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This highly accessible introduction to the fundamentals of fuzzy sets and their applications covers fuzzy numbers, fuzzy programming, fuzzy controllers, qualitative fuzzy data analysis, and much more.
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.
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.
This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words — a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.
This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.
Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.
This book provides a timely and comprehensive overview of current theories and methods in fuzzy logic, as well as relevant applications in a variety of fields of science and technology. Dedicated to Lotfi A. Zadeh on his one year death anniversary, the book goes beyond a pure commemorative text. Yet, it offers a fresh perspective on a number of relevant topics, such as computing with words, theory of perceptions, possibility theory, and decision-making in a fuzzy environment. Written by Zadeh’s closest colleagues and friends, the different chapters are intended both as a timely reference guide and a source of inspiration for scientists, developers and researchers who have been dealing with fuzzy sets or would like to learn more about their potential for their future research.
The 7th International Workshop on Fuzzy Logic and Applications, held in Camogli, Italy in July 2007, presented the latest findings in the field. This volume features the refereed proceedings from that meeting. It includes 84 full papers as well as three keynote speeches. The papers are organized into topical sections covering fuzzy set theory, fuzzy information access and retrieval, fuzzy machine learning, and fuzzy architectures and systems.
Ten years ago, Zadeh has brought into vogue the use of a name. Scientists no is an increasing less than poets strike off words that fit a situation. Today there recognition that for understanding vagueness, a fuzzy approach is required. We are just going through ~ transient period. From discussions of general philosophy to practical methods for system analysis. Unfortunately, much of the existing research is scattered. The practitioner interested in these methods face the challenge of sorting through a vast amount of literature to find a core on which to build. One of the objects of this book was to facilitate communication by bringing toge ther different viewpoints and coloring them from a common viewpoint. Since the romanian version appeared, at the very beginning of 1974, there has been a rapid growth in the literature of fuzzy modelling. A minor revision would have left the book quite out-of-date. The opportunity has been taken to correct, clarify, and update. Inexactness is implicit in human behaviour and erare humanum est. It is a pleasure to acknowledge the help we have received in preparing this version. The opportunity to see an english edition was a powerful stimulus, and we are grateful to Salomon Klaczko for making this possible. Another debt is to all fuzzy authors we have quoted. Their fascinating papers kindled our interest in the subject.