fuzzy sets uncertainty and information

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Fuzzy Sets Uncertainty And Information

Author : Klir
ISBN : 8120306953
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File Size : 61. 29 MB
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Uncertainty And Information

Author : George J. Klir
ISBN : 9780471755562
Genre : Technology & Engineering
File Size : 57. 11 MB
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Deal with information and uncertainty properly and efficiently using tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized Information Theory contains comprehensive and up-to-date coverage of results that have emerged from a research program begun by the author in the early 1990s under the name "generalized information theory" (GIT). This ongoing research program aims to develop a formal mathematical treatment of the interrelated concepts of uncertainty and information in all their varieties. In GIT, as in classical information theory, uncertainty (predictive, retrodictive, diagnostic, prescriptive, and the like) is viewed as a manifestation of information deficiency, while information is viewed as anything capable of reducing the uncertainty. A broad conceptual framework for GIT is obtained by expanding the formalized language of classical set theory to include more expressive formalized languages based on fuzzy sets of various types, and by expanding classical theory of additive measures to include more expressive non-additive measures of various types. This landmark book examines each of several theories for dealing with particular types of uncertainty at the following four levels: * Mathematical formalization of the conceived type of uncertainty * Calculus for manipulating this particular type of uncertainty * Justifiable ways of measuring the amount of uncertainty in any situation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complex material and demonstrate practical applications, generous historical and bibliographical notes, end-of-chapter exercises to test readers' newfound knowledge, glossaries, and an Instructor's Manual, this is an excellent graduate-level textbook, as well as an outstanding reference for researchers and practitioners who deal with the various problems involving uncertainty and information. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Uncertainty Based Information

Author : George Klir
ISBN : 9783790818697
Genre : Mathematics
File Size : 81. 91 MB
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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.

Imprecision And Uncertainty In Information Representation And Processing

Author : Plamen Angelov
ISBN : 9783319263021
Genre : Computers
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The book offers a comprehensive and timely overview of advanced mathematical tools for both uncertainty analysis and modeling of parallel processes, with a special emphasis on intuitionistic fuzzy sets and generalized nets. The different chapters, written by active researchers in their respective areas, are structured to provide a coherent picture of this interdisciplinary yet still evolving field of science. They describe key tools and give practical insights into and research perspectives on the use of Atanassov's intuitionistic fuzzy sets and logic, and generalized nets for describing and dealing with uncertainty in different areas of science, technology and business, in a single, to date unique book. Here, readers find theoretical chapters, dealing with intuitionistic fuzzy operators, membership functions and algorithms, among other topics, as well as application-oriented chapters, reporting on the implementation of methods and relevant case studies in management science, the IT industry, medicine and/or education. With this book, the editors wish to pay homage to Professor Krassimir Todorov Atanassov for his pioneering work on both generalized nets and intuitionistic fuzzy set.

Fundamentals Of Fuzzy Sets

Author : Didier Dubois
ISBN : 9781461544296
Genre : Mathematics
File Size : 71. 15 MB
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Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

