Davender S. Malik - Böcker

The huge number and broad range of the existing and potential applications of fuzzy logic have precipitated a veritable avalanche of books published on the subject. Most, however, focus on particular areas of application. Many do no more than scratch the surface of the theory that holds the power and promise of fuzzy logic.Fuzzy Automata and Languages: Theory and Applications offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. After introducing background material, the authors study max-min machines and max-product machines, developing their respective algebras and exploring properties such as equivalences, homomorphisms, irreducibility, and minimality. The focus then turns to fuzzy context-free grammars and languages, with special attention to trees, fuzzy dendrolanguage generating systems, and normal forms. A treatment of algebraic fuzzy automata theory follows, along with additional results on fuzzy languages, minimization of fuzzy automata, and recognition of fuzzy languages. Although the book is theoretical in nature, the authors also discuss applications in a variety of fields, including databases, medicine, learning systems, and pattern recognition.Much of the information on fuzzy languages is new and never before presented in book form. Fuzzy Automata and Languages incorporates virtually all of the important material published thus far. It stands alone as a complete reference on the subject and belongs on the shelves of anyone interested in fuzzy mathematics or its applications.

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow’s theorem, and Black’s median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu’s degree of similarity of two fuzzy choice functions.

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, An 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 contextsIntroduces foundational concepts in fuzzy sets, evidence theory, fuzzy similarity measures, and their implications in sustainability, climate change, and human traffickingEquips mathematics students with essential tools to understand and apply fuzzy logic in diverse fields, enhancing their analytical and problem-solving skillsIncludes engaging research projects and exercises across chapters that reinforce learning and apply fuzzy mathematics to real-world scenarios and global challenges

Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the "union" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow’s theorem, and Black’s median voter theorem for fuzzy preferences. It examines how unambiguous and exact choices are generated by fuzzy preferences and whether exact choices induced by fuzzy preferences satisfy certain plausible rationality relations. The authors also extend known Arrowian results involving fuzzy set theory to results involving intuitionistic fuzzy sets as well as the Gibbard–Satterthwaite theorem to the case of fuzzy weak preference relations. The final chapter discusses Georgescu’s degree of similarity of two fuzzy choice functions.

The huge number and broad range of the existing and potential applications of fuzzy logic have precipitated a veritable avalanche of books published on the subject. Most, however, focus on particular areas of application. Many do no more than scratch the surface of the theory that holds the power and promise of fuzzy logic.Fuzzy Automata and Languages: Theory and Applications offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. After introducing background material, the authors study max-min machines and max-product machines, developing their respective algebras and exploring properties such as equivalences, homomorphisms, irreducibility, and minimality. The focus then turns to fuzzy context-free grammars and languages, with special attention to trees, fuzzy dendrolanguage generating systems, and normal forms. A treatment of algebraic fuzzy automata theory follows, along with additional results on fuzzy languages, minimization of fuzzy automata, and recognition of fuzzy languages. Although the book is theoretical in nature, the authors also discuss applications in a variety of fields, including databases, medicine, learning systems, and pattern recognition.Much of the information on fuzzy languages is new and never before presented in book form. Fuzzy Automata and Languages incorporates virtually all of the important material published thus far. It stands alone as a complete reference on the subject and belongs on the shelves of anyone interested in fuzzy mathematics or its applications.

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.

Mathematics of Uncertainty Applied to Global Issues explores how mathematical tools can illuminate some of the most pressing challenges facing our world today. Authored by John N. Mordeson, Sunil Mathew, and Davender S. Malik, this book bridges the gap between abstract mathematical theory and real-world global concerns.Addressing critical issues such as sustainability, the mistreatment of women, nuclear power, smart cities, and digitalization, the book demonstrates how fuzzy set theory and fuzzy similarity measures can be used to analyse complex, uncertain, and interconnected systems. By examining rankings of countries, states, and cities across diverse indicators—including environmental performance, social justice, human development, and technological advancement—the authors reveal hidden relationships and patterns among global challenges.The text develops foundational concepts in fuzzy mathematics and extends them to innovative methodologies for comparing multiple rankings. Through applications ranging from refugee crises and biodiversity targets to urban sustainability and artificial intelligence, the book provides a unique quantitative perspective on global development issues.Combining rigorous theory with meaningful applications, this volume serves as a valuable resource for advanced undergraduate and graduate students, researchers, and educators in mathematics, data science, and the social sciences. It offers not only analytical tools but also insights into how mathematics can contribute to understanding and addressing the complexities of an uncertain world.

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

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.

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas.

The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. The book concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. Basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages are reviewed and introduced, as well as certain fuzzy ideals of a semigroup and advanced characterizations and properties of fuzzy semigroups.

The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. The book concentrates on theoretical aspects, but also includes applications in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. Basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages are reviewed and introduced, as well as certain fuzzy ideals of a semigroup and advanced characterizations and properties of fuzzy semigroups.

The subject of the book could be described as fuzzy discrete structures. The book deals with fuzzy logic, fuzzy switching functions, fuzzy decision trees, fuzzy networks, fuzzy petri nets, fuzzy path problems, fuzzy automata, and fuzzy languages. The notion of a fuzzy decision tree and a branch-bound-backtrack algorithm is presented. In the appendix, this algorithm is described in C++. Network flow problems with various capacities are examined. Fuzzy shortest path techniques are presented whereby there is an actual path which corresponds to the fuzzy shortest path. Recent results on fuzzy automata and fuzzy languages are also presented.

The subject of the book could be described as fuzzy discrete structures. The book deals with fuzzy logic, fuzzy switching functions, fuzzy decision trees, fuzzy networks, fuzzy petri nets, fuzzy path problems, fuzzy automata, and fuzzy languages. The notion of a fuzzy decision tree and a branch-bound-backtrack algorithm is presented. In the appendix, this algorithm is described in C++. Network flow problems with various capacities are examined. Fuzzy shortest path techniques are presented whereby there is an actual path which corresponds to the fuzzy shortest path. Recent results on fuzzy automata and fuzzy languages are also presented.