Although the use of fuzzy control methods has grown nearly to the level of classical control, the true understanding of fuzzy control lags seriously behind. Moreover, most engineers are well versed in either traditional control or in fuzzy control-rarely both. Each has applications for which it is better suited, but without a good understanding of both, engineers cannot make a sound determination of which technique to use for a given situation.

A First Course in Fuzzy and Neural Control is designed to build the foundation needed to make those decisions. It begins with an introduction to standard control theory, then makes a smooth transition to complex problems that require innovative fuzzy, neural, and fuzzy-neural techniques. For each method, the authors clearly answer the questions: What is this new control method? Why is it needed? How is it implemented? Real-world examples, exercises, and ideas for student projects reinforce the concepts presented.

Developed from lecture notes for a highly successful course titled The Fundamentals of Soft Computing, the text is written in the same reader-friendly style as the authors' popular A First Course in Fuzzy Logic text. A First Course in Fuzzy and Neural Control requires only a basic background in mathematics and engineering and does not overwhelm students with unnecessary material but serves to motivate them toward more advanced studies.

Modelling Invasive Alien Plant Species: Fuzzy Based Uncertainty presents the application of different fuzzy set theory techniques in developing risk assessment models for invasive plant species- those whose introduction and spread outside their natural range threatens local biodiversity. Invasion risk of species is expressed by biological traits which would be considered as the risk factors accompanied with uncertainty and imprecision. The book considers both quantitative and qualitative inputs in modelling the invasive risk by incorporating different mathematical models based on fuzzy set theory operators, interval methods, and fuzzy linguistic operators. The proposed models can be applied for investigating risk of invasive alien plant species in various regions and conditions. Features: Uniquely merges mathematical models with biological expressions. Presents different factor-based models as a case study on the risk of invasive alien plant species. Explains how users can perform primary-level risk assessment through fuzzy modeling techniques. Appropriate for upper-level students, researchers, and practicing professionals, this book shows how conventional approaches such as probability theory can be of limited use to solve issues of uncertainty, and how they fuzzy set theory plays a better role in understanding uncertain system dynamics, such invasive plant modelling.

Surfaces are a central to geographical analysis. Their generation and manipulation are a key component of geographical information systems (GISs). However, geographical surface data is often not precise. When surfaces are used to model geographical entities, the data inherently contains uncertainty in terms of both position and attribute. Fuzzy Surface in GIS and Geographical Analysis sets out a process to identify the uncertainty in geographic entities. It describes how to successfully obtain, model, analyze, and display data, as well as interpret results within the context of GIS. Focusing on uncertainty that arises from transitional boundaries, the book limits its study to three types of uncertainties: intervals, fuzzy sets, and possibility distributions. The book explains that uncertainty in geographical data typically stems from these three and it is only natural to incorporate them into the analysis and display of surface data. The book defines the mathematics associated with each method for analysis, then develops related algorithms, and moves on to illustrate various applications. Fuzzy Surface in GIS and Geographical Analysis clearly defines how to develop a routine that will adequately account for the uncertainties inherent in surface data.

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.

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.

Classical and Fuzzy Concepts in Mathematical Logic and Applications provides a broad, thorough coverage of the fundamentals of two-valued logic, multivalued logic, and fuzzy logic. Exploring the parallels between classical and fuzzy mathematical logic, the book examines the use of logic in computer science, addresses questions in automatic deduction, and describes efficient computer implementation of proof techniques. Specific issues discussed include: oPropositional and predicate logic oLogic networks oLogic programming oProof of correctness oSemantics oSyntax oCompletenesss oNon-contradiction oTheorems of Herbrand and Kalman The authors consider that the teaching of logic for computer science is biased by the absence of motivations, comments, relevant and convincing examples, graphic aids, and the use of color to distinguish language and metalanguage. Classical and Fuzzy Concepts in Mathematical Logic and Applications discusses how the presence of these facts trigger a stirring, decisive insight into the understanding process. This view shapes this work, reflecting the authors' subjective balance between the scientific and pedagogic components of the textbook. Usually, problems in logic lack relevance, creating a gap between classroom learning and applications to real-life problems. The book includes a variety of application-oriented problems at the end of almost every section, including programming problems in PROLOG III. With the possibility of carrying out proofs with PROLOG III and other software packages, readers will gain a first-hand experience and thus a deeper understanding of the idea of formal proof.

