This volume contains the papers selected for presentation at the Seventh Int- national Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing (RSFDGrC 99) held in the Yamaguchi Resort Center, Ube, Y- aguchi, Japan, November 9-11, 1999. The workshop was organized by Inter- tional Rough Set Society, BISC Special Interest Group on Granular Comp- ing (GrC), Polish-JapaneseInstitute of Information Technology, and Yamaguchi University. RSFDGrC 99providedaninternationalforumforsharingoriginalresearch results and practical development experiences among experts in these emerging ?elds.An importantfeatureoftheworkshopwasto stresstheroleofthe integ- tion of intelligent information techniques. That is, to promote a deep fusion of these approaches to AI, Soft Computing, and Database communities in order to solve real world, large, complex problems concerned with uncertainty and fuz- ness. In particular, rough and fuzzy set methods in data mining and granular computing were on display. The total of 89 papers coming from 21 countries and touching a wide spectrum of topics related to both theory and applications were submitted to RSFDGrC 99. Out of them 45 papers were selected for regular presentations and 15 for short presentations. Seven technical sessions were organized, namely: Rough Set Theory and Its Applications; Fuzzy Set Theory and Its Applications; Non-Classical Logic and Approximate Reasoning; Information Granulation and Granular Computing; Data Mining and Knowledge Discovery; Machine Lea- ing; Intelligent Agents and Systems. TheRSFDGrC 99programwasenrichedbyfourinvitedspeakers: Zdzis law Pawlak, Lot? A. Zadeh, Philip Yu, and Setsuo Arikawa, from Soft Computing, Database, and AI communities. A special session on Rough Computing: Fo- dations and Applications was organized by James F. Peters."

Fuzzy sets were introduced by Zadeh (1965) as a means of representing and manipulating data that was not precise, but rather fuzzy. Fuzzy logic pro vides an inference morphology that enables approximate human reasoning capabilities to be applied to knowledge-based systems. The theory of fuzzy logic provides a mathematical strength to capture the uncertainties associ ated with human cognitive processes, such as thinking and reasoning. The conventional approaches to knowledge representation lack the means for rep resentating the meaning of fuzzy concepts. As a consequence, the approaches based on first order logic and classical probablity theory do not provide an appropriate conceptual framework for dealing with the representation of com monsense knowledge, since such knowledge is by its nature both lexically imprecise and noncategorical. The developement of fuzzy logic was motivated in large measure by the need for a conceptual framework which can address the issue of uncertainty and lexical imprecision. Some of the essential characteristics of fuzzy logic relate to the following [242]. * In fuzzy logic, exact reasoning is viewed as a limiting case of ap proximate reasoning. * In fuzzy logic, everything is a matter of degree. * In fuzzy logic, knowledge is interpreted a collection of elastic or, equivalently, fuzzy constraint on a collection of variables. * Inference is viewed as a process of propagation of elastic con straints. * Any logical system can be fuzzified. There are two main characteristics of fuzzy systems that give them better performance fur specific applications.

Fuzzy sets were first proposed by Lotfi Zadeh in his seminal paper [366] in 1965, and ever since have been a center of many discussions, fervently admired and condemned. Both proponents and opponents consider the argu ments pointless because none of them would step back from their territory. And stiH, discussions burst out from a single sparkle like a conference pa per or a message on some fuzzy-mail newsgroup. Here is an excerpt from an e-mail messagepostedin1993tofuzzy-mail@vexpert. dbai. twvien. ac. at. by somebody who signed "Dave". , . . . Why then the "logic" in "fuzzy logic"? I don't think anyone has successfully used fuzzy sets for logical inference, nor do I think anyone wiH. In my admittedly neophyte opinion, "fuzzy logic" is a misnomer, an oxymoron. (1 would be delighted to be proven wrong on that. ) . . . I carne to the fuzzy literature with an open mind (and open wal let), high hopes and keen interest. I am very much disiHusioned with "fuzzy" per se, but I did happen across some extremely interesting things along the way. " Dave, thanks for the nice quote! Enthusiastic on the surface, are not many of us suspicious deep down? In some books and journals the word fuzzy is religiously avoided: fuzzy set theory is viewed as a second-hand cheap trick whose aim is nothing else but to devalue good classical theories and open up the way to lazy ignorants and newcomers.

