This monograph discusses decision making methods under bipolar fuzzy graphical models with the aim of overcoming the lack of mathematical approach towards bipolar information―positive and negative. It investigates the properties of bipolar fuzzy graphs, their distance functions, and concept of their isomorphism. It presents certain notions, including irregular bipolar fuzzy graphs, domination in bipolar fuzzy graphs, bipolar fuzzy circuits, energy in bipolar fuzzy graphs, bipolar single-valued neutrosophic competition graphs, and bipolar neutrosophic graph structures. This book also presents the applications of mentioned concepts to real-world problems in areas of product manufacturing, international relations, psychology, global terrorism and more, making it valuable for researchers, computer scientists, social scientists and alike.
Author(s): Muhammad Akram, Musavarah Sarwar, Wieslaw A. Dudek
Series: Studies in Fuzziness and Soft Computing, 401
Publisher: Springer
Year: 2020
Language: English
Pages: 452
City: Cham
Foreword
Preface
Contents
About the Authors
List of Figures
List of Tables
1 Bipolar Fuzzy Sets and Bipolar Fuzzy Graphs
1.1 Introduction
1.2 Bipolar Fuzzy Graphs
1.3 Isomorphism of Bipolar Fuzzy Graphs
1.4 Complex Bipolar Fuzzy Graphs
1.5 Bipolar Fuzzy Digraphs
1.6 Applications of Bipolar Fuzzy Digraphs to Decision Making
1.6.1 Bipolar Fuzzy Neurons in Medical Diagnosis
1.6.2 Social Networking
1.6.3 Bipolar Fuzzy Organizational Model
1.6.4 Bipolar Fuzzy Graphs in Marketability
1.6.5 Vulnerability Assessment of Gas Pipeline Networks
1.6.6 Bipolar Fuzzy Digraph in Travel Time
1.6.7 Comparison Analysis
1.7 Conclusions
References
2 Distance Measures in Bipolar Fuzzy Graphs
2.1 Introduction
2.2 Distance in Bipolar Fuzzy Graphs
2.3 Metric in Bipolar Fuzzy Graphs
2.4 Self-centered Bipolar Fuzzy Graphs
2.5 Antipodal Bipolar Fuzzy Graphs
2.6 Applications of Bipolar Fuzzy Graphs
2.6.1 Product Manufacturing
2.6.2 Safe Route and Shortest Path Problem
2.7 Conclusions
References
3 Special Types of Bipolar Fuzzy Graphs
3.1 Introduction
3.2 Regular and Irregular Bipolar Fuzzy Graphs
3.3 Bipolar Fuzzy Line Graphs
3.4 Cayley Bipolar Fuzzy Graphs
3.5 Conclusions
References
4 Bipolar Fuzzy Competition Graphs
4.1 Introduction
4.2 Bipolar Fuzzy Competition Graphs
4.3 Bipolar Fuzzy k-competition Graphs
4.4 Complex Bipolar Fuzzy Competition Graphs
4.5 Applications of Bipolar Fuzzy Competition Graphs
4.5.1 Variants of Bipolar Fuzzy Competition Graphs in Food Webs
4.5.2 Competitive Market
4.5.3 Political Competition
4.5.4 Social Competition in Bipolar Fuzzy Environment
4.5.5 Interactions and Conflicts in Communication Networks
4.6 Conclusions
References
5 Bipolar Fuzzy Planar Graphs
5.1 Introduction
5.2 Bipolar Fuzzy Planar Graphs
5.3 Bipolar Fuzzy Bridges
5.4 Bipolar Fuzzy Cut Vertices and Bipolar Fuzzy Blocks
5.5 Bipolar Fuzzy Cycles and Bipolar Fuzzy Trees
5.6 Applications of Bipolar Fuzzy Planar Graphs
5.6.1 Road Network Model to Monitor Traffic
5.6.2 Modeling of Electrical Connections
5.7 Conclusions
References
6 Domination in Bipolar Fuzzy Graphs
6.1 Introduction
6.2 Types of Domination in Bipolar Fuzzy Graphs
6.3 Irredundance in Bipolar Fuzzy Graphs
6.4 Applications of Domination in Decision-Making Problems
6.4.1 Facility Location Problem
6.4.2 Representatives in Youth Development Council
6.4.3 Transmission Tower Location Problem
6.5 Conclusions
References
7 Bipolar Fuzzy Circuits
7.1 Introduction
7.2 Bipolar Fuzzy Circuits
7.2.1 Circuit Rectangles
7.3 Bipolar Fuzzy Soft Circuits
7.4 Decision Support Systems
7.4.1 Ordering of Machines Using Bipolar Fuzzy Matroids
7.4.2 Network Analysis
7.4.3 Ordering of Tasks Using Bipolar Fuzzy Soft Matroids
7.5 Conclusions
References
8 Energy of Bipolar Fuzzy Graphs
8.1 Introduction
8.2 Energy of Bipolar Fuzzy Graphs
8.3 Laplacian Energy of Bipolar Fuzzy Graphs
8.4 Signless Laplacian Energy of Bipolar Fuzzy Graphs
8.5 Dominating and Double Dominating Energy of Bipolar Fuzzy Graphs
8.6 Applications of Energy to Decision-Making Problems
8.6.1 Smooth Communication Problem
8.6.2 Selection of a Business Partner
8.7 Conclusions
References
9 Bipolar Neutrosophic Competition Graphs
9.1 Introduction
9.2 Certain Types of Bipolar Neutrosophic Competition Graphs
9.3 Bipolar Neutrosophic Neighborhood Graphs
9.4 Applications of Competition Graphs in Bipolar Neutrosophic Environment
9.4.1 Designation Competition in an Organization
9.4.2 Competition in Textile Market
9.4.3 Competition in Sports
9.5 Conclusions
References
10 Bipolar Neutrosophic Graph Structures
10.1 Introduction
10.2 Operations on Bipolar Neutrosophic Graph Structures
10.3 Isomorphism in Bipolar Neutrosophic Graph Structures
10.4 Applications of Bipolar Single-Valued Neutrosophic Graph Structures
10.4.1 International Relations
10.4.2 Psychological Improvement of Patients
10.4.3 Uncovering the Undercover Reasons of Global Terrorism
10.5 Conclusions
References
Index