The emergence of fuzzy logic and its applications has dramatically changed the face of industrial control engineering. Over the last two decades, fuzzy logic has allowed control engineers to meet and overcome the challenges of developing effective controllers for increasingly complex systems with poorly defined dynamics. Today's engineers need a working knowledge of the principles and techniques of fuzzy logic-Intelligent Control provides it.

The author first introduces the traditional control techniques and contrasts them with intelligent control. He then presents several methods of representing and processing knowledge and introduces fuzzy logic as one such method. He highlights the advantages of fuzzy logic over other techniques, indicates its limitations, and describes in detail a hierarchical control structure appropriate for use in intelligent control systems. He introduces a variety of applications, most in the areas of robotics and mechatronics but with others including air conditioning and process/production control. One appendix provides discussion of some advanced analytical concepts of fuzzy logic, another describes a commercially available software system for developing fuzzy logic application.

Intelligent Control is filled with worked examples, exercises, problems, and references. No prior knowledge of the subject nor advanced mathematics are needed to comprehend much of the book, making it well-suited as a senior undergraduate or first-year graduate text and a convenient reference tool for practicing professionals.

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.

For more than 2000 years, Western science has been based on absolutes. Things are black or white, alive or dead, all or nothing. As human beings we know the world is not really like this, that degrees exist between the extremes. But until now science has been unable to accommodate these uncertainties. Fuzzy logic is a scientific revolution that has been waiting to happen for decades – and its central tenets will dramatically change the relationship human beings have with the world. The question is to what degree.

In this absorbing, iconoclastic account of the head-spinning possibilities for fuzzy technology, Bart Kosko, fuzzy logic's most famous and combative apostle, urges us to abandon the debilitating binary world and turn to the East, for the future will be 'fuzzy'.

‘One day I learned that science was not true. I do not recall the day but I recall the moment. The God of the twentieth century was no longer God.’

"An exciting alternative form of logic"
TIM CRANE, 'Sunday Telegraph'

"'Fuzzy Thinking' is about… a radically different way of structuring our thoughts and experience … that transforms our perception of reality."
DANAH ZOHAR, 'Independent on Sunday'

"'Fuzzy Logic' works… It will become a significant technological force"
MICHAEL WHITE, 'The Times'

"Bart Kosko is an extraordinary and polymathic combination of talents"
PROFESSOR MARVIN MINSKY, 'MIT'

"Bart Kosko is the quintessential scientific cyberpunk – a hip, street-smart prophet of life in the Information Age"
LOS ANGELES TIMES

"Fuzzy Logic is the cocaine of science"
PROFESSOR WILLIAM KAHAN, 'UC Berkeley'

Since its inception, fuzzy logic has attracted an incredible amount of interest, and this interest continues to grow at an exponential rate. As such, scientists, researchers, educators and practitioners of fuzzy logic continue to expand on the applicability of what and how fuzzy can be utilised in the real-world. In this book, the authors present key application areas where fuzzy has had significant success. The chapters cover a plethora of application domains, proving credence to the versatility and robustness of a fuzzy approach. A better understanding of fuzzy will ultimately allow for a better appreciation of fuzzy. This book provides the reader with a varied range of examples to illustrate what fuzzy logic can be capable of and how it can be applied. The text will be ideal for individuals new to the notion of fuzzy, as well as for early career academics who wish to further expand on their knowledge of fuzzy applications. The book is also suitable as a supporting text for advanced undergraduate and graduate-level modules on fuzzy logic, soft computing, and applications of AI.

