Fuzzy Mathematics, Graphs, and Similarity Measures
Analysis and Application Across Global Challenges
- 1st Edition - October 15, 2024
- Imprint: Academic Press
- Authors: John Mordeson, Sunil Mathew
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 3 9 4 9 - 3
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 3 9 5 0 - 9
Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and simila… Read more
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Request a sales quoteFuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change.
Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor’s manual supports teaching across a range of course contexts.
Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor’s manual supports teaching across a range of course contexts.
- Instructs on core analytical techniques of mathematics of uncertainty, from fuzzy graphs to similarity measures, with applications
- Introduces lattice isomorphisms, fuzzy graph indices, and fuzzy graph structures as basis for analysis
- Covers analysis and application across a range of world challenges and SDG aligned topics, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change
- Includes cases studies and student exercises across each chapter, as well as an online instructor’s manual
Undergraduate, postgraduate, and PhD mathematics students
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- About the authors
- Preface
- Acknowledgments
- Chapter 1: Preliminaries
- 1.1. Fuzzy sets
- 1.2. Evidence theory
- 1.3. Fuzzy similarity measures
- 1.4. Implication operations and similarity operations
- 1.5. Fuzzy graphs
- 1.6. Lattices
- 1.7. Exercises
- Chapter 2: Lattice isomorphisms, trafficking, and global challenges
- 2.1. Fuzzy sets and lattice isomorphisms
- 2.2. New view of fuzzy subsets
- 2.3. Global challenges
- 2.4. Exercises
- Chapter 3: Global cybersecurity
- 3.1. Global cybersecurity and cybersecurity threat
- 3.2. Risk
- 3.3. Global cybercrime risk rankings
- 3.4. Exercises
- Chapter 4: Terrorism and bioterrorism
- 4.1. Global terrorism index
- 4.2. Terrorism: Interpol global policing goals and SDGs
- 4.3. Achievement of goals
- 4.4. Fuzzy similarity measures
- 4.5. Scores and ranks by averages
- 4.6. Terrorism and the SDGs
- 4.7. Appendix: the Interpol global policing goals and the SDGs
- 4.8. GTI index
- 4.9. Bioterrorism
- 4.10. Exercises
- Chapter 5: Fuzzy implication operators: health security and political risk
- 5.1. Preliminary results
- 5.2. Main results
- 5.3. Security index
- 5.4. Natural disasters, political stability, and political risk
- 5.5. Exercises
- Chapter 6: Fuzzy implication operators applied to country health
- 6.1. Preliminary results
- 6.2. Main results
- 6.3. Country health
- 6.4. Natural disaster, political stability, and political risk
- 6.5. Sustainable development goals and air pollution
- 6.6. Exercises
- Chapter 7: Mistreatment of women and children
- 7.1. Preliminary results
- 7.2. Godel and Goguen implication operators
- 7.3. Women and children and similarity results
- 7.4. Exercises
- Chapter 8: Space debris and sustainability
- 8.1. Space competitiveness index
- 8.2. Countries dominating space
- 8.3. Responsibility for space junk
- 8.4. Sustainability and space
- 8.5. Space debris and artificial intelligence
- 8.6. Space debris and cybersecurity
- 8.7. Exercises
- Chapter 9: Telecommunications
- 9.1. Telecommunications output and network readiness
- 9.2. Internet speed
- 9.3. Spam and scam
- 9.4. Artificial intelligence
- 9.5. Exercises
- Chapter 10: Eccentric connectivity
- 10.1. Eccentric connectivity index
- 10.2. Modified eccentric connectivity index
- 10.3. Algorithm
- 10.4. Application
- 10.5. Exercises
- Chapter 11: Neighborhood connectivity index
- 11.1. Neighborhood connectivity index of a fuzzy graph
- 11.2. Fuzzy graph operations
- 11.3. Algorithm
- 11.4. Application
- 11.5. Exercises
- Chapter 12: Sigma index
- 12.1. Sigma index of a fuzzy graph
- 12.2. Average sigma index of a fuzzy graph
- 12.3. Algorithm
- 12.4. Application
- 12.5. Exercises
- Chapter 13: Banhatti indices
- 13.1. First and second K-Banhatti indices
- 13.2. Fuzzy graph operations and the K-Banhatti indices
- 13.3. Algorithm for Banhatti indices
- 13.4. Application
- 13.5. Exercises
- Chapter 14: Generalized cycle connectivity of fuzzy graphs
- 14.1. Generalized cycle connectivity
- 14.2. Generalized cyclic cutvertices and bridges
- 14.3. g-Cyclic vertex connectivity and edge connectivity
- 14.4. Cyclically stable fuzzy graphs
- 14.5. Algorithm
- 14.5.1. gm-Cyclic edge connectivity process
- 14.5.2. Illustration
- 14.6. Application
- 14.7. Exercises
- Chapter 15: Fuzzy vertex and edge connectivity
- 15.1. Average fuzzy vertex connectivity
- 15.2. Average fuzzy edge connectivity
- 15.3. Application
- 15.4. Exercises
- Bibliography
- Index
- Edition: 1
- Published: October 15, 2024
- No. of pages (Paperback): 294
- No. of pages (eBook): 250
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9780443339493
- eBook ISBN: 9780443339509
JM
John Mordeson
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, and has published over 20 books and 250 journal articles. He is on the editorial board of numerous journals, and has served as an external examiner of PhD candidates from various countries. He has refereed for numerous journals and ranting agencies, and is particularly interested in applying mathematics of uncertainty to combat global problems.
Affiliations and expertise
Professor Emeritus of Mathematics, Creighton University, USASM
Sunil Mathew
Dr. Sunil Mathew is Associate Professor in the Department of Mathematics at NIT, Calicut, India. He received his Masters from St. Joseph's College, Devagiri, in Calicut, and PhD from the National Institute of Technology, Calicut in the area of Fuzzy Graph Theory. He has published over 125 research papers and written 10 books. He is a member of several academic bodies and associations. He is an editor and reviewer of several international journals. He has experience of more than 20 years in teaching and research, and his current research topics include fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos.
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Affiliations and expertise
Associate Professor, Department of Mathematics, NIT, Calicut, IndiaRead Fuzzy Mathematics, Graphs, and Similarity Measures on ScienceDirect