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El. knyga: Fuzzy Graph Theory with Applications to Human Trafficking

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This book reports on advanced concepts in fuzzy graph theory, showing a set of tools that can be successfully applied to understanding and modeling illegal human trafficking. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book gives a special emphasis to applications of the theory. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the concept of independence and domination in fuzzy graphs, as well as directed fuzzy networks, incidence graphs and many more. 

1 Strengthening and Weakening Members of a Network
1(56)
1.1 Fuzzy Sets
1(3)
1.2 Fuzzy Relations
4(4)
1.3 Definitions and Basic Properties of Fuzzy Graphs
8(2)
1.4 Connectivity in Fuzzy Graphs
10(1)
1.5 Connectedness in a Directed Graph
11(1)
1.6 Strengthening and Weakening Members of a Group
12(3)
1.7 Inclusive Connectedness Categories
15(2)
1.8 Exclusive Connectedness Categories
17(2)
1.9 Articulation Points
19(3)
1.10 An Application of Fuzzy Graphs to the Problem Concerning Group Structure
22(2)
1.11 Weakening and Strengthening Points of a Fuzzy Graph
24(5)
1.12 Intuitionistic Fuzzy Graphs: Weakening and Strengthening Members of a Group
29(11)
1.13 Fuzzy Graphs and Complementary Fuzzy Graphs
40(17)
References
54(3)
2 Domination in Fuzzy Graphs
57(30)
2.1 Preliminaries
57(3)
2.2 Domination in Fuzzy Graphs
60(4)
2.3 Strong and Weak Domination
64(4)
2.4 Independent Domination and Irredundance
68(5)
2.5 Non Deterministic Flow in Fuzzy Networks
73(6)
2.6 Application of DFN in Human Trafficking
79(2)
2.7 Strong Independence and Domination in DFN
81(6)
References
83(4)
3 Fuzzy Incidence Graphs
87(52)
3.1 Fuzzy Incidence Graphs
87(10)
3.2 Cutvertices, Bridges, and Cutpairs
97(4)
3.3 Connectivity in Fuzzy Incidence Graphs
101(8)
3.4 Fuzzy End Nodes in Fuzzy Incidence Graphs
109(3)
3.5 Human Trafficking and Fuzzy Influence Graphs
112(2)
3.6 Fuzzy Influence Graphs
114(6)
3.7 Social Influence
120(6)
3.8 Fuzzy Incidence Blocks and Illegal Migration
126(7)
3.9 Cyclically Strong Incidence Graphs
133(3)
3.10 Illegal Migration
136(3)
References
137(2)
4 Networks
139(18)
4.1 Network Models
139(1)
4.2 A Maximal Flow Algorithm
140(1)
4.3 The Max Flow, Min Cut Theorem
141(1)
4.4 Reduction Nodes and Arcs
142(4)
4.5 Strength Reducing Sets
146(3)
4.6 Flow Problems in DFN
149(3)
4.7 Network Flow
152(5)
References
154(3)
5 Complementary Fuzzy Incidence Graphs
157(24)
5.1 (s, t]-Fuzzy Incidence Graphs
157(2)
5.2 (s, t]-Fuzzy Incidence Cut Vertices and (s, t]-Fuzzy Incidence End Vertices
159(2)
5.3 Complementary Fuzzy Incidence Graphs
161(1)
5.4 Complementary Quasi-Fuzzy Incidence Graphs
162(2)
5.5 Complementary Fuzzy Cut Vertices and Fuzzy End Vertices
164(4)
5.6 Illegal Immigration and Vague Fuzzy Incidence Graphs
168(1)
5.7 Eccentricity of Vague Fuzzy Incidence Graphs
169(12)
References
180(1)
6 Human Trafficking: Source, Transit, Destination Designations
181(28)
6.1 Introduction
181(1)
6.2 Source Transit and Destination
182(6)
6.3 Regional Flow Upper Bounds
188(8)
6.4 Fuzzy Incidence Graphs: Applications to Human Trafficking
196(1)
6.5 Application
197(12)
References
208(1)
7 Human Trafficking: Policy Intervention
209(36)
7.1 Introduction
209(1)
7.2 Analytic Hierarchy Process
210(2)
7.3 Guiasu and Dempster Rule of Combination Methods
212(7)
7.4 Yen Method
219(2)
7.5 Set Valued Statistical Method
221(1)
7.6 Testing Policy Intervention
222(5)
7.7 Descriptions
227(1)
7.8 Local Look at Human Trafficking
228(1)
7.9 The Model
229(5)
7.10 Dempster's Rule of Combination
234(2)
7.11 Preference Relations
236(1)
7.12 Outranking Relations
237(3)
7.13 Descriptions
240(5)
References
242(3)
Index 245
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 is a President of the Society for Mathematics of Uncertainty. He has published fteen books and two hundred 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 problem of human trafcking.





Dr. Sunil Mathew is currently 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 seventy-ve research papers and written two 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 twenty years in teaching and research. His current research topics include fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos.

Dr. Davender S. Malik is a Professor of Mathematics at Creighton University. He received his Ph.D. from Ohio University and has published more than fty-ve papers and eighteen books on abstract algebra, applied mathematics, graph theory, fuzzy automata theory and languages, fuzzy logic and its applications, programming, data structures, and discrete mathematics.