Non Additive Measure And Integral

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Non-Additive Measure and Integral

Author : D. Denneberg
Publisher : Springer Science & Business Media
ISBN 13 : 9401724342
Total Pages : 182 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Non-Additive Measure and Integral by : D. Denneberg

Download or read book Non-Additive Measure and Integral written by D. Denneberg and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-Additive Measures

Author : Vicenc Torra
Publisher : Springer
ISBN 13 : 3319031554
Total Pages : 201 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Non-Additive Measures by : Vicenc Torra

Download or read book Non-Additive Measures written by Vicenc Torra and published by Springer. This book was released on 2013-10-23 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.

An Introduction to Measure Theory

Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Measure Theory by : Terence Tao

Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Computational Science – ICCS 2008

Author : Marian Bubak
Publisher : Springer Science & Business Media
ISBN 13 : 3540693866
Total Pages : 771 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Computational Science – ICCS 2008 by : Marian Bubak

Download or read book Computational Science – ICCS 2008 written by Marian Bubak and published by Springer Science & Business Media. This book was released on 2008-06-11 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set LNCS 5101-5103 constitutes the refereed proceedings of the 8th International Conference on Computational Science, ICCS 2008, held in Krakow, Poland in June 2008. The 167 revised papers of the main conference track presented together with the abstracts of 7 keynote talks and the 100 revised papers from 14 workshops were carefully reviewed and selected for inclusion in the three volumes. The main conference track was divided into approximately 20 parallel sessions addressing topics such as e-science applications and systems, scheduling and load balancing, software services and tools, new hardware and its applications, computer networks, simulation of complex systems, image processing and visualization, optimization techniques, numerical linear algebra, and numerical algorithms. The second volume contains workshop papers related to various computational research areas, e.g.: computer graphics and geometric modeling, simulation of multiphysics multiscale systems, computational chemistry and its applications, computational finance and business intelligence, physical, biological and social networks, geocomputation, and teaching computational science. The third volume is mostly related to computer science topics such as bioinformatics' challenges to computer science, tools for program development and analysis in computational science, software engineering for large-scale computing, collaborative and cooperative environments, applications of workflows in computational science, as well as intelligent agents and evolvable systems.

Measure and Integration

Author : Heinz König
Publisher : Springer Science & Business Media
ISBN 13 : 3540618589
Total Pages : 277 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Measure and Integration by : Heinz König

Download or read book Measure and Integration written by Heinz König and published by Springer Science & Business Media. This book was released on 1997 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents and elementary integrals. It develops the new approach started around 1970 by Topsoe and others into a systematic theory. The theory is much more powerful than the traditional means and has striking implications all over measure theory and beyond.

Measure, Integral and Probability

Author : Marek Capinski
Publisher : Springer Science & Business Media
ISBN 13 : 1447136314
Total Pages : 229 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Measure, Integral and Probability by : Marek Capinski

Download or read book Measure, Integral and Probability written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Optimization Based Data Mining: Theory and Applications

Author : Yong Shi
Publisher : Springer Science & Business Media
ISBN 13 : 0857295047
Total Pages : 316 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis Optimization Based Data Mining: Theory and Applications by : Yong Shi

Download or read book Optimization Based Data Mining: Theory and Applications written by Yong Shi and published by Springer Science & Business Media. This book was released on 2011-05-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization techniques have been widely adopted to implement various data mining algorithms. In addition to well-known Support Vector Machines (SVMs) (which are based on quadratic programming), different versions of Multiple Criteria Programming (MCP) have been extensively used in data separations. Since optimization based data mining methods differ from statistics, decision tree induction, and neural networks, their theoretical inspiration has attracted many researchers who are interested in algorithm development of data mining. Optimization based Data Mining: Theory and Applications, mainly focuses on MCP and SVM especially their recent theoretical progress and real-life applications in various fields. These include finance, web services, bio-informatics and petroleum engineering, which has triggered the interest of practitioners who look for new methods to improve the results of data mining for knowledge discovery. Most of the material in this book is directly from the research and application activities that the authors’ research group has conducted over the last ten years. Aimed at practitioners and graduates who have a fundamental knowledge in data mining, it demonstrates the basic concepts and foundations on how to use optimization techniques to deal with data mining problems.

Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators

Author : George A. Anastassiou
Publisher : Springer
ISBN 13 : 3030042871
Total Pages : 347 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators by : George A. Anastassiou

Download or read book Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators written by George A. Anastassiou and published by Springer. This book was released on 2018-12-07 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.

Theory of Random Sets

Author : Ilya Molchanov
Publisher : Springer Science & Business Media
ISBN 13 : 9781852338923
Total Pages : 508 pages
Book Rating : 4.3/5 (389 download)

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Book Synopsis Theory of Random Sets by : Ilya Molchanov

Download or read book Theory of Random Sets written by Ilya Molchanov and published by Springer Science & Business Media. This book was released on 2005-05-11 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine

Integrated Uncertainty Management and Applications

Author : Van-Nam Huynh
Publisher : Springer Science & Business Media
ISBN 13 : 3642119603
Total Pages : 560 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Integrated Uncertainty Management and Applications by : Van-Nam Huynh

Download or read book Integrated Uncertainty Management and Applications written by Van-Nam Huynh and published by Springer Science & Business Media. This book was released on 2010-03-26 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving practical problems often requires the integration of information and knowledge from many different sources, taking into account uncertainty and impreciseness. The 2010 International Symposium on Integrated Uncertainty Management and Applications (IUM’2010), which takes place at the Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan, between 9th–11th April, is therefore conceived as a forum for the discussion and exchange of research results, ideas for and experience of application among researchers and practitioners involved with all aspects of uncertainty modelling and management.

Nonlinear Integrals and Their Applications in Data Mining

Author :
Publisher :
ISBN 13 : 9814470988
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Integrals and Their Applications in Data Mining by :

Download or read book Nonlinear Integrals and Their Applications in Data Mining written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measure, Integration & Real Analysis

Author : Sheldon Axler
Publisher : Springer Nature
ISBN 13 : 3030331431
Total Pages : 430 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