Introduction to Fuzzy Mathematics - Edition 1 - By John Mordeson, Davender S. Malik and Sunil Mathew Elsevier Educate

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Introduction to Fuzzy Mathematics,

Edition 1 With Applications to Global Problems

By John Mordeson, Davender S. Malik and Sunil Mathew

Publication Date: 01 Mar 2026

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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.

Key Features

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

About the author

By John Mordeson, Professor Emeritus of Mathematics, Creighton University, USA; Davender S. Malik, Professor of Mathematics, Creighton University, Omaha, Nebraska, USA and Sunil Mathew, Associate Professor, Department of Mathematics, NIT, Calicut, India

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

ISBN: 9780443440977

Page Count: 250

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Undergraduate, postgraduate, and PhD mathematics students

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