Mathematics of Fuzzy Sets and Fuzzy Logic


Book Description

This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.




Fuzzy Rule-Based Inference


Book Description




Genetic Fuzzy Systems: Evolutionary Tuning And Learning Of Fuzzy Knowledge Bases


Book Description

In recent years, a great number of publications have explored the use of genetic algorithms as a tool for designing fuzzy systems. Genetic Fuzzy Systems explores and discusses this symbiosis of evolutionary computation and fuzzy logic. The book summarizes and analyzes the novel field of genetic fuzzy systems, paying special attention to genetic algorithms that adapt and learn the knowledge base of a fuzzy-rule-based system. It introduces the general concepts, foundations and design principles of genetic fuzzy systems and covers the topic of genetic tuning of fuzzy systems. It also introduces the three fundamental approaches to genetic learning processes in fuzzy systems: the Michigan, Pittsburgh and Iterative-learning methods. Finally, it explores hybrid genetic fuzzy systems such as genetic fuzzy clustering or genetic neuro-fuzzy systems and describes a number of applications from different areas.Genetic Fuzzy System represents a comprehensive treatise on the design of the fuzzy-rule-based systems using genetic algorithms, both from a theoretical and a practical perspective. It is a valuable compendium for scientists and engineers concerned with research and applications in the domain of fuzzy systems and genetic algorithms.




Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications


Book Description

Soft computing is a consortium of computing methodologies that provide a foundation for the conception, design, and deployment of intelligent systems and aims to formalize the human ability to make rational decisions in an environment of uncertainty and imprecision. This book is based on a NATO Advanced Study Institute held in 1996 on soft computing and its applications. The distinguished contributors consider the principal constituents of soft computing, namely fuzzy logic, neurocomputing, genetic computing, and probabilistic reasoning, the relations between them, and their fusion in industrial applications. Two areas emphasized in the book are how to achieve a synergistic combination of the main constituents of soft computing and how the combination can be used to achieve a high Machine Intelligence Quotient.




Fuzzy Expert Systems and Fuzzy Reasoning


Book Description

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!




Fuzzy Systems Engineering


Book Description

This book is devoted to reporting innovative and significant progress in fuzzy system engineering. Given the maturation of fuzzy logic, this book is dedicated to exploring the recent breakthroughs in fuzziness and soft computing in favour of intelligent system engineering. This monograph presents novel developments of the fuzzy theory as well as interesting applications of the fuzzy logic exploiting the theory to engineer intelligent systems.




Uncertain Rule-Based Fuzzy Systems


Book Description

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.




Fuzzy Systems


Book Description

The analysis and control of complex systems have been the main motivation for the emergence of fuzzy set theory since its inception. It is also a major research field where many applications, especially industrial ones, have made fuzzy logic famous. This unique handbook is devoted to an extensive, organized, and up-to-date presentation of fuzzy systems engineering methods. The book includes detailed material and extensive bibliographies, written by leading experts in the field, on topics such as: Use of fuzzy logic in various control systems. Fuzzy rule-based modeling and its universal approximation properties. Learning and tuning techniques for fuzzy models, using neural networks and genetic algorithms. Fuzzy control methods, including issues such as stability analysis and design techniques, as well as the relationship with traditional linear control. Fuzzy sets relation to the study of chaotic systems, and the fuzzy extension of set-valued approaches to systems modeling through the use of differential inclusions. Fuzzy Systems: Modeling and Control is part of The Handbooks of Fuzzy Sets Series. The series provides a complete picture of contemporary fuzzy set theory and its applications. This volume is a key reference for systems engineers and scientists seeking a guide to the vast amount of literature in fuzzy logic modeling and control.




Fuzzy Logic


Book Description

Fuzzy Logic: A Practical Approach focuses on the processes and approaches involved in fuzzy logic, including fuzzy sets, numbers, and decisions. The book first elaborates on fuzzy numbers and logic, fuzzy systems on the job, and Fuzzy Knowledge Builder. Discussions focus on formatting the knowledge base for an inference engine, personnel detection system, using a knowledge base in an inference engine, fuzzy business systems, industrial fuzzy systems, fuzzy sets and numbers, and quantifying word-based rules. The text then elaborates on designing a fuzzy decision and Fuzzy Thought Amplifier for complex situations. Topics include origins of cognitive maps, Fuzzy Thought Amplifier, training a map to predict the future, introducing the Fuzzy Decision Maker, and merging interests. The publication takes a look at fuzzy associative memory, fuzzy sets as hypercube points, and disk files and descriptions, including Fuzzy Thought Amplifier, Fuzzy Decision Maker, and composing and creating a memory. The text is a valuable source of data for researchers interested in fuzzy logic.




Uncertain Rule-based Fuzzy Logic Systems


Book Description

Jerry Mendel explains the complete development of fuzzy logic systems and explores a new methodology to build better and more intelligent systems. Two case studies are carried throughout the book to illustrate and expand on the theories introduced.