This volume constitutes the thoroughly refereed post-workshop proceedings of an international workshop on fuzzy logic in Artificial Intelligence held in Negoya, Japan during IJCAI '97.
The 17 revised full papers presented have gone through two rounds of reviewing and revision. Three papers by leading authorities in the area are devoted to the general relevance of fuzzy logic and fuzzy sets to AI. The remaining papers address various relevant issues ranging from theory to application in areas like knowledge representation, induction, logic programming, robotics, pattern recognition, etc.

Fuzzy systems and soft computing are new computing techniques that are tolerant to imprecision, uncertainty and partial truths. Applications of these techniques in nuclear engineering present a tremendous challenge due to its strict nuclear safety regulation. The fields of nuclear engineering, fuzzy systems and soft computing have nevertheless matured considerably during the last decade. This book presents new application potentials for Fuzzy Systems and Soft Computing in Nuclear Engineering. The root of this book can be traced back to the series of the first, second and third international workshops on Fuzzy Logic and Intelligent Technologies in Nuclear Science (FUNS), which were successfully held in Mol, September 14-16, 1994 (FLINS'94), in Mol, September 25-27, 1996 (FLINS'96), and in Antwerp, September 14-16, 1998 (FLINS'98). The conferences were organised by the Belgian Nuclear Research Centre (SCKeCEN) and aimed at bringing together scientists, researchers, and engineers from academia and industry, at introducing the principles of fuzzy logic, neural networks, genetic algorithms and other soft computing methodologies, to the field of nuclear engineering, and at applying these techniques to complex problem solving within nuclear industry and related research fields. This book, as its title suggests, consists of nuclear engineering applications of fuzzy systems (Chapters 1-10) and soft computing (Chapters 11-21). Nine pertinent chapters are based on the extended version of papers at FLINS'98 and the other 12 chapters are original contributions with up-to-date coverage of fuzzy and soft computing applications by leading researchers written exclusively for this book."

1. When I was asked by the editors of this book to write a foreword, I was seized by panic. Obviously, neither I am an expert in Knowledge Representation in Fuzzy Databases nor I could have been beforehand unaware that the book's contributors would be some of the most outstanding researchers in the field. However, Amparo Vila's gentle insistence gradually broke down my initial resistance, and panic then gave way to worry. Which paving stones did I have at my disposal for making an entrance to the book? After thinking about it for some time, I concluded that it would be pretentious on my part to focus on the subjects which are dealt with directly in the contributions presented, and that it would instead be better to confine myself to making some general reflections on knowledge representation given by imprecise information using fuzzy sets; reflections which have been suggested to me by some words in the following articles such as: graded notions, fuzzy objects, uncertainty, fuzzy implications, fuzzy inference, empty intersection, etc.

In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n," "U," "+" and ."" over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility." The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy," motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character."

Information is precious. It reduces our uncertainty in making decisions. Knowledge about the outcome of an uncertain event gives the possessor an advantage. It changes the course of lives, nations, and history itself. Information is the food of Maxwell's demon. His power comes from know ing which particles are hot and which particles are cold. His existence was paradoxical to classical physics and only the realization that information too was a source of power led to his taming. Information has recently become a commodity, traded and sold like or ange juice or hog bellies. Colleges give degrees in information science and information management. Technology of the computer age has provided access to information in overwhelming quantity. Information has become something worth studying in its own right. The purpose of this volume is to introduce key developments and results in the area of generalized information theory, a theory that deals with uncertainty-based information within mathematical frameworks that are broader than classical set theory and probability theory. The volume is organized as follows."

