Introduction to Fuzzy Mathematics
With Applications to Global Problems
- 1st Edition - March 1, 2026
- Imprint: Academic Press
- Authors: John Mordeson, Davender S. Malik, Sunil Mathew
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 4 4 0 9 7 - 7
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 4 4 0 9 8 - 4
Delve into the intricate landscape of fuzzy mathematics, where the boundaries of traditional mathematical disciplines—analysis, abstract algebra, geometry, topology, and graph… Read more
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Delve into the intricate landscape of fuzzy mathematics, where the boundaries of traditional mathematical disciplines—analysis, abstract algebra, geometry, topology, and graph theory—are blurred to address pressing global issues.
Through a rigorous examination of fuzzy sets and similarity measures, Introduction to Fuzzy Mathematics: With Applications to Global Problems lays the groundwork for innovative solutions to complex problems, from medical diagnostics to sustainability, refugee crises and the fight against human trafficking. Meanwhile, research projects and exercises integrated across chapters reinforce learning and apply fuzzy mathematics to real-world scenarios. Chapters are meticulously organized to guide readers through foundational concepts, including fuzzy sets, evidence theory, and implication operators, before advancing to applications in sustainability and climate change. Further, the book examines refugee dynamics and public health models, culminating in a thorough exploration of fuzzy algebraic structures, geometry, topology, and graph theory.
This comprehensive resource not only enhances understanding of fuzzy mathematics but also equips readers—researchers, practitioners, and policymakers alike—with the tools to tackle critical global issues. By integrating mathematical rigor with real-life applications, the book serves as a vital reference for anyone seeking to navigate the complexities of our world through the lens of fuzzy mathematics.
Through a rigorous examination of fuzzy sets and similarity measures, Introduction to Fuzzy Mathematics: With Applications to Global Problems lays the groundwork for innovative solutions to complex problems, from medical diagnostics to sustainability, refugee crises and the fight against human trafficking. Meanwhile, research projects and exercises integrated across chapters reinforce learning and apply fuzzy mathematics to real-world scenarios. Chapters are meticulously organized to guide readers through foundational concepts, including fuzzy sets, evidence theory, and implication operators, before advancing to applications in sustainability and climate change. Further, the book examines refugee dynamics and public health models, culminating in a thorough exploration of fuzzy algebraic structures, geometry, topology, and graph theory.
This comprehensive resource not only enhances understanding of fuzzy mathematics but also equips readers—researchers, practitioners, and policymakers alike—with the tools to tackle critical global issues. By integrating mathematical rigor with real-life applications, the book serves as a vital reference for anyone seeking to navigate the complexities of our world through the lens of fuzzy mathematics.
- Explores the innovative realm of fuzzy mathematics, addressing its foundations and application across analysis, algebra, geometry, topology, and graph theory in real-world contexts
- Introduces foundational concepts in fuzzy sets, evidence theory, fuzzy similarity measures, and their implications in sustainability, climate change, and human trafficking
- Equips mathematics students with essential tools to understand and apply fuzzy logic in diverse fields, enhancing their analytical and problem-solving skills
- Includes engaging research projects and exercises across chapters that reinforce learning and apply fuzzy mathematics to real-world scenarios and global challenges
Undergraduate, postgraduate, and PhD mathematics students
1. Preliminaries
1.1. Fuzzy Sets
1.2. Evidence Theory
1.3. Fuzzy Similarity Measures
1.4. Implication Operators
1.5. Fuzzy Graphs
2. Sustainability
2.1. Sustainable Development Goals
2.2. Sustainability and Climate Change Rankings
