-Rung Orthopair Fuzzy Hypergraphs
6.13 Comparative Analysis
References
7 Granular Computing Based on q-Rung Picture Fuzzy Hypergraphs
7.1 Introduction
7.2 q-Rung Picture Fuzzy Hierarchical Quotient Space Structure
7.3 A q-Rung Picture Fuzzy Hypergraph Model of Granular Computing
7.3.1 Model Construction
7.3.2 The Construction of Hierarchical Structures
7.3.3 Zooming-In and Zooming-Out Operators
7.4 A Level Hypergraph Partition Model
References
8 Granular Computing Based on m-Polar Fuzzy Hypergraphs
8.1 Introduction
8.2 Fundamental Features of m-Polar Fuzzy Hypergraphs
8.2.1 Uncertainty Measures of m-Polar Fuzzy Hierarchical Quotient Space Structure
8.2.2 Information Entropy of m-Polar Fuzzy Hierarchical Quotient Space Structure
8.3 An m-Polar Fuzzy Hypergraph Model of Granular Computing
8.4 Formation of Hierarchical Structures
8.5 A Granular Computing Model of Web Searching Engines
References
9 Some Types of Hypergraphs for Single-Valued Neutrosophic Structures
9.1 Introduction
9.2 Single-Valued Neutrosophic Hypergraphs
9.3 Intuitionistic Single-Valued Neutrosophic Hypergraphs
9.4 Clustering Problem
9.5 Single-Valued Neutrosophic Directed Hypergraphs
9.6 Single-Valued Neutrosophic Line Directed Hypergraphs
9.7 Applications of Neutrosophic Directed Hypergraphs
9.7.1 Production and Manufacturing Networks
9.7.2 Collaboration Network
9.7.3 Social Networking
9.8 Complex Neutrosophic Hypergraphs
9.9 T-Related Complex Neutrosophic Hypergraphs
9.10 Applications of Complex Neutrosophic Hypergraphs
9.10.1 Modeling of Intersecting Research Communities
9.10.2 Influence of Modern Teaching Strategies on Educational Institutes
9.11 Comparative Analysis
References
10 (Directed) Hypergraphs for Bipolar Neutrosophic Structures
10.1 Introduction
10.2 Bipolar Neutrosophic Hypergraphs
10.3 Transversals of Bipolar Neutrosophic Hypergraphs
10.4 Applications of Bipolar Neutrosophic Hypergraphs
10.4.1 Super-Dyadic Managements in Marketing Channels
10.4.2 Production of New Alleles Using Mutations
10.5 Bipolar Neutrosophic Directed Hypergraphs
10.6 Applications of Bipolar Neutrosophic Directed Hypergraphs
10.6.1 Affiliation with an Apprenticeship Group
10.6.2 Portrayal of Compatible Chemicals
References
Index