The primary purpose of this book is to present information about selected topics on the interactions and applications of fuzzy + neural. Most of the discussion centers around our own research in these areas. Fuzzy + neural can mean many things: (1) approximations between fuzzy systems and neu ral nets (Chapter 4); (2) building hybrid neural nets to equal fuzzy systems (Chapter 5); (3) using neura.l nets to solve fuzzy problems (Chapter 6); (4) approximations between fuzzy neural nets and other fuzzy systems (Chap ter 8); (5) constructing hybrid fuzzy neural nets for certain fuzzy systems (Chapters 9, 10); or (6) computing with words (Chapter 11). This book is not intend to be used primarily as a text book for a course in fuzzy + neural because we have not included problems at the end of each chapter, we have omitted most proofs (given in the references), and we have given very few references. We wanted to keep the mathematical prerequisites to a minimum so all longer, involved, proofs were omitted. Elementary dif ferential calculus is the only prerequisite needed since we do mention partial derivatives once or twice."

Some recent fuzzy database modeling advances for the non-traditional applications are introduced in this book. The focus is on database models for modeling complex information and uncertainty at the conceptual, logical, physical design levels and from integrity constraints defined on the fuzzy relations.
The database models addressed here are; the conceptual data models, including the ExIFO and ExIFO2 data models, the logical database models, including the extended NF2 database model, fuzzy object-oriented database model, and the fuzzy deductive object-oriented database model. Integrity constraints are defined on the fuzzy relations are also addressed. A continuing reason for the limited adoption of fuzzy database systems has been performance. There have been few efforts at defining physical structures that accomodate fuzzy information. A new access structure and data organization for fuzzy information is introduced in this book.

The papers on rough set theory and its applications placed in this volume present a wide spectrum of problems representative to the present. stage of this theory. Researchers from many countries reveal their rec.ent results on various aspects of rough sets. The papers are not confined only to mathematical theory but also include algorithmic aspects, applications and information about software designed for data analysis based on this theory. The volume contains also list of selected publications on rough sets which can be very useful to every one engaged in research or applications in this domain and sometimes perhaps unaware of results of other authors. The book shows that rough set theory is a vivid and vigorous domain with serious results to its credit and bright perspective for future developments. It lays on the crossroads of fuzzy sets, theory of evidence, neural networks, Petri nets and many other branches of AI, logic and mathematics. These diverse connec tions seem to be a very fertile feature of rough set theory and have essentially contributed to its wide and rapid expansion. It is worth mentioning that its philosophical roots stretch down from Leibniz, Frege and Russell up to Popper. Therefore many concepts dwelled on in rough set theory are not entirely new, nevertheless the theory can be viewed as an independent discipline on its own rights. Rough set theory has found many interesting real life applications in medicine, banking, industry and others."

During the past few years two principally different approaches to the design of fuzzy controllers have emerged: heuristics-based design and model-based design. The main motivation for the heuristics-based design is given by the fact that many industrial processes are still controlled in one of the following two ways: - The process is controlled manually by an experienced operator. - The process is controlled by an automatic control system which needs manual, on-line 'trimming' of its parameters by an experienced operator. In both cases it is enough to translate in terms of a set of fuzzy if-then rules the operator's manual control algorithm or manual on-line 'trimming' strategy in order to obtain an equally good, or even better, wholly automatic fuzzy control system. This implies that the design of a fuzzy controller can only be done after a manual control algorithm or trimming strategy exists. It is admitted in the literature on fuzzy control that the heuristics-based approach to the design of fuzzy controllers is very difficult to apply to multiple-inputjmultiple-output control problems which represent the largest part of challenging industrial process control applications. Furthermore, the heuristics-based design lacks systematic and formally verifiable tuning tech niques. Also, studies of the stability, performance, and robustness of a closed loop system incorporating a heuristics-based fuzzy controller can only be done via extensive simulations."

