Fuzzy Logic Foundations and Industrial Applications is an organized edited collection of contributed chapters covering basic fuzzy logic theory, fuzzy linear programming, and applications. Special emphasis has been given to coverage of recent research results, and to industrial applications of fuzzy logic. The chapters are new works that have been written exclusively for this book by many of the leading and prominent researchers (such as Ronald Yager, Ellen Hisdal, Etienne Kerre, and others) in this field. The contributions are original and each chapter is self-contained. The authors have been careful to indicate direct links between fuzzy set theory and its industrial applications. Fuzzy Logic Foundations and Industrial Applications is an invaluable work that provides researchers and industrial engineers with up-to-date coverage of new results on fuzzy logic and relates these results to their industrial use.

The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature. Although there are now many books about fuzzy set theory, and mainly about its applications, e. g. in control theory, there is not really a book available which introduces the elementary theory of fuzzy sets, in what I would like to call "a good degree of generality." To write a book which would treat the entire range of results concerning the basic theoretical concepts in great detail and which would also deal with all possible variants and alternatives of the theory, such as e. g. rough sets and L-fuzzy sets for arbitrary lattices L, with the possibility-probability theories and interpretations, with the foundation of fuzzy set theory via multi-valued logic or via categorical methods and so on, would have been an altogether different project. This book is far more modest in its mathematical content and in its scope.

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 Modelling: Paradigms and Practice provides an up-to-date and authoritative compendium of fuzzy models, identification algorithms and applications. Chapters in this book have been written by the leading scholars and researchers in their respective subject areas. Several of these chapters include both theoretical material and applications. The editor of this volume has organized and edited the chapters into a coherent and uniform framework. The objective of this book is to provide researchers and practitioners involved in the development of models for complex systems with an understanding of fuzzy modelling, and an appreciation of what makes these models unique. The chapters are organized into three major parts covering relational models, fuzzy neural networks and rule-based models. The material on relational models includes theory along with a large number of implemented case studies, including some on speech recognition, prediction, and ecological systems. The part on fuzzy neural networks covers some fundamentals, such as neurocomputing, fuzzy neurocomputing, etc., identifies the nature of the relationship that exists between fuzzy systems and neural networks, and includes extensive coverage of their architectures. The last part addresses the main design principles governing the development of rule-based models. Fuzzy Modelling: Paradigms and Practice provides a wealth of specific fuzzy modelling paradigms, algorithms and tools used in systems modelling. Also included is a panoply of case studies from various computer, engineering and science disciplines. This should be a primary reference work for researchers and practitioners developing models of complex systems.

Introduction to Fuzzy Reliability treats fuzzy methodology in hardware reliability and software reliability in a relatively systematic manner. The contents of this book are organized as follows. Chapter 1 places reliability engineering in the scope of a broader area, i.e. system failure engineering. Readers will find that although this book is confined to hardware and software reliability, it may be useful for other aspects of system failure engineering, like maintenance and quality control. Chapter 2 contains the elementary knowledge of fuzzy sets and possibility spaces which are required reading for the rest of this book. This chapter is included for the overall completeness of the book, but a few points (e.g. definition of conditional possibility and existence theorem of possibility space) may be new. Chapter 3 discusses how to calculate probist system reliability when the component reliabilities are represented by fuzzy numbers, and how to analyze fault trees when probabilities of basic events are fuzzy. Chapter 4 presents the basic theory of profust reliability, whereas Chapter 5 analyzes the profust reliability behavior of a number of engineering systems. Chapters 6 and 7 are devoted to probist reliability theory from two different perspectives. Chapter 8 discusses how to model software reliability behavior by using fuzzy methodology. Chapter 9 includes a number of mathematical problems which are raised by applications of fuzzy methodology in hardware and software reliability, but may be important for fuzzy set and possibility theories.

Fuzzy controllers are a class of knowledge based controllers using artificial intelligence techniques with origins in fuzzy logic. They can be found either as stand-alone control elements or as integral parts of distributed control systems including conventional controllers in a wide range of industrial process control systems and consumer products. Applications of fuzzy controllers have become a well established practice for Japanese manufacturers of control equipment and systems, and are becoming more and more common in Europe and America. The main aim of this book is to show that fuzzy control is not totally ad hoc, that there exist formal techniques for the analysis of a fuzzy controller, and that fuzzy control can be implemented even when no expert knowledge is available. Thus the book is mainly oriented toward control engineers and theorists, although parts can be read without any knowledge of control theory and may be of interest to Al people. This 2nd, revised edition incorporates suggestions from numerous reviewers and updates and reorganizes some of the material.

