Hans-Jürgen Zimmermann - Böcker

This volume contains the proceedings of the Second Joint IFSA-EC and EURO-WGFS Workshop on Progress in Fuzzy Sets in Europe held on April 6 -8, 1989 in Vienna, Austria. The workshop was organized by Prof. Dr. Wolfgang H. Janko from the University of Economics in Vienna under the auspices of IFSA-EC, the European chapter of the International Fuzzy Systems Association, and EURO-WGFS, the working group on Fuzzy Sets of the Association of Eu­ ropean Operational Research Societies. The workshop gathered more than 30 participants coming from Western European countries (Austria, Bel­ gium, England, Germany, Finland, France, Hungary, Italy, Scotland and Spain) Eastern European countries (Bulgaria, the German Federal Repu­ blic, Hungary and Poland) and non-European countries such as China and Japan. The 15 selected and refereed papers included in the volume are in prin­ ciple the author's own versions, with limited editorial changes and small corrections. They are arranged in alphabetical order. I wish to thank all the contributors for their valuable papers and an outstan­ ding cooperation in the editorial project. I also would like to express my sincere thanks to Professor Dr. H. J. Zimmermann for the cooperation in the refereeing procedure.

Since its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have been made in many directions. The primary goal of this book is to provide an introduction to fuzzy set theory and to also act as a textbook. To balance the character of a textbook with the dynamic nature of this research, references have been added to develop a deeper understanding for the interested reader. The text updates the research agenda 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. Chapters have been updated and extended, exercises are included, and a teacher's manual is available upon request.

This work presents developments and applications in the area of computational intelligence, which essentially describes methods and approaches that mimic biologically intelligent behaviour in order to solve problems that have been difficult to solve by classical mathematics. Fuzzy technology, artificial neural nets and evolutionary computing are considered to be such approaches. The Editors have assembled contributions in the areas of fuzzy sets, neural sets and machine learning, as well as combinations of them (so-called hybrid methods) in the first part of the book. The second part of the book is dedicated to applications in the areas that are considered to be most relevant to computational intelligence.

The field of "intelligent interfaces and systems" has witnessed a rapid growth during the last decade of the 20th century. An impressive number of papers, conference tutorials, and volumes have been devoted to the topic. In 1990, intelligent systems constituted a rather exotic topic and many were skeptical as to whether such systems would amount to more than a nice name. Nowadays, intelligent systems represent a powerful tool in many applications, in all industrial fields. Their development evolved on both the horizontal dimension, with a constantly increasing number of applications, and on the vertical dimension, by including more capabilities ranging from sensoric to neurofuzzy systems, intelligent agents, speech and image understanding, and decision-making in complex environments. Representing a comprehensive coverage of the field of intelligent systems and interfaces, this text includes information about fundamental aspects, software-, sensors-, and hardware-related issues.Moreover, the contributors to this volume offer, beyond a systematic overview of intelligent interfaces and systems, deep, practical knowledge in building and using intelligent systems in various applications. Special emphasis is placed on specific aspects and requirements in applications. The text is a tool for the scientific community in all areas of applied intelligent technologies. The chapters are written by a selected pool of experts in the field of intelligent systems. The contributors thoroughly review the state of the art, explain the problems to be addressed and show how these problems can be solved. Extensive references are included, offering the reader a perspective on the currently available literature and trends.

This text gives an overview of the research results of a number of European research groups that are active and play a leading role in the field of fuzzy modelling and control. It contains 12 chapters divided into three parts. Chapters in the first part address the position of fuzzy systems in control engineering and in the AI community. State-of-the-art surveys on fuzzy modelling and control are presented along with a critical assessment of the role of these methodologists in control engineering. The second part is concerned with several analysis and design issues in fuzzy control systems. The analytical issues addressed include the algebraic representation of fuzzy models of different types, their approximation properties, and stability analysis of fuzzy control systems. Several design aspects are addressed, including performance specification for control systems in a fuzzy decision-making framework and complexity reduction in multivariable fuzzy systems. In the third part of the book, a number of applications of fuzzy control are presented.It is shown that fuzzy control in combination with other techniques such as fuzzy data analysis is an effective approach to the control of modern processes which present many challenges for the design of control systems. One has to cope with problems such as process nonlinearity, time-varying characteristics for incomplete process knowledge. Examples of real-world industrial applications presented in this book are a blast furnace, a lime kiln and a solar plant. Other examples of challenging problems in which fuzzy logic plays an important role and which are included in this book are mobile robotics and aircraft control. The aim of this book is to address both theoretical and practical subjects in a balanced way. It should therefore be useful for readers from the academic world and also from industry who want to apply fuzzy control in practice.

