Fuzzy Sets in Decision Analysis, Operations Research and Statistics includes chapters on fuzzy preference modeling, multiple criteria analysis, ranking and sorting methods, group decision-making and fuzzy game theory. It also presents optimization techniques such as fuzzy linear and non-linear programming, applications to graph problems and fuzzy combinatorial methods such as fuzzy dynamic programming. In addition, the book also accounts for advances in fuzzy data analysis, fuzzy statistics, and applications to reliability analysis. These topics are covered within four parts: Decision Making, Mathematical Programming, Statistics and Data Analysis, and Reliability, Maintenance and Replacement. The scope and content of the book has resulted from multiple interactions between the editor of the volume, the series editors, the series advisory board, and experts in each chapter area. Each chapter was written by a well-known researcher on the topic and reviewed by other experts in the area. These expert reviewers sometimes became co-authors because of the extent of their contribution to the chapter. As a result, twenty-five authors from twelve countries and four continents were involved in the creation of the 13 chapters, which enhances the international character of the project and gives an idea of how carefully the Handbook has been developed.

Many-valued logics is becoming increasingly important in many branches of science. This is the second volume of a comprehensive two-volume handbook on many-valued logics by two leading members of the famous Polish school of logic. While the first volume of 1992 was mainly concerned with theoretical foundations, this volume emphasizes automated reasoning, practical applications, and latest developments in closely related fields, such as fuzzy logics and rough set theory. It offers an extensive overview of Gentzen deduction systems and multi-sequential systems in many-valued logics and shows the application of the resolution principle to this logics. It discusses applications in such areas as software specification and electronic circuit verification and presents fuzzy logics and rough set theory in detail.

It is frequently observed that most decision-making problems involve several objectives, and the aim of the decision makers is to find the best decision by fulfilling the aspiration levels of all the objectives. Multi-objective decision making is especially suitable for the design and planning steps and allows a decision maker to achieve the optimal or aspired goals by considering the various interactions of the given constraints. Multi-Objective Stochastic Programming in Fuzzy Environments discusses optimization problems with fuzzy random variables following several types of probability distributions and different types of fuzzy numbers with different defuzzification processes in probabilistic situations. The content within this publication examines such topics as waste management, agricultural systems, and fuzzy set theory. It is designed for academicians, researchers, and students.

Fuzziology studies the fuzziness inherent in what we know about ourselves, the sources and nature of our experience, our thoughts and feelings, drives for understanding and urges to create and realise our potential. This kind of fuzziness is at the core of our existence, at the essence of our humanness. It affects any field of human activity, be it mathematical study of fuzzy equations and fuzzy integrals; engineering design and implementation of fuzzy logic-based methodologies; fuzzy control systems or fuzzy robots. Social fuzziology investigates the role of fuzziness in understanding the dynamic complexity of human existence in the social world. It is a study of the nexus between the complex demands of life -individual and social -and the fuzziness of thinking. Since human evolution over 2 billion years has seen the co-evolution of social complexity with human language and thought, it is likely that the fuzziness of language and thought is especially intimately formed by the demands of social complexity, just as social complexity is sustained by the inherent fuzziness of language and thought. Social fuzziology is not simply one field of application of fuzziology. Given the initial state of the development of fuzziology, social fuzziology needs to develop hand in hand with fuzziology, each helping to advance the other.

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

Geometric properties and relations play central roles in the description and processing of spatial data. The properties and relations studied by mathematicians usually have precise definitions, but verbal descriptions often involve imprecisely defined concepts such as elongatedness or proximity. The methods used in soft computing provide a framework for formulating and manipulating such concepts. This volume contains eight papers on the soft definition and manipulation of spatial relations and gives a comprehensive summary on the subject.