It is the business of science not to create laws, but to discover them. We do not originate the constitution of our own minds, greatly as it may be in our power to modify their character. And as the laws of the human intellect do not depend upon our will, so the forms of science, of (1. 1) which they constitute the basis, are in all essential regards independent of individual choice. George Boole 10, p. llJ 1. 1 Comparison with Traditional Logic The logic of this book is a probability logic built on top of a yes-no or 2-valued logic. It is divided into two parts, part I: BP Logic, and part II: M Logic. 'BP' stands for 'Bayes Postulate'. This postulate says that in the absence of knowl edge concerning a probability distribution over a universe or space one should assume 1 a uniform distribution. 2 The M logic of part II does not make use of Bayes postulate or of any other postulates or axioms. It relies exclusively on purely deductive reasoning following from the definition of probabilities. The M logic goes an important step further than the BP logic in that it can distinguish between certain types of information supply sentences which have the same representation in the BP logic as well as in traditional first order logic, although they clearly have different meanings (see example 6. 1. 2; also comments to the Paris-Rome problem of eqs. (1. 8), (1. 9) below)."

In 1982, Professor Pawlak published his seminal paper on what he called "rough sets" - a work which opened a new direction in the development of theories of incomplete information. Today, a decade and a half later, the theory of rough sets has evolved into a far-reaching methodology for dealing with a wide variety of issues centering on incompleteness and imprecision of information - issues which playa key role in the conception and design of intelligent information systems. "Incomplete Information: Rough Set Analysis" - or RSA for short - presents an up-to-date and highly authoritative account of the current status of the basic theory, its many extensions and wide-ranging applications. Edited by Professor Ewa Orlowska, one of the leading contributors to the theory of rough sets, RSA is a collection of nineteen well-integrated chapters authored by experts in rough set theory and related fields. A common thread that runs through these chapters ties the concept of incompleteness of information to those of indiscernibility and similarity.

This book presents the main tools for aggregation of information given by several members of a group or expressed in multiple criteria, and for fusion of data provided by several sources. It focuses on the case where the availability knowledge is imperfect, which means that uncertainty and/or imprecision must be taken into account. The book contains both theoretical and applied studies of aggregation and fusion methods in the main frameworks: probability theory, evidence theory, fuzzy set and possibility theory. The latter is more developed because it allows to manage both imprecise and uncertain knowledge. Applications to decision-making, image processing, control and classification are described.

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.

This book includes a selection of twelve carefully revised papers chosen from the papers accepted for presentation at the 4th IEEE/Nagoya-University World Wisepersons Workshop held in Nagoya in November 1995.
The combining of the technologies of fuzzy logic, neural networks, and evolutionary computation is expected to open up a new paradigm of machine learning for the realization of human-like information generating systems. The excellent papers presented are organized in sections on fuzzy and evolutionary computation, fuzzy and learning automata, fuzzy and neural networks, genetic algorithms, and CAM-brain.

This thoroughly refereed and well organized collection of papers is largely based on papers originally presented at the IJCAI'95 Workshop on Fuzzy Logic in AI, held in Montreal, Canada, in August 1995. Additionally, a few papers were invited in order to round off the scope and competent coverage of relevant topics.
The 20 revised full papers included are organized in sections on hybrid and novel architectures, machine learning and data mining, image processing and computer vision, and theoretical developments. Focusing on the most pressing problems of AI, the volume supports the view that fuzzy systems combined with traditional AI leads the move towards the next generation of intelligent systems.

Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start.

Model based fuzzy control uses a given conventional or fuzzy open loop model of the plant under control to derive the set of fuzzy if-then rules for the fuzzy controller. Of central interest are the stability, performance, and robustness properties of the resulting closed loop system involving a conventional or fuzzy model and a fuzzy controller. The major objective of model based fuzzy control is to use the full range of linear and nonlinear design and analysis methods to design such fuzzy controllers with properties superior to non-fuzzy controllers designed using the same techniques. This objective has already been achieved for fuzzy sliding mode controllers and fuzzy gain schedulers - the main topics of this book. A comprehensive and up-to-date treatment of model based fuzzy control and its relationship to conventional control, the text is intended to serve as a guide for scientists and practitioners and to provide introductory material on fuzzy control for courses in control theory.

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.

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.

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.

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 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.