Fuzzy Logic For The Management Of Uncertainty

Author : Lotfi Asker Zadeh
ISBN : UOM:39015025259287
Genre : Computers
File Size : 28. 78 MB
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Fuzzy systems are mathematically based systems that enable computers to handle vague, imprecise, or ambiguous information. Edited by two of the top names in this field and written by a team of international experts, here is the most up-to-date and complete compilation of articles in fuzzy logic research. All chapters are original works prepared specifically for this volume, including articles on applications and tools. Fuzzy Logic for the Management of Uncertainty covers many important topics, including: Developments in mathematics that have paved the road for fuzzy logic; Deep, and of a broad perspective, exposition of virtually all approaches used in contemporary science for the representation and handling of imperfect (uncertain, imprecise, vague, ambiguous, etc.) information; Coverage of practically all relevant and promising directions and approaches in fuzzy logic research including LT--fuzzy logic, model theoretic approaches, intuitionistic fuzzy logic, nonmonotonic fuzzy logic, modifier fuzzy logic; VLSI fuzzy logic-based chips that have triggered the implementation of fuzzy logic in so many fields of science and technology; A broad coverage of fuzzy logic in approximate reasoning, including basic issues related to the role of fuzzy logic for approximate reasoning, analyses of various definitions of fuzzy implication that is a crucial element in fuzzy logic-based reasoning schemes, general issues related to reasoning and inference based on fuzzy logic, inconsistencies and explanations in imprecise reasoning and databases; Use of fuzzy logic for knowledge representation, including the use of fuzzy relations, fuzzy linguistic modifiers, etc.; Use of fuzzy logic for knowledge acquisition and elicitation, mainly for machine learning; Use of fuzzy logic for the modelling of neurons and neural networks; Use of fuzzy logic for the development of fuzzified higher level computer languages, notably for the fuzzification of LISP; Use of fuzzy logic for the management of uncertainty in implemented knowledge-based systems; Use of fuzzy logic for the validation of knowledge-based systems; Use of fuzzy logic in intelligent database management systems.

Uncertainty Analysis In Engineering And Sciences Fuzzy Logic Statistics And Neural Network Approach

Author : Bilal M. Ayyub
ISBN : 9781461554738
Genre : Computers
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Uncertainty has been of concern to engineers, managers and . scientists for many centuries. In management sciences there have existed definitions of uncertainty in a rather narrow sense since the beginning of this century. In engineering and uncertainty has for a long time been considered as in sciences, however, synonymous with random, stochastic, statistic, or probabilistic. Only since the early sixties views on uncertainty have ~ecome more heterogeneous and more tools to model uncertainty than statistics have been proposed by several scientists. The problem of modeling uncertainty adequately has become more important the more complex systems have become, the faster the scientific and engineering world develops, and the more important, but also more difficult, forecasting of future states of systems have become. The first question one should probably ask is whether uncertainty is a phenomenon, a feature of real world systems, a state of mind or a label for a situation in which a human being wants to make statements about phenomena, i. e. , reality, models, and theories, respectively. One cart also ask whether uncertainty is an objective fact or just a subjective impression which is closely related to individual persons. Whether uncertainty is an objective feature of physical real systems seems to be a philosophical question. This shall not be answered in this volume.

Fundamentals Of Uncertainty Calculi With Applications To Fuzzy Inference

Author : Michel Grabisch
ISBN : 9789401584494
Genre : Business & Economics
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With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys tems. These attempts involve emulating human reasoning, and researchers have tried to model such reasoning from various points of view. But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions. Thus the general problem of reasoning with knowledge is the core of design methodology. The attempt to use human knowledge in its most natural sense, that is, through linguistic descriptions, is novel and controversial. The novelty lies in the recognition of a new type of un certainty, namely fuzziness in natural language, and the controversality lies in the mathematical modeling process. As R. Bellman [7] once said, decision making under uncertainty is one of the attributes of human intelligence. When uncertainty is understood as the impossi bility to predict occurrences of events, the context is familiar to statisticians. As such, efforts to use probability theory as an essential tool for building intelligent systems have been pursued (Pearl [203], Neapolitan [182)). The methodology seems alright if the uncertain knowledge in a given problem can be modeled as probability measures.

Views On Fuzzy Sets And Systems From Different Perspectives

Author : Rudolf Seising
ISBN : 9783540938019
Genre : Computers
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This book presents the complete philosophy of Fuzzy Set Theory. It offers a collection of views from scholars involved in various research projects concerning fuzziness in science, technology, economic systems, social sciences, logics and philosophy.

Fuzzy Set Theory And Its Applications

Author : Hans-Jürgen Zimmermann
ISBN : 9789401587020
Genre : Mathematics
File Size : 31. 4 MB
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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.

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