It took many decades for Peirce's coneept of a relation to find its way into the microelectronic innards of control systems of eement kilns, subway trains, and tunnel-digging machinery. But what is amazing is that the more we leam about the basically simple coneept of a relation, the more aware we become of its fundamental importanee and wide ranging ramifications. The work by Di Nola, Pedrycz, Sanchez, and Sessa takes us a long distanee in this direction by opening new vistas on both the theory and applications of fuzzy relations - relations which serve to model the imprecise coneepts which pervade the real world. Di Nola, Pedrycz, Sanchez, and Sessa focus their attention on a eentral problem in the theory of fuzzy relations, namely the solution of fuzzy relational equations. The theory of such equations was initiated by Sanchez in 1976, ina seminal paper dealing with the resolution of composite fuzzy relational equations. Sinee then, hundreds of papers have been written on this and related topics, with major contributions originating in France, Italy, Spain, Germany, Poland, Japan, China, the Soviet Union, India, and other countries. The bibliography included in this volume highlights the widespread interest in the theory of fuzzy relational equations and the broad spectrum of its applications.

Soft computing encompasses various computational methodologies, which, unlike conventional algorithms, are tolerant of imprecision, uncertainty, and partial truth. Soft computing technologies offer adaptability as a characteristic feature and thus permit the tracking of a problem through a changing environment. Besides some recent developments in areas like rough sets and probabilistic networks, fuzzy logic, evolutionary algorithms, and artificial neural networks are core ingredients of soft computing, which are all bio-inspired and can easily be combined synergetically.This book presents a well-balanced integration of fuzzy logic, evolutionary computing, and neural information processing. The three constituents are introduced to the reader systematically and brought together in differentiated combinations step by step. The text was developed from courses given by the authors and offers numerous illustrations as

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.

Dynamic Fuzzy Pattern Recognition with Applications to Finance and Engineering focuses on fuzzy clustering methods which have proven to be very powerful in pattern recognition and considers the entire process of dynamic pattern recognition. This book sets a general framework for Dynamic Pattern Recognition, describing in detail the monitoring process using fuzzy tools and the adaptation process in which the classifiers have to be adapted, using the observations of the dynamic process. It then focuses on the problem of a changing cluster structure (new clusters, merging of clusters, splitting of clusters and the detection of gradual changes in the cluster structure). Finally, the book integrates these parts into a complete algorithm for dynamic fuzzy classifier design and classification.

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.

As understanding of the engineering design and configuration processes grows, the recognition that these processes intrinsically involve imprecise information is also growing. This book collects some of the most recent work in the area of representation and manipulation of imprecise information during the syn thesis of new designs and selection of configurations. These authors all utilize the mathematics of fuzzy sets to represent information that has not-yet been reduced to precise descriptions, and in most cases also use the mathematics of probability to represent more traditional stochastic uncertainties such as un controlled manufacturing variations, etc. These advances form the nucleus of new formal methods to solve design, configuration, and concurrent engineering problems. Hans-Jurgen Sebastian Aachen, Germany Erik K. Antonsson Pasadena, California ACKNOWLEDGMENTS We wish to thank H.-J. Zimmermann for inviting us to write this book. We are also grateful to him for many discussions about this new field Fuzzy Engineering Design which have been very stimulating. We wish to thank our collaborators in particular: B. Funke, M. Tharigen, K. Miiller, S. Jarvinen, T. Goudarzi-Pour, and T. Kriese in Aachen who worked in the PROKON project and who elaborated some of the results presented in the book. We also wish to thank Michael J. Scott for providing invaluable editorial assis tance. Finally, the book would not have been possible without the many contributions and suggestions of Alex Greene of Kluwer Academic Publishers. 1 MODELING IMPRECISION IN ENGINEERING DESIGN Erik K. Antonsson, Ph.D., P.E."

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.