Since the late 1980s, a large number of very user-friendly tools for fuzzy control, fuzzy expert systems, and fuzzy data analysis have emerged. This has changed the character of this area and started the area of `fuzzy technology'. The next large step in the development occurred in 1992 when almost independently in Europe, Japan and the USA, the three areas of fuzzy technology, artificial neural nets and genetic algorithms joined forces under the title of `computational intelligence' or `soft computing'. The synergies which were possible between these three areas have been exploited very successfully. Practical Applications of Fuzzy Sets focuses on model and real applications of fuzzy sets, and is structured into four major parts: engineering and natural sciences; medicine; management; and behavioral, cognitive and social sciences. This book will be useful for practitioners of fuzzy technology, scientists and students who are looking for applications of their models and methods, for topics of their theses, and even for venture capitalists who look for attractive possibilities for investments.

Seeking to update the research agenda in the field of fuzzy set theory, this textbook includes 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, and exercises are included. A Teacher's Manual is also available on request.

In the two decades since its inception by L. Zadeh, the theory of fuzzy sets has matured into a wide-ranging collection of concepts, models, and tech­ niques for dealing with complex phenomena which do not lend themselves to analysis by classical methods based on probability theory and bivalent logic. Nevertheless, a question which is frequently raised by the skeptics is: Are there, in fact, any significant problem areas in which the use of the theory of fuzzy sets leads to results which could not be obtained by classical methods? The approximately 5000 publications in this area, which are scattered over many areas such as artificial intelligence, computer science, control engineering, decision making, logic, operations research, pattern recognition, robotics and others, provide an affirmative answer to this question. In spite of the large number of publications, good and comprehensive textbooks which could facilitate the access of newcomers to this area and support teaching were missing until recently. To help to close this gap and to provide a textbook for courses in fuzzy set theory which can also be used as an introduction to this field, the first volume ofthis book was published in 1985 [Zimmermann 1985 b]. This volume tried to cover fuzzy set theory and its applications as extensively as possible. Applications could, therefore, only be described to a limited extent and not very detailed.

The field of "intelligent interfaces and systems" has seen a fast growth last decade. An impressive number of papers, conference tutorials, and volumes were devoted to the topic. Ten years ago, intelligent systems constituted a rather exotic topic and many were skeptic that such systems amount to more than a nice name. Nowadays, intelligent systems represent a powerful tool in many applications, in all industrial fields. Their development evolved on both the horizontal dimension, with a constantly increasing number of applications, and on the vertical dimension, by including more capabilities going from sensoric to neurofuzzy systems, intelligent agents, speech and image understanding, and decision making in complex environments. The domain constituted by the intelligent systems is now too large to be covered in a single volume. Consequently, the Editors considered a balance between several selected sub-fields, to insure the unity of the volume, yet allowing a large enough horizon and a consistent understanding of the entire field, including real-life applications. The volume represents a comprehensive coverage of the field, including fundamental aspects, software-, sensors-, and hardware-related issues. Moreover, the contributors to this volume offer, beyond a systematic overview of intelligent interfaces and systems, deep, practical knowledge in building and using intelligent systems in various applications. A special emphasis is on specific aspects and requirements in applications. In addition, the second Editor proposes two chapters addressing the management of projects dealing with intelligent systems.

Since the late 1980s, a large number of very user-friendly tools for fuzzy control, fuzzy expert systems, and fuzzy data analysis have emerged. This has changed the character of this area and started the area of `fuzzy technology'. The next large step in the development occurred in 1992 when almost independently in Europe, Japan and the USA, the three areas of fuzzy technology, artificial neural nets and genetic algorithms joined forces under the title of `computational intelligence' or `soft computing'. The synergies which were possible between these three areas have been exploited very successfully. Practical Applications of Fuzzy Sets focuses on model and real applications of fuzzy sets, and is structured into four major parts: engineering and natural sciences; medicine; management; and behavioral, cognitive and social sciences. This book will be useful for practitioners of fuzzy technology, scientists and students who are looking for applications of their models and methods, for topics of their theses, and even for venture capitalists who look for attractive possibilities for investments.

Probleme, Modelle, Algorithmen Eine zunehmende Anzahl von Autoren [siehe z. B. Boothroyd 1978, S. 110, Müller­ Merbach 1979, Checkland 1983] vertreten die Auffassung, daß es zwei verschiedene Begriffe des Operations Research (OR) gibt: Ein Operations Research aus der Sicht des Praktikers und eins aus der Sicht des Mathematikers. Während das OR aus der Sicht des Praktikers "die modellgestützte Vorbereitung von Entscheidungen zur Gestaltung und Lenkung von Mensch-Maschine-Systemen zur Aufgabe hat" [Müller­ Merbach 1979, S. 295], sieht der Mathematiker das OR "als Teilgebiet der ange­ wandten Mathematik" [Gaede 1974] an. Wie es zu dieser Situation kam, wird näher im Kapitel I dieses Buches beschrieben. Hier wird allerdings die Meinung vertreten, daß es zwar zwei Teile des Gebietes OR geben mag, daß sie jedoch beide wichtig und notwendig für das OR sind und sich aus der Geschichte des OR erklären lassen. Um dies für den Leser leichter verständlich zu machen, ist es nützlich, zunächst auf den hier benutzten Begriff des "Problems" etwas näher einzugehen. Bild 0 skizziert die hier angenommenen Zusammenhänge. Diese Darstellung ist jedoch auf keinen Fall als ein zeitliches Ablaufschema zu interpretieren.

