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| Author | : Michel Grabisch |
| Publisher | : Physica |
| Total Pages | : 504 |
| Release | : 2000-01-24 |
| Genre | : Business & Economics |
| ISBN | : |
Download Fuzzy Measures and Integrals Book in PDF, ePub and Kindle
Concepts similar to fuzzy measure have been introduced independently in many domains: in non-expected utility theory, cooperative game theory, complexity analysis, measure theory, etc. This book reflects all these facets. It gathers survey papers written by leading researchers in the field, covering a selection of most significant topics. The first part is devoted to fundamental and theoretical material, while the second part deals with more applied topics such as decision making and pattern recognition. The book is of interest to researchers in decision making, artificial intelligence, applied mathematics, mathematical social sciences, etc.
| Author | : |
| Publisher | : |
| Total Pages | : 112 |
| Release | : 1999 |
| Genre | : Fuzzy sets |
| ISBN | : |
Download Fuzzy Measures and Integrals Book in PDF, ePub and Kindle
| Author | : Zhenyuan Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475753039 |
Download Fuzzy Measure Theory Book in PDF, ePub and Kindle
Providing the first comprehensive treatment of the subject, this groundbreaking work is solidly founded on a decade of concentrated research, some of which is published here for the first time, as well as practical, ''hands on'' classroom experience. The clarity of presentation and abundance of examples and exercises make it suitable as a graduate level text in mathematics, decision making, artificial intelligence, and engineering courses.
| Author | : D. Denneberg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 182 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 9401724342 |
Download Non-Additive Measure and Integral Book in PDF, ePub and Kindle
Non-Additive Measure and Integral is the first systematic approach to the subject. Much of the additive theory (convergence theorems, Lebesgue spaces, representation theorems) is generalized, at least for submodular measures which are characterized by having a subadditive integral. The theory is of interest for applications to economic decision theory (decisions under risk and uncertainty), to statistics (including belief functions, fuzzy measures) to cooperative game theory, artificial intelligence, insurance, etc. Non-Additive Measure and Integral collects the results of scattered and often isolated approaches to non-additive measures and their integrals which originate in pure mathematics, potential theory, statistics, game theory, economic decision theory and other fields of application. It unifies, simplifies and generalizes known results and supplements the theory with new results, thus providing a sound basis for applications and further research in this growing field of increasing interest. It also contains fundamental results of sigma-additive and finitely additive measure and integration theory and sheds new light on additive theory. Non-Additive Measure and Integral employs distribution functions and quantile functions as basis tools, thus remaining close to the familiar language of probability theory. In addition to serving as an important reference, the book can be used as a mathematics textbook for graduate courses or seminars, containing many exercises to support or supplement the text.
| Author | : Tamalika Chaira |
| Publisher | : John Wiley & Sons |
| Total Pages | : 304 |
| Release | : 2019-03-21 |
| Genre | : Technology & Engineering |
| ISBN | : 1119544211 |
Download Fuzzy Set and Its Extension Book in PDF, ePub and Kindle
Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design.
| Author | : Michel Grabisch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 354 |
| Release | : 2013-04-17 |
| Genre | : Business & Economics |
| ISBN | : 9401584494 |
Download Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference Book in PDF, ePub and Kindle
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.
| Author | : E Ruspini |
| Publisher | : CRC Press |
| Total Pages | : 1229 |
| Release | : 2020-03-05 |
| Genre | : Computers |
| ISBN | : 1420050397 |
Download Handbook of Fuzzy Computation Book in PDF, ePub and Kindle
Initially conceived as a methodology for the representation and manipulation of imprecise and vague information, fuzzy computation has found wide use in problems that fall well beyond its originally intended scope of application. Many scientists and engineers now use the paradigms of fuzzy computation to tackle problems that are either intractable
| Author | : Vicenç Torra |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 284 |
| Release | : 2007-05-11 |
| Genre | : Computers |
| ISBN | : 3540687912 |
Download Modeling Decisions Book in PDF, ePub and Kindle
This book covers the underlying science and application issues related to aggregation operators, focusing on tools used in practical applications that involve numerical information. It will thus be required reading for engineers, statisticians and computer scientists of all kinds. Starting with detailed introductions to information fusion and integration, measurement and probability theory, fuzzy sets, and functional equations, the authors then cover numerous topics in detail, including the synthesis of judgements, fuzzy measures, weighted means and fuzzy integrals.
| Author | : Zhenyuan Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2010-07-07 |
| Genre | : Mathematics |
| ISBN | : 0387768521 |
Download Generalized Measure Theory Book in PDF, ePub and Kindle
Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds 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.
| Author | : Yoobong Kim |
| Publisher | : |
| Total Pages | : 122 |
| Release | : 1985 |
| Genre | : |
| ISBN | : |
Download Theory of Fuzzy Measures and Integrals Book in PDF, ePub and Kindle