It is known that many control processes are characterized by both quantitative and qualitative complexity. Tbe quantitative complexity is usually expressed in a large number of state variables, respectively high dimensional mathematical model. Tbe qualitative complexity is usually associated with uncertain behaviour, respectively approximately known mathematical model. If the above two aspects of complexity are considered separately, the corresponding control problem can be easily solved. On one hand, large scale systems theory has existed for more than 20 years and has proved its capabilities in solving high dimensional control problems on the basis of decomposition, hierarchy, decentralization and multilayers. On the other hand, the fuzzy linguistic approach is almost at the same age and has shown its advantages in solving approximately formulated control problems on the basis of linguistic reasoning and logical inference. However, if both aspects of complexity are considered together, the corresponding control problem becomes non-trivial and does not have an easy solution. Modem control theory and practice have reacted accordingly to the above mentioned new cballenges of tbe day by utilizing the latest achievements in computer technology and artificial intelligence distributed computation and intelligent operation. In this respect, a new field has emerged in the last decade, called " Distributed intelligent control systems" . However, the majority of the familiar works in this field are still either on an empirical or on a conceptual level and this is a significant drawback.

This volume presents the results of approximately 15 years of work from researchers around the world on the use of fuzzy set theory to represent imprecision in databases. The maturity of the research in the discipline and the recent developments in commercial/industrial fuzzy databases provided an opportunity to produce this survey. Fuzzy Databases: Principles and Applications is self-contained providing background material on fuzzy sets and database theory. It is comprehensive covering all of the major approaches and models of fuzzy databases that have been developed including coverage of commercial/industrial systems and applications. Background and introductory material are provided in the first two chapters. The major approaches in fuzzy databases comprise the second part of the volume. This includes the use of similarity and proximity measures as the fuzzy techniques used to extend the relational data modeling and the use of possibility theory approaches in the relational model. Coverage includes extensions to the data model, querying approaches, functional dependencies and other topics including implementation issues, information measures, database security, alternative fuzzy data models, the IFO model, and the network data models. A number of object-oriented extensions are also discussed. The use of fuzzy data modeling in geographical information systems (GIS) and use of rough sets in rough and fuzzy rough relational data models are presented. Major emphasis has been given to applications and commercialization of fuzzy databases. Several specific industrial/commercial products and applications are described. These include approaches to developing fuzzy front-end systems andspecial-purpose systems incorporating fuzziness.

This book presents 14 rigorously reviewed revised papers selected from more than 50 submissions for the 1994 IEEE/ Nagoya-University World Wisepersons Workshop, WWW'94, held in August 1994 in Nagoya, Japan.The combination of approaches based on fuzzy logic, neural networks and genetic algorithms are expected to open a new paradigm of machine learning for the realization of human-like information processing systems. The first six papers in this volume are devoted to the combination of fuzzy logic and neural networks; four papers are on how to combine fuzzy logic and genetic algorithms. Four papers investigate challenging applications of fuzzy systems and of fuzzy-genetic algorithms.

One of the attractions of fuzzy logic is its utility in solving many real engineering problems. As many have realised, the major obstacles in building a real intelligent machine involve dealing with random disturbances, processing large amounts of imprecise data, interacting with a dynamically changing environment, and coping with uncertainty. Neural-fuzzy techniques help one to solve many of these problems. Fuzzy Logic and Intelligent Systems reflects the most recent developments in neural networks and fuzzy logic, and their application in intelligent systems. In addition, the balance between theoretical work and applications makes the book suitable for both researchers and engineers, as well as for graduate students.

This volume contains the thoroughly refereed and revised papers accepted for presentation at the IJCAI '91 Workshops on Fuzzy Logic and Fuzzy Control, held during the International Joint Conference on AI at Sydney, Australia in August 1991. The 14 technical contributions are devoted to several theoretical and applicational aspects of fuzzy logic and fuzzy control; they are presented in sections on theoretical aspects of fuzzy reasoning and fuzzy control, fuzzy neural networks, fuzzy control applications, fuzzy logic planning, and fuzzy circuits. In addition, there is a substantial introduction by the volume editors on the latest developments in the field that brings the papers presented into line.