Problems in decision making and in other areas such as pattern recogni­ tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha­ racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru­ ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do­ main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

Fuzzy Set Theory - and its Applications, Fourth Edition updates the research agenda 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.

Advances in Computational Intelligence and Learning: Methods and Applications presents new developments and applications in the area of Computational Intelligence, which essentially describes methods and approaches that mimic biologically intelligent behavior in order to solve problems that have been difficult to solve by classical mathematics. Generally Fuzzy Technology, Artificial Neural Nets and Evolutionary Computing are considered to be such approaches.The Editors have assembled new contributions in the areas of fuzzy sets, neural sets and machine learning, as well as combinations of them (so called hybrid methods) in the first part of the book. The second part of the book is dedicated to applications in the areas that are considered to be most relevant to Computational Intelligence.

Fuzzy Algorithms for Control gives an overview of the research results of a number of European research groups that are active and play a leading role in the field of fuzzy modeling and control. It contains 12 chapters divided into three parts. Chapters in the first part address the position of fuzzy systems in control engineering and in the AI community. State-of-the-art surveys on fuzzy modeling and control are presented along with a critical assessment of the role of these methodologists in control engineering. The second part is concerned with several analysis and design issues in fuzzy control systems. The analytical issues addressed include the algebraic representation of fuzzy models of different types, their approximation properties, and stability analysis of fuzzy control systems. Several design aspects are addressed, including performance specification for control systems in a fuzzy decision-making framework and complexity reduction in multivariable fuzzy systems. In the third part of the book, a number of applications of fuzzy control are presented. It is shown that fuzzy control in combination with other techniques such as fuzzy data analysis is an effective approach to the control of modern processes which present many challenges for the design of control systems. One has to cope with problems such as process nonlinearity, time-varying characteristics for incomplete process knowledge. Examples of real-world industrial applications presented in this book are a blast furnace, a lime kiln and a solar plant. Other examples of challenging problems in which fuzzy logic plays an important role and which are included in this book are mobile robotics and aircraft control. The aim of this book is to address both theoretical and practical subjects in a balanced way. It will therefore be useful for readers from the academic world and also from industry who want to apply fuzzy control in practice.

This volume contains the proceedings of the Second Joint IFSA-EC and EURO-WGFS Workshop on Progress in Fuzzy Sets in Europe held on April 6 -8, 1989 in Vienna, Austria. The workshop was organized by Prof. Dr. Wolfgang H. Janko from the University of Economics in Vienna under the auspices of IFSA-EC, the European chapter of the International Fuzzy Systems Association, and EURO-WGFS, the working group on Fuzzy Sets of the Association of Eu­ ropean Operational Research Societies. The workshop gathered more than 30 participants coming from Western European countries (Austria, Bel­ gium, England, Germany, Finland, France, Hungary, Italy, Scotland and Spain) Eastern European countries (Bulgaria, the German Federal Repu­ blic, Hungary and Poland) and non-European countries such as China and Japan. The 15 selected and refereed papers included in the volume are in prin­ ciple the author's own versions, with limited editorial changes and small corrections. They are arranged in alphabetical order. I wish to thank all the contributors for their valuable papers and an outstan­ ding cooperation in the editorial project. I also would like to express my sincere thanks to Professor Dr. H. J. Zimmermann for the cooperation in the refereeing procedure.

In the two decades since its inception by L. Zadeh, the theory of fuzzy sets has matured into a wide-ranging collection of concepts, models, and tech­ niques for dealing with complex phenomena which do not lend themselves to analysis by classical methods based on probability theory and bivalent logic. Nevertheless, a question which is frequently raised by the skeptics is: Are there, in fact, any significant problem areas in which the use of the theory of fuzzy sets leads to results which could not be obtained by classical methods? The approximately 5000 publications in this area, which are scattered over many areas such as artificial intelligence, computer science, control engineering, decision making, logic, operations research, pattern recognition, robotics and others, provide an affirmative answer to this question. In spite of the large number of publications, good and comprehensive textbooks which could facilitate the access of newcomers to this area and support teaching were missing until recently. To help to close this gap and to provide a textbook for courses in fuzzy set theory which can also be used as an introduction to this field, the first volume ofthis book was published in 1985 [Zimmermann 1985 b]. This volume tried to cover fuzzy set theory and its applications as extensively as possible. Applications could, therefore, only be described to a limited extent and not very detailed.

Problems in decision making and in other areas such as pattern recogni­ tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha­ racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru­ ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do­ main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.