2.3. Fuzzy Similarity Measure of Rankings
2.4. Regions
3. Climate Change
3.1. Climate Change Performance Index
3.2. Regions CCPI
3.3. ND-Country Index
3.4. ND-GAIN and World Risk Report
4. Human Trafficking
4.1. Introduction
4.2. Personal Stories
4.3. Fuzzy Similarity Measures
4.4. Regions
5. Medical Applications of Fuzzy Sets
5.1. Medical Diagnosis: Degrees of Belief
5.2. Inferences Based on Belief Functions
5.3. Medical Diagnosis Using Possibility Measure
5.4. Vitamin D Receptor Gene and Bone Mineral Density: Belief Functions
6. Origin and Harbor of Refugees
6.1. Introduction
6.2. Preliminaries
6.3. Main Results
6.4. Fuzzy Similarity Measures of Country Refugee Rankings
7. SIR, SEIR, and SEIRS Models
7.1. SIR Model
7.2. SIER Model
7.3. Social Distancing
7.4. SIR and SEIR Models Merged
8. Integration and Differentiation of Fuzzy Functions
8.1. Fuzzy Numbers
8.2. Fuzzy Integration
8.3. Fuzzy Differentiation
8.4. Fuzzy SIR Model
9. Fuzzy Algebra
9.1. Algebraic Structures
9.2. Groups
9.3. Rings and Ideals
9.4. Varieties and Robotic Arms
9.5. Fuzzy Abstract Algebraic Structures
9.6. Free Monoids and Coding theory
9.7. Algebraic Coding Theory
10. Fuzzy Geometry
10.1. Points and Lines
10.2. Circles and Polygons
10.3. Rosenfeld's Context
11. Fuzzy Topology
11.1. Topological Space
11.2. Fuzzy Topological Spaces
11.3. Sequences of Fuzzy Subsets
11.4. F-continuous Functions
11.5. Compact Fuzzy Subsets
12. Fuzzy Graph Theory
12.1. Fuzzy Graphs and Subgraphs
12.2. Connectivity in Fuzzy Graphs
12.3. Fuzzy Trees and Cycles
12.4. Blocks in Fuzzy Graphs
12.5. Theta Fuzzy Graphs
12.6. Incidence Fuzzy Graphs
12.7. Influence Fuzzy Graphs
12.8. Applications of Fuzzy Graphs
1.1. Fuzzy Sets
1.2. Evidence Theory
1.3. Fuzzy Similarity Measures
1.4. Implication Operators
1.5. Fuzzy Graphs
2. Sustainability
2.1. Sustainable Development Goals
2.2. Sustainability and Climate Change Rankings
2.3. Fuzzy Similarity Measure of Rankings
2.4. Regions
3. Climate Change
3.1. Climate Change Performance Index
3.2. Regions CCPI
3.3. ND-Country Index
3.4. ND-GAIN and World Risk Report
4. Human Trafficking
4.1. Introduction
4.2. Personal Stories
4.3. Fuzzy Similarity Measures
4.4. Regions
5. Medical Applications of Fuzzy Sets
5.1. Medical Diagnosis: Degrees of Belief
5.2. Inferences Based on Belief Functions
5.3. Medical Diagnosis Using Possibility Measure
5.4. Vitamin D Receptor Gene and Bone Mineral Density: Belief Functions
6. Origin and Harbor of Refugees
6.1. Introduction
6.2. Preliminaries
6.3. Main Results
6.4. Fuzzy Similarity Measures of Country Refugee Rankings
7. SIR, SEIR, and SEIRS Models
7.1. SIR Model
7.2. SIER Model
7.3. Social Distancing
7.4. SIR and SEIR Models Merged
8. Integration and Differentiation of Fuzzy Functions
8.1. Fuzzy Numbers
8.2. Fuzzy Integration
8.3. Fuzzy Differentiation
8.4. Fuzzy SIR Model
9. Fuzzy Algebra
9.1. Algebraic Structures
9.2. Groups
9.3. Rings and Ideals
9.4. Varieties and Robotic Arms
9.5. Fuzzy Abstract Algebraic Structures
9.6. Free Monoids and Coding theory
9.7. Algebraic Coding Theory
10. Fuzzy Geometry
10.1. Points and Lines
10.2. Circles and Polygons
10.3. Rosenfeld's Context
11. Fuzzy Topology
11.1. Topological Space
11.2. Fuzzy Topological Spaces
11.3. Sequences of Fuzzy Subsets
11.4. F-continuous Functions
11.5. Compact Fuzzy Subsets
12. Fuzzy Graph Theory
12.1. Fuzzy Graphs and Subgraphs
12.2. Connectivity in Fuzzy Graphs
12.3. Fuzzy Trees and Cycles
12.4. Blocks in Fuzzy Graphs
12.5. Theta Fuzzy Graphs
12.6. Incidence Fuzzy Graphs
12.7. Influence Fuzzy Graphs
12.8. Applications of Fuzzy Graphs
- Edition: 1
- Published: March 1, 2026
- Imprint: Academic Press
- Language: English
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, USADM
Davender S. Malik
Dr. Davender S. Malik is a Professor of Mathematics at Creighton University, Omaha, Nebraska. He received his Ph.D. from Ohio University and has published more than 65 papers and 20 books on abstract algebra, applied mathematics, graph theory and automata theory and languages, fuzzy logic and its applications, programming, data structures and discrete mathematics.
Affiliations and expertise
Professor of Mathematics, Creighton University, Omaha, Nebraska, 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, India