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.

This book is the result of some years of research carried out at the Vrije Universiteit of Amsterdam and at the Joint Research Centre of the European Commission. The awareness of actual and potential conflicts between economic progress in production, consumption, and technology and the environment has led to the concept of "sustainable development," implying that economic and ecological values are well balanced in evaluation and decision making. The linkages between ecosystems and economic systems are the focus of ecological economics. In ecological economics, a multidimensional approach to economic and policy-making is emphasised. In this book, the introduction of multicriteria decision aid techniques in the framework of ecological economics is widely discussed. Since such techniques are based on a "constructive" rationality and allow one to take into account conflictual, multidimensional, incommensurable and uncertain effects of decisions, they can be considered perfectly consistent with the methodological foundations of ecological economics. Since here the assumption is accepted that efficiency, equity and sustainability are the three conflictual values of economics, a mathematical procedure able to deal with these issues in an operational framework is developed, with a particular view on imprecise information in a practical environmental planning context. Given the problem of the differences in the measurement levels of the variables used for economic-ecological modelling, multicriteria methods able to deal with mixed information (both qualitative and quantitative measurements) can be considered particularly useful. Another problem related to the available information concerns the uncertainty (stochastic and/or fuzzy) contained in this information.

The volume "Fuzziness in Database Management Systems" is a highly informative, well-organized and up-to-date collection of contributions authored by many of the leading experts in its field. Among the contributors are the editors, Professors Patrick Bose and Janusz Kacprzyk, both of whom are known internationally. The book is like a movie with an all-star cast. The issue of fuzziness in database management systems has a long history. It begins in 1968 and 1971, when I spent my sabbatical leaves at the IBM Research Laboratory in San Jose, California, as a visiting scholar. During these periods I was associated with Dr. E.F. Codd, the father of relational models of database systems, and came in contact with the developers ofiBMs System Rand SQL. These associations and contacts at a time when the methodology of relational models of data was in its formative stages, made me aware of the basic importance of such models and the desirability of extending them to fuzzy database systems and fuzzy query languages. This perception was reflected in my 1973 ffiM report which led to the paper on the concept of a linguistic variable and later to the paper on the meaning representation language PRUF (Possibilistic Relational Universal Fuzzy). More directly related to database issues during that period were the theses of my students V. Tahani, J. Yang, A. Bolour, M. Shen and R. Sheng, and many subsequent reports by both graduate and undergraduate students at Berkeley.

This book provides a comprehensive, up-to-date account on recent applications of fuzzy sets and possibility theory in reliability and safety analysis. Various aspects of system's reliability, quality control, reliability and safety of man-machine systems fault analysis, risk assessment and analysis, structural, seismic, safety, etc. are discussed. The book provides new tools for handling non-probabilistic aspects of uncertainty in these problems. It is the first in this field in the world literature.

Fuzzy knowledge and fuzzy systems affect our lives today as systems enter the world of commerce. Fuzzy systems are incorporated in domestic appliances (washing machine, air conditioning, microwave, telephone) and in transport systems (a pilotless helicopter has recently completed a test flight). Future applications are expected to have dramatic implications for the demand for labor, among other things. It was with such thoughts in mind that this first international survey of future applications of fuzzy logic has been undertaken. The results are likely to be predictive for a decade beyond the millenium. The predictive element is combined with a bibliography which serves as an historical anchor as well as being both extensive and extremely useful. Analysis and Evaluation of Fuzzy Systems is thus a milestone in the development of fuzzy logic and applications of three representative subsystems: Fuzzy Control, Fuzzy Pattern Recognition and Fuzzy Communications.

Fuzzy logic is a recent revolutionary technology' which has brought together researchers from mathematics, engineering, computer science, cognitive and behavioral sciences, etc. The work in fuzzy technology at the Laboratory for International Fuzzy Engineering (LIFE) has been specifically applied to engineering problems. This book reflects the results of the work that has been undertaken at LIFE with chapters treating the following topical areas: Decision Support Systems, Intelligent Plant Operations Support, Fuzzy Modeling and Process Control, System Design, Image Understanding, Behavior Decisions for Mobile Robots, the Fuzzy Computer, and Fuzzy Neuro Systems. The book is a thorough analysis of research which has been implemented in the areas of fuzzy engineering technology. The analysis can be used to improve these specific applications or, perhaps more importantly, to investigate more sophisticated fuzzy control applications.