An original, systematic-solution approach to uncertain nonlinear systems control and modeling using fuzzy equations and fuzzy differential equations There are various numerical and analytical approaches to the modeling and control of uncertain nonlinear systems. Fuzzy logic theory is an increasingly popular method used to solve inconvenience problems in nonlinear modeling. Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number presents a structured approach to the control and modeling of uncertain nonlinear systems in industry using fuzzy equations and fuzzy differential equations. The first major work to explore methods based on neural networks and Bernstein neural networks, this innovative volume provides a framework for control and modeling of uncertain nonlinear systems with applications to industry. Readers learn how to use fuzzy techniques to solve scientific and engineering problems and understand intelligent control design and applications. The text assembles the results of four years of research on control of uncertain nonlinear systems with dual fuzzy equations, fuzzy modeling for uncertain nonlinear systems with fuzzy equations, the numerical solution of fuzzy equations with Z-numbers, and the numerical solution of fuzzy differential equations with Z-numbers. Using clear and accessible language to explain concepts and principles applicable to real-world scenarios, this book: Presents the modeling and control of uncertain nonlinear systems with fuzzy equations and fuzzy differential equations Includes an overview of uncertain nonlinear systems for non-specialists Teaches readers to use simulation, modeling and verification skills valuable for scientific research and engineering systems development Reinforces comprehension with illustrations, tables, examples, and simulations Modeling and Control of Uncertain Nonlinear Systems with Fuzzy Equations and Z-Number is suitable as a textbook for advanced students, academic and industrial researchers, and practitioners in fields of systems engineering, learning control systems, neural networks, computational intelligence, and fuzzy logic control.

Contents:
HVAC Control Systems. Basic concepts. HVAC control strategies. Distributed control. System configuration. References. Device Technology. Sensors. Control elements. PID controllers. References. System modelling. Simple room modelling for control analysis. Accounting for fabric in room modelling. Heat emitter and non-linear modelling. A coupled room and emitter model. Component modelling. References. System Stability. Feedback control. Stability test. Feedforward control. Model reduction. References. Discrete-time Systems. The z-transformation. Representing discrete-time systems. Stability tests in discrete-time. The sampling interval. Digital control algorithms. References. Multivariable Systems. State-space representation of systems. The transfer function matrix. The multivariable control problem. Design of multivariable compensators. References. System Identification and Controller Tuning. System identification. Assessing the quality of response. Fixed parameter controller tuning method. References. Adaptive Control. Adaptive controllers. Direct and indirect adaptive control algorithms. Model reference adaptive control. Gain scheduling. Progress in HVAC adaptive control. References. Advanced Methods. Robust Control. Expert systems. Fuzzy logic control. Artificial neural networks. References.

Much has happened in the field of inference and decision making during the past decade or so. This fully updated and revised third edition of Comparative Statistical Inference presents a wide ranging, balanced account of the fundamental issues across the full spectrum of inference and decision making. As in earlier editions, the material is set in a historical context to more powerfully illustrate the ideas and concepts.

• Includes fully updated and revised material from the successful second edition
• Discusses all recent major developments
• Particular attention is given to the nature and importance of basic concepts (probability, utility, likelihood, etc.)
• Includes extensive references and bibliograph

Recent changes in emphasis, principle and methodology are carefully explained and evaluated. These include major developments in the use of modified forms of the likelihood function, the computational and interpretative advantages opened up by the Gibbs sampler and Markov Chain Monte Carlo methods, advances in predictive methods in classical Bayesian contexts (including the prequential approach) and broader incorporation of multiparameter issues. With the many additions and changes, the essence of this successful book remains unchanged providing the reader with a thorough explanation of the many approaches to inference and decision making.

Fuzzy logic-based circuits are instrumental in computer hardware applications. Currently, they are widely relied upon to recognize gradual and relative properties in electronic and real data. This comprehensive edited volume focuses on 'fuzzy technology'. Presented in four clearly organized thematic sections, coverage includes fuzzy set theory, fuzzy logic control, examples of fuzzy logic implementations and finally examples of neuro-fuzzy hybrid systems and their applications, featuring explanation of classical fuzzy logic, fuzzy arithmetic operations, approximate reasoning and fuzzy control in terms of Boolean logic, set theory, and control theory; detailed discussion of digital and analog implementation of fuzzy logic discrete and VLSI circuits; coverage of fuzzy control-based systematic design methodology, and assessment of the compatibility of conventional control with crisp fuzzy control; an overview of the latest fuzzy logic digital and analog hardware applications including CMOS and CAD tools; and includes the chapter-by-chapter synopses and exercises. Written by a team of internationally renowned computer science specialists, this is a forward-looking account of the emergence of neuro-fuzzy systems. Professional computer scientists and engineers developing fuzzy logic applications will find this an invaluable reference. Researchers and students in the broad field of artificial intelligence will find this a source of inspiration.

