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E-grāmata: Applications of Mathematics of Uncertainty: Grand Challenges-Human Trafficking-Coronavirus-Biodiversity and Extinction

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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.

1 Preliminaries
1(28)
1.1 Fuzzy Sets
1(2)
1.2 Evidence Theory
3(1)
1.3 Guiasu, AHP, Yen, and Dempster Methods
4(3)
1.4 Sustainable Development Goals
7(1)
1.5 Fuzzy Similarity Measures
8(8)
1.6 Fuzzy Graphs and Fuzzy Incidence Graphs
16(6)
1.7 Abstract Algebra
22(2)
1.8 Abduction
24(5)
References
26(3)
2 Coronavirus
29(10)
2.1 SIR Model
31(1)
2.2 SEIR Model
32(1)
2.3 Social Distancing
33(2)
2.4 SIR and SEIR Merged
35(4)
References
36(3)
3 Differentiation of Fuzzy Functions
39(18)
3.1 Fuzzy Integration
39(2)
3.2 Fuzzy Numbers
41(3)
3.3 Differentiation
44(9)
3.4 Fuzzy SIR Model
53(4)
References
56(1)
4 Soft Numbers
57(24)
4.1 Soft Logic
59(7)
4.2 Soft Fuzzy Numbers
66(1)
4.3 Soft Algebraic Structures
66(2)
4.4 Calculus
68(1)
4.5 Soft Functions
69(2)
4.6 Soft Fuzzy Derivative
71(4)
4.7 Fuzzy Cognitive Maps
75(6)
References
78(3)
5 Nonstandard Fuzzy Sets
81(18)
5.1 Nonstandard Analysis
81(3)
5.2 Nonstandard Fuzzy Numbers and Nonstandard Fuzzy Functions
84(3)
5.3 Nonstandard Fuzzy Algebra
87(2)
5.4 Nonstandard Fuzzy Subgraphs
89(10)
References
97(2)
6 Fuzzy Graphs Applied to Human Trafficking
99(22)
6.1 Connectivity Remainder
99(5)
6.2 Connectivity Remainder of Vertex Deleted Subgraphs
104(7)
6.3 Algorithms
111(4)
6.4 Application to Human Trafficking
115(3)
6.5 Directed Graphs
118(3)
References
120(1)
7 More on Fuzzy Graph Connectivity
121(32)
7.1 Cyclic Connectivity Index
121(4)
7.2 CCI of Blocks, θ-Fuzzy Graphs and Complete Fuzzy Graphs
125(5)
7.3 Average Cyclic Connectivity Index (ACCI) of Fuzzy Graphs
130(2)
7.4 Algorithms Related with CCI
132(6)
7.5 Connectivity Status
138(7)
7.6 Connectivity Status Analysis of Vertices in a Fuzzy Graph
145(2)
7.7 Status Sequence of a Fuzzy Graph
147(2)
7.8 Algorithms Related with CS
149(4)
References
151(2)
8 Fuzzy Influence Graph: A Model for Human Trafficking
153(26)
8.1 Fuzzy Influence Graphs
153(19)
8.2 FIG Model for Human Trafficking Networks
172(7)
References
178(1)
9 Grand Challenges
179(28)
9.1 Gates Grand Challenges
179(3)
9.2 WCRP Grand Challenges
182(2)
9.3 The 12 Grand Challenges for Social Work
184(11)
9.4 Grand Challenges for Engineering
195(9)
9.5 Space
204(3)
References
205(2)
10 Psychology Impact of Human Trafficking
207(20)
10.1 Psychological Tactics Used by Human Traffickers
207(1)
10.2 Psychological Impact of Human Trafficking
208(1)
10.3 Support of Victims
209(2)
10.3.1 Medical Health Needs
211(1)
10.4 Protection for Survivors
211(10)
10.5 Psychological Health Consequences
221(6)
References
226(1)
11 Bribery and Corruption
227(20)
11.1 Bribery
228(8)
11.2 Different Types of Bribery Across Business Sectors
236(2)
11.3 Basel and CPI Indices
238(9)
References
244(3)
12 Global Starvation and Coronavirus
247(12)
12.1 Climate Vulnerability and Global Hunger
247(4)
12.2 Vulnerability Versus Global Food Security
251(3)
12.3 Global Food Security Versus Global Hunger
254(5)
References
257(2)
13 Biodiversity and Extinction
259(12)
13.1 Biodiversity Rankings
260(11)
References
270(1)
14 KnowYourCountry
271(28)
14.1 Money Laundering and Human Trafficking
271(10)
14.2 KnowYourCountry FATF-MER Assessment
281(10)
14.2.1 Effectiveness
281(1)
14.2.2 Immediate Outcomes
281(4)
14.2.3 Technical Compliance
285(6)
14.3 Tier Placement
291(8)
References
297(2)
Index 299
Dr. John N Mordeson is Professor Emeritus of Mathematics at Creighton University. He received his B. S., M. S., and Ph. D from Iowa State University. He is a member of Phi Kappa Phi. He has published 20 books and over 200 journal articles. He is on the editorial board of numerous journals. He has served as an external examiner of Ph. D. candidates from India, South Africa, Bulgaria, and Pakistan. He has refereed for numerous journals and granting agencies. He is particularly interested in applying mathematics of uncertainty to combat the problems of climate change, human tracking, and biodiversity. Dr. Sunil Mathew is a Faculty Member in the Department of Mathematics, NIT Calicut, India. He has acquired his masters from St. Josephs College Devagiri, Calicut, and Ph. D. from National Institute of Technology Calicut in the area of Fuzzy Graph Theory. He has published more than 100 research papers and written ve books. He is a member of several academic bodies and associations. He is editor and reviewer of several international journals. He has an experience of 20 years in teaching and research. His current research topics include fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos. Dr. Binu M received her Ph. D in 2019 from the Department of Mathematics, National Institute of Technology Calicut, India, in the area of Connectivity in Fuzzy Graph Theory. She is a faculty member at Cooperative Academy of Professional Education (CAPE) Kerala, India. Her present research includes fuzzy logic, graph theory and network science. Dr. Binu has published several research papers and co-authored a book.
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