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Generalized Measure Theory: 25 (IFSR International Series in Systems Science and Systems Engineering) - Softcover
Inhaltsangabe
This textbook provides an exhaustive review of generalized measures, from the theoretical background to the latest applications. It is designed as a main text for graduate courses on Generalized Measure Theory, Fuzzy Measure Theory, Theory of Nonadditive Measures and Theory of Monotone Measures. It can also be used as a reference in courses on Fuzzy Sets, Fuzzy Control and Fuzzy Logic.
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This comprehensive text examines the relatively new mathematical area of generalized measure theory. This area expands classical measure theory by abandoning the requirement of additivity and replacing it with various weaker requirements. Each of these weaker requirements characterizes a class of nonadditive measures. This results in new concepts and methods that allow us to deal with many problems in a more realistic way. For example, it allows us to work with imprecise probabilities.
The exposition of generalized measure theory unfolds systematically. It begins with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory.
Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.
About the Authors:
Zhenyuan Wang is currently a Professor in the Department of Mathematics of University of Nebraska at Omaha. His research interests have been in the areas of nonadditive measures, nonlinear integrals, probability and statistics, and data mining. He has published one book and many papers in these areas.
George J. Klir is currently a Distinguished Professor of Systems Science at Binghamton University (SUNY at Binghamton). He has published 29 books and well over 300 papers in a wide range of areas. His current research interests are primarily in the areas of fuzzy systems, soft computing, and generalized information theory.
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Generalized Measure Theory
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Generalized Measure Theory (Paperback)
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ISBN 13: 9781441945761
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Paperback. Zustand: new. Paperback. In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term fuzzy measure was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. That is, the book dealt with nonnegative set functions that were mo- tone, vanished at the empty set, and possessed appropriate continuity properties when defined on infinite sets. It seems that Fuzzy Measure Theory was the only book available on the market at that time devoted to this emerging new mathematical theory. Some ten years after its publication we began to see that the subject had expanded so much that a second edition of the book, or even a new book on the subject, was needed. We eventually decided to write a new book because the new material we wished to include was too extensive forand far beyond the usual scopeof a second edition. More importantly, we felt that some fundamental changes regarding this topics scope and terminology would be desirable and timely. In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term fuzzy measure was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781441945761
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Generalized Measure Theory (IFSR International Series in Systems Science and Systems Engineering, 25)
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Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The expositionunfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory.Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory. 400 pp. Englisch. Bestandsnummer des Verkäufers 9781441945761
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Generalized Measure Theory (IFSR International Series in Systems Science and Systems Engineering, 25)
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Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Most up-to-date textbook in the field, covering recent applicationsNumerous examples motivate the theory and exercises at the end of the chapter provide practice to the studentUseful to an interdisciplinary cadre of mathematicians, engineer. Bestandsnummer des Verkäufers 4174919
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Generalized Measure Theory
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Springer US, Springer US Dez 2010, 2010
ISBN 10: 1441945768
ISBN 13: 9781441945761
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Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term ¿¿fuzzy measure¿¿ was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. That is, the book dealt with nonnegative set functions that were mo- tone, vanished at the empty set, and possessed appropriate continuity properties when defined on infinite sets. It seems that Fuzzy Measure Theory was the only book available on the market at that time devoted to this emerging new mathematical theory. Some ten years after its publication we began to see that the subject had expanded so much that a second edition of the book, or even a new book on the subject, was needed. We eventually decided to write a new book because the new material we wished to include was too extensive for¿and far beyond the usual scope¿of a second edition. More importantly, we felt that some fundamental changes regarding this topic¿s scope and terminology would be desirable and timely.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 400 pp. Englisch. Bestandsnummer des Verkäufers 9781441945761
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Generalized Measure Theory
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In 1992 we published a book entitled Fuzzy Measure Theory (Plenum Press, New York), in which the term ''fuzzy measure'' was used for set functions obtained by replacing the additivity requirement of classical measures with weaker requirements of monotonicity with respect to set inclusion and con- nuity. That is, the book dealt with nonnegative set functions that were mo- tone, vanished at the empty set, and possessed appropriate continuity properties when defined on infinite sets. It seems that Fuzzy Measure Theory was the only book available on the market at that time devoted to this emerging new mathematical theory. Some ten years after its publication we began to see that the subject had expanded so much that a second edition of the book, or even a new book on the subject, was needed. We eventually decided to write a new book because the new material we wished to include was too extensive for-and far beyond the usual scope-of a second edition. More importantly, we felt that some fundamental changes regarding this topic's scope and terminology would be desirable and timely. Bestandsnummer des Verkäufers 9781441945761
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