Fuzzy set theory provides a framework for representing uncertainty. As increasing importance is being given to uncertainty management in intelligent systems, fuzzy inferencing procedures are vital. Using Fest (Fuzzy Expert System Tools), the authors focus on the parameters of fuzzy rule-based systems. The book then goes on to show how Fest can be used for inference of indistinct data and algorithmic descriptions. Divided into three parts, this comprehensive text covers the characteristics of expert systems and fuzzy sets theory, knowledge representation and the inference process. Features include:
* Incorporation of uncertainty management and fuzzy logic in soft expert systems
* Coverage of the processes of knowledge acquisition, representation, and generation
* Novel ideas in approaching fuzzy inferencing
* Notions pertaining to flexible grammar and the use of synonyms
Written by international experts, this is an invaluable reference for engineers and computer scientists working in the areas of expert systems, fuzzy logic systems and applications of fuzzy logic both in industry and academia. The accompanying disk will allow readers to practice the methods introduced and thus highlight the power of fuzzy logic when combined with expert system technology.

Fuzzy Logic has gained increasing acceptance as a way to deal with complexity and uncertainty in many areas of science and engineering. This book is the first to address its practical applications to chemical systems. Ten distinguished authors discuss the role of fuzzy logic in the characterization of a variety of chemical concepts, including chirality, quantum systems, molecular engineering and design, and hierarchical classification methods. Fuzzy Logic in Chemistry will appeal to both students and professionals who are seeking to learn more about theory and applications in an area of growing importance to the physical sciences.
Key Features
* The first book on the applications of fuzzy logic in chemistry
* Covers a topic relevant to many disciplines, including molecular design
* Discusses applications of fuzzy logic to the physical sciences, a rapidly growing area
* Features chapters from highly distinguished authors in the physical sciences

Electrical Engineering Electric Power Applications of Fuzzy Systems Let world-renowned electrical engineers introduce you to the latest developments in the application of one of the fastest growing artificial intelligence techniques for power systems--fuzzy system theory. Compiled and edited by well-known power systems educator Mohamed E. El-Hawary, Electric Power Applications of Fuzzy Systems assembles a distinguished panel of highly regarded experts to bring you original, up-to-date coverage of the applications of fuzzy systems. This volume presents theoretical background material from a practical point of view and then explores a number of applications of fuzzy systems. Each chapter features an informative introduction. Look for succinct, practical discussions on:

• Fuzzy sets
• Fuzzy controllers
• Fuzzy perspectives on power system reliability, condition monitoring, and diagnostics
• Ground-breaking chapter on applications in operational planning
• Up-to-the-minute chapter on fuzzy applications in deregulated environment

Electric Power Applications of Fuzzy Systems will help you understand how the application of fuzzy theory in power systems is revolutionizing the way we look at many areas of practice. It is essential for power system engineers who want to launch into real-world applications of this increasingly popular technique.

Multistage Fuzzy Control a model-based approach to fuzzy control and decision making Fuzzy techniques are used to cope with imprecision in the control process. This authoritative book explains the essential principles of fuzzy logic and describes both the theoretical and practical advantages of the new model-based, prescriptive approach. Professor Kacprzyk offers a comprehensive and in depth examination of the issues underlying multistage control and decision analysis, addressing in particular fuzzy dynamic systems, fuzzy events, fuzzy probabilities and fuzzy quantifiers. The text also comprises an introduction to the basic concepts of fuzzy sets, fuzzy logic and fuzzy systems, complemented by real-world examples of the use of the model-based prescriptive approach to improve the efficiency of fuzzy control systems. Highly experienced in fuzzy control research, the author identifies new trends in the development of fuzzy sets and their direct application to decision-making processes. Fuzzy control engineers, researchers and postgraduate students will find this an ideal reference, offering a wealth of ideas for enhancing the performance of fuzzy control systems and equipping them with the tools to resolve genuine problems. Multistage Fuzzy Control is an essential handbook for those wishing to resolve real-world problems in control and decision analysis through the use of fuzzy-logic-based methods.

