This book provides an examination of major problems facing the world using mathematics of uncertainty. These problems include climate change, coronavirus pandemic, human tracking, biodiversity, and other grand challenges. Mathematics of uncertainty is used in a modern more general sense than traditional mathematics. Since accurate data is impossible to obtain concerning human tracking and other global problems, mathematics of uncertainty is an ideal discipline to study these problems. The authors place several scientific studies into different mathematical settings such as nonstandard analysis and soft logic. Fuzzy differentiation is used to model the spread of diseases such as the coronavirus. The book uses fuzzy graph theory to examine the problems of human tracking and illegal immigration. The book is an excellent reference source for advanced under-graduate and graduate students in mathematics and the social sciences as well as for researchers and teachers.
Author(s): John N. Mordeson, Sunil Mathew, M. Binu
Series: Studies in Systems, Decision and Control, 391
Publisher: Springer
Year: 2021
Language: English
Pages: 317
City: Cham
Preface
Contents
About the Authors
1 Preliminaries
1.1 Fuzzy Sets
1.2 Evidence Theory
1.3 Guiasu, AHP, Yen, and Dempster Methods
1.4 Sustainable Development Goals
1.5 Fuzzy Similarity Measures
1.6 Fuzzy Graphs and Fuzzy Incidence Graphs
1.7 Abstract Algebra
1.8 Abduction
References
2 Coronavirus
2.1 SIR Model
2.2 SEIR Model
2.3 Social Distancing
2.4 SIR and SEIR Merged
References
3 Differentiation of Fuzzy Functions
3.1 Fuzzy Integration
3.2 Fuzzy Numbers
3.3 Differentiation
3.4 Fuzzy SIR Model
References
4 Soft Numbers
4.1 Soft Logic
4.2 Soft Fuzzy Numbers
4.3 Soft Algebraic Structures
4.4 Calculus
4.5 Soft Functions
4.6 Soft Fuzzy Derivative
4.7 Fuzzy Cognitive Maps
References
5 Nonstandard Fuzzy Sets
5.1 Nonstandard Analysis
5.2 Nonstandard Fuzzy Numbers and Nonstandard Fuzzy Functions
5.3 Nonstandard Fuzzy Algebra
5.4 Nonstandard Fuzzy Subgraphs
References
6 Fuzzy Graphs Applied to Human Trafficking
6.1 Connectivity Remainder
6.2 Connectivity Remainder of Vertex Deleted Subgraphs
6.3 Algorithms
6.4 Application to Human Trafficking
6.5 Directed Graphs
References
7 More on Fuzzy Graph Connectivity
7.1 Cyclic Connectivity Index
7.2 CCI of Blocks, θ-Fuzzy Graphs and Complete Fuzzy Graphs
7.3 Average Cyclic Connectivity Index (ACCI) of Fuzzy Graphs
7.4 Algorithms Related with CCI
7.5 Connectivity Status
7.6 Connectivity Status Analysis of Vertices in a Fuzzy Graph
7.7 Status Sequence of a Fuzzy Graph
7.8 Algorithms Related with CS
References
8 Fuzzy Influence Graph: A Model for Human Trafficking
8.1 Fuzzy Influence Graphs
8.2 FIG Model for Human Trafficking Networks
References
9 Grand Challenges
9.1 Gates Grand Challenges
9.2 WCRP Grand Challenges
9.3 The 12 Grand Challenges for Social Work
9.4 Grand Challenges for Engineering
9.5 Space
References
10 Psychology Impact of Human Trafficking
10.1 Psychological Tactics Used by Human Traffickers
10.2 Psychological Impact of Human Trafficking
10.3 Support of Victims
10.3.1 Medical Health Needs
10.4 Protection for Survivors
10.5 Psychological Health Consequences
References
11 Bribery and Corruption
11.1 Bribery
11.2 Different Types of Bribery Across Business Sectors
11.3 Basel and CPI Indices
References
12 Global Starvation and Coronavirus
12.1 Climate Vulnerability and Global Hunger
12.2 Vulnerability Versus Global Food Security
12.3 Global Food Security Versus Global Hunger
References
13 Biodiversity and Extinction
13.1 Biodiversity Rankings
References
14 KnowYourCountry
14.1 Money Laundering and Human Trafficking
14.2 KnowYourCountry FATF-MER Assessment
14.2.1 Effectiveness
14.2.2 Immediate Outcomes
14.2.3 Technical Compliance
14.3 Tier Placement
References
Index
