Today, Fuzzy Set Theory is the core discipline of so-called ‘soft’ computing, and provides new impetus for research in the field of artificial intelligence. In this fascinating book, the history of Fuzzy Set Theory and the ways it was first used are incorporated into the history of 20th century science and technology. Influences from philosophy, system theory and cybernetics stemming from the earliest part of the 20th century are considered alongside those of communication and control theory from mid-century.

Hier lernen Sie, Expertensysteme auf der Basis von Fuzzy Logic zu konstruieren, die sich für den praktischen Einsatz eignen. Expertensysteme werden zunächst allgemein definiert, und die zugrundeliegende Mathematik wird eingeführt. Regelbasierte Systeme werden gründlicher besprochen als in jedem anderen Buch mit ähnlichem Thema. Am Ende jedes Kapitels können Sie Ihren Wissensstand anhand von Übungsaufgaben überprüfen. Von einem zugehörigen ftp-Server können Sie Ergänzungsmaterial abrufen. Für Praktiker und Forscher aus dem akademischen Umfeld gleichermaßen geeignet!

Provides an introduction to the fundamental concepts of fuzziness together with a compilation of recent advances in the application to medicine. The tutorials in the first part of the book range from basic concepts through theoretical frameworks to rule simplification through data clustering methodologies and the design of multivariate rule bases through self-learning by mapping fuzzy systems onto neural network structures. The case studies which follow are representative of the wide range of applications currently pursued in relation to medicine. The majority of applications presented in this book are about bridging the gap between low-level sensor measurements and intermediate or high-level data representations. The book offers a comprehensive perspective from leading authorities world-wide and provides a tantalising glimpse into the role of sophisticated knowledge engineering methods in shaping the landscape of medical technology in the future.

Examines the methodology and algorithms of fuzzy sets considered mainly in the context of control engineering and system modelling and analysis. Special emphasis is focused on the processing of fuzzy information realized with the aid of fuzzy relational structures and their extensions.

This book is open access under a CC BY 4.0 license. This open access book offers comprehensive coverage on Ordered Fuzzy Numbers, providing readers with both the basic information and the necessary expertise to use them in a variety of real-world applications. The respective chapters, written by leading researchers, discuss the main techniques and applications, together with the advantages and shortcomings of these tools in comparison to other fuzzy number representation models. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easy-to-understand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike.

Fuzzy logic refers to a large subject dealing with a set of methods to characterize and quantify uncertainty in engineering systems that arise from ambiguity, imprecision, fuzziness, and lack of knowledge. Fuzzy logic is a reasoning system based on a foundation of fuzzy set theory, itself an extension of classical set theory, where set membership can be partial as opposed to all or none, as in the binary features of classical logic. Fuzzy logic is a relatively new discipline in which major advances have been made over the last decade or so with regard to theory and applications. Following on from the successful first edition, this fully updated new edition is therefore very timely and much anticipated. Concentration on the topics of fuzzy logic combined with an abundance of worked examples, chapter problems and commercial case studies is designed to help motivate a mainstream engineering audience, and the book is further strengthened by the inclusion of an online solutions manual as well as dedicated software codes. Senior undergraduate and postgraduate students in most engineering disciplines, academics and practicing engineers, plus some working in economics, control theory, operational research etc, will all find this a valuable addition to their bookshelves.

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.

This book is an essential contribution to the description of fuzziness in information systems. Usually users want to retrieve data or summarized information from a database and are interested in classifying it or building rule-based systems on it. But they are often not aware of the nature of this data and/or are unable to determine clear search criteria. The book examines theoretical and practical approaches to fuzziness in information systems based on statistical data related to territorial units. Chapter 1 discusses the theory of fuzzy sets and fuzzy logic to enable readers to understand the information presented in the book. Chapter 2 is devoted to flexible queries and includes issues like constructing fuzzy sets for query conditions, and aggregation operators for commutative and non-commutative conditions, while Chapter 3 focuses on linguistic summaries. Chapter 4 presents fuzzy logic control architecture adjusted specifically for the aims of business and governmental agencies, and shows fuzzy rules and procedures for solving inference tasks. Chapter 5 covers the fuzzification of classical relational databases with an emphasis on storing fuzzy data in classical relational databases in such a way that existing data and normal forms are not affected. This book also examines practical aspects of user-friendly interfaces for storing, updating, querying and summarizing. Lastly, Chapter 6 briefly discusses possible integration of fuzzy queries, summarization and inference related to crisp and fuzzy databases. The main target audience of the book is researchers and students working in the fields of data analysis, database design and business intelligence. As it does not go too deeply into the foundation and mathematical theory of fuzzy logic and relational algebra, it is also of interest to advanced professionals developing tailored applications based on fuzzy sets.

The second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material.

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.