Fuzzy Control Synthesis and Analysis Edited by Shehu S. Farinwata Ford Motor Company, Research Laboratory, Dearborn, Michigan, USA Dimitar Filev Ford Motor Company, AMTDC, Redford, Michigan, USA Reza Langari Texas A & M University, College Station, Texas, USA Fuzzy techniques are used to cope with imprecision in the basic elements of a process under control. Written by an international team of researchers this edited volume covers the modeling, analysis and synthesis of fuzzy control systems. Features include:
? Comprehensive coverage of fuzzy dynamical systems, robustness, stability and sensitivity -- giving the reader a good grasp of the fundamentals of fuzzy control
? Focus on the analytical structures of new fuzzy modeling approaches based on the Takagi-Sugeno-Kang (TSK) or Takagi-Sugeno (TS) model
? Applications of fuzzy control to aircraft systems, rocket engines and automotive engines
? Problems and examples illustrating how fuzzy approaches may be applied to the modeling, analysis and synthesis of closed-loop systems
Design and control engineers will value the advanced control techniques and new design and analysis tools presented. Postgraduates studying fuzzy control will find this book a useful reference on synthesis, systems analysis and advanced nonlinear control methods.

This volume provides an up-to-date picture of the current status of theoretical and empirical developments in the application of fuzzy sets in psychology. Fuzzy set theory could benefit researchers in at least two ways: first, as a metaphor or model for ordinary thought, and secondly, as an aid to data analysis and theory construction. One can find examples for both kinds in the volume, which will be of interest both to the advanced student in the field as well as to anyone possessing a basic scientific background.

Provides a truly accessible introduction and a fully integrated approach to fuzzy systems and neural networks—the definitive text for students and practicing engineers Researchers are already applying neural networks and fuzzy systems in series, from the use of fuzzy inputs and outputs for neural networks to the employment of individual neural networks to quantify the shape of a fuzzy membership function. But the integration of these two fields into a "neurofuzzy" technology holds even greater potential benefits in reducing computing time and optimizing results. Fuzzy and Neural Approaches in Engineering presents a detailed examination of the fundamentals of fuzzy systems and neural networks and then joins them synergistically—combining the feature extraction and modeling capabilities of the neural network with the representation capabilities of fuzzy systems. Exploring the value of relating genetic algorithms and expert systems to fuzzy and neural technologies, this forward-thinking text highlights an entire range of dynamic possibilities within soft computing. With examples specifically designed to illuminate key concepts and overcome the obstacles of notation and overly mathematical presentations often encountered in other sources, plus tables, figures, and an up-to-date bibliography, this unique work is both an important reference and a practical guide to neural networks and fuzzy systems.

This book offers a rigorous mathematical analysis of fuzzy geometrical ideas. It demonstrates the use of fuzzy points for interpreting an imprecise location and for representing an imprecise line by a fuzzy line. Further, it shows that a fuzzy circle can be used to represent a circle when its description is not known precisely, and that fuzzy conic sections can be used to describe imprecise conic sections. Moreover, it discusses fundamental notions on fuzzy geometry, including the concepts of fuzzy line segment and fuzzy distance, as well as key fuzzy operations, and includes several diagrams and numerical illustrations to make the topic more understandable. The book fills an important gap in the literature, providing the first comprehensive reference guide on the fuzzy mathematics of imprecise image subsets and imprecise geometrical objects. Mainly intended for researchers active in fuzzy optimization, it also includes chapters relevant for those working on fuzzy image processing and pattern recognition. Furthermore, it is a valuable resource for beginners interested in basic operations on fuzzy numbers, and can be used in university courses on fuzzy geometry, dealing with imprecise locations, imprecise lines, imprecise circles, and imprecise conic sections.

Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining - or fibring - systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate.

Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. Fuzzy topology is one such branch, combining ordered structure with topological structure. This branch of mathematics, emerged from the background - processing fuzziness, and locale theory, proposed from the angle of pure mathematics by the great French mathematician Ehresmann, comprise the two most active aspects of topology on lattice, which affect each other.This book is the first monograph to systematically reflect the up-to-date state of fuzzy topology. It emphasizes the so-called "pointed approach" and the effects of stratification structure appearing in fuzzy sets.The monograph can serve as a reference book for mathematicians, researchers, and graduate students working in this branch of mathematics. After an appropriate rearrangements of the chapters and sections, it can also be used as a text for undergraduates.

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.

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

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.