This volume constitutes the proceedings of the Second Fuzzy Logic in AI Workshop, held in conjunction with IJCAI '93 in ChambA(c)ry, France in August 1993.
The book contains full revised versions of the papers presented at the workshop and covers several aspects of fuzzy logic in contributions from renowned researchers. This volume reflects the aim of the workshop, namely to serve as a platform for fruitful contacts between fuzzy engineering researchers interested in AI and AI researchers interested in fuzzy logic applications in engineering: when it comes to designing intelligent systems they are confronted with the same problems and questions and hope for the same successful results.

The objective of this book is two-fold. Firstly, it is aimed at bringing to gether key research articles concerned with methodologies for knowledge discovery in databases and their applications. Secondly, it also contains articles discussing fundamentals of rough sets and their relationship to fuzzy sets, machine learning, management of uncertainty and systems of logic for formal reasoning about knowledge. Applications of rough sets in different areas such as medicine, logic design, image processing and expert systems are also represented. The articles included in the book are based on selected papers presented at the International Workshop on Rough Sets and Knowledge Discovery held in Banff, Canada in 1993. The primary methodological approach emphasized in the book is the mathematical theory of rough sets, a relatively new branch of mathematics concerned with the modeling and analysis of classification problems with imprecise, uncertain, or incomplete information. The methods of the theory of rough sets have applications in many sub-areas of artificial intelligence including knowledge discovery, machine learning, formal reasoning in the presence of uncertainty, knowledge acquisition, and others. This spectrum of applications is reflected in this book where articles, although centered around knowledge discovery problems, touch a number of related issues. The book is intended to provide an important reference material for students, researchers, and developers working in the areas of knowledge discovery, machine learning, reasoning with uncertainty, adaptive expert systems, and pattern classification."

The widespread use of fuzzy set theory in almost every science attests to its intuitive appeal and the powerful insights it offers. Despite its relevance as a tool for evaluating non-stochastic behavioural uncertainty and its clear applicability to the business world, fuzzy mathematics has yet to establish itself in mainstream economic analysis.Fuzzy Sets and Economics presents a clear and concise introduction to fuzzy mathematics and demonstrates its adaptability to the analysis of oligopolistic competition. In particular, the author indicates how the economic evaluation of non-cooperative oligopoly markets is changed when fuzzy set mathematics is used. The neoclassical view that oligopolistic competition is inefficient is shown only to apply in the short run while policy matters, such as antitrust, and some basic economic fundamentals, such as the supply-demand paradigm, are affected by the introduction of a fuzzy mathematics framework.

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.

In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory, artificial intelligence/expert system, etc. In this volume, methods and applications of crisp, fuzzy and possibilistic multiple objective decision making are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, it presents solutions for real-world problems including production/manufacturing, location, logistics, environment management, banking/finance, personnel, marketing, accounting, agriculture economics and data analysis. This book is a guided tour through the literature in the rapidly growing fields of operations research and decision making and includes the most up-to-date bibliographical listing of literature on the topic.

In recent years it has become apparent that an important part of the theory of artificial intelligence is concerned with reasoning on the basis of uncertain, incomplete, or inconsistent information. A variety of formalisms have been developed, including nonmonotonic logic, fuzzy sets, possibility theory, belief functions, and dynamic models of reasoning such as belief revision and Bayesian networks. Several European research projects have been formed in the area and the first European conference was held in 1991. This volume contains the papers accepted for presentation at ECSQARU-93, the European Conference on Symbolicand Quantitative Approaches to Reasoning and Uncertainty, held at the University of Granada, Spain, November 8-10, 1993.

In decision theory there are basically two appr hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process.

This volume contains the proceedings of the Eighth Austrian Artificial Intelligence Conference, held in Linz, Austria, in June 1993. The focus of the conference was on "Fuzzy Logic in Artificial Intelligence." The volume contains abstracts of two invited talks and full versions of 17 carefully selected papers. The invited talks were: "The role of fuzzylogic and soft computing in the conception and design of intelligent systems" by Lotfi A. Zadeh, and "A contextual approach for AI systems development" by Irina V. Ezhkova. The contributed papers are grouped into sections on theoretical issues, machine learning, expert systems, robotics and control, applications to medicine, and applications to car driving. Additionally, the volume contains descriptions of the four workshops that took place during the conference.