In recent years, substantial efforts are being made in the development of reliability theory including fuzzy reliability theories and their applications to various real-life problems. Fuzzy set theory is widely used in decision making and multi criteria such as management and engineering, as well as other important domains in order to evaluate the uncertainty of real-life systems. Fuzzy reliability has proven to have effective tools and techniques based on real set theory for proposed models within various engineering fields, and current research focuses on these applications. Advancements in Fuzzy Reliability Theory introduces the concept of reliability fuzzy set theory including various methods, techniques, and algorithms. The chapters present the latest findings and research in fuzzy reliability theory applications in engineering areas. While examining the implementation of fuzzy reliability theory among various industries such as mining, construction, automobile, engineering, and more, this book is ideal for engineers, practitioners, researchers, academicians, and students interested in fuzzy reliability theory applications in engineering areas.

This book mainly introduces the latest development of generalized intuitionistic multiplicative fuzzy calculus and its application. The book pursues three major objectives: (1) to introduce the calculus models with concrete mathematical expressions for generalized intuitionistic multiplicative fuzzy information; (2) to introduce new information fusion methods based on the definite integral models; and (3) to clarify the involved approaches bymilitary case. The book is especially valuable for readers to understand how the theoretical framework of generalized intuitionistic multiplicative fuzzy calculus is constructed, not only discrete or continuous but also correlative (generalized) intuitionistic (multiplicative) fuzzy information is aggregated based on the definite integral models and the theory with a military practice is integrated, which would deepen the understanding and give researchers more inspiration in practical decision analysis under uncertainties.

This is the first book to provide a comprehensive and systematic introduction to the ranking methods for interval-valued intuitionistic fuzzy sets, multi-criteria decision-making methods with interval-valued intuitionistic fuzzy sets, and group decision-making methods with interval-valued intuitionistic fuzzy preference relations. Including numerous application examples and illustrations with tables and figures and presenting the authors' latest research developments, it is a valuable resource for researchers and professionals in the fields of fuzzy mathematics, operations research, information science, management science and decision analysis.

Since its inception, fuzzy logic has attracted an incredible amount of interest, and this interest continues to grow at an exponential rate. As such, scientists, researchers, educators and practitioners of fuzzy logic continue to expand on the applicability of what and how fuzzy can be utilised in the real-world. In this book, the authors present key application areas where fuzzy has had significant success. The chapters cover a plethora of application domains, proving credence to the versatility and robustness of a fuzzy approach. A better understanding of fuzzy will ultimately allow for a better appreciation of fuzzy. This book provides the reader with a varied range of examples to illustrate what fuzzy logic can be capable of and how it can be applied. The text will be ideal for individuals new to the notion of fuzzy, as well as for early career academics who wish to further expand on their knowledge of fuzzy applications. The book is also suitable as a supporting text for advanced undergraduate and graduate-level modules on fuzzy logic, soft computing, and applications of AI.

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

In recent years, substantial efforts are being made in the development of reliability theory including fuzzy reliability theories and their applications to various real-life problems. Fuzzy set theory is widely used in decision making and multi criteria such as management and engineering, as well as other important domains in order to evaluate the uncertainty of real-life systems. Fuzzy reliability has proven to have effective tools and techniques based on real set theory for proposed models within various engineering fields, and current research focuses on these applications. Advancements in Fuzzy Reliability Theory introduces the concept of reliability fuzzy set theory including various methods, techniques, and algorithms. The chapters present the latest findings and research in fuzzy reliability theory applications in engineering areas. While examining the implementation of fuzzy reliability theory among various industries such as mining, construction, automobile, engineering, and more, this book is ideal for engineers, practitioners, researchers, academicians, and students interested in fuzzy reliability theory applications in engineering areas.