Fuzzy Set Theory And Advanced Mathematical Applications

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

Fuzzy Set Theory: Foundations and Applications serves as a simple introduction to basic elements of fuzzy set theory. The emphasis is on a conceptual rather than a theoretical presentation of the material. Fuzzy Set Theory also contains an overview of the corresponding elements of classical set theory - including basic ideas of classical relations - as well as an overview of classical logic. Because the inclusion of background material in these classical foundations provides a self-contained course of study, students from many different academic backgrounds will have access to this important new theory.

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.

FUZZY LOGIC APPLICATIONS IN COMPUTER SCIENCE AND MATHEMATICSTICS The prime objective of developing this book is to provide meticulous details about the basic and advanced concepts of fuzzy logic and its all-around applications to different fields of mathematics and engineering. The basic steps of fuzzy inference systems starting from the core foundation of the fuzzy concepts are presented in this book. The fuzzy theory is a mathematical concept and, at the same time, it is applied to many versatile engineering fields and research domains related to computer science. The fuzzy system offers some knowledge about uncertainty and is also related to the theory of probability. A fuzzy logic-based model acts as the classifier for many different types of data belonging to several classes. Covered in this book are topics such as the fundamental concepts of mathematics, fuzzy logic concepts, probability and possibility theories, and evolutionary computing to some extent. The combined fields of neural network and fuzzy domain (known as the neuro-fuzzy system) are explained and elaborated. Each chapter has been produced in a very lucid manner, with grading from simple to complex to accommodate the anticipated different audiences. The application-oriented approach is the unique feature of this book. Audience This book will be read and used by a broad audience including applied mathematicians, computer scientists, and industry engineers.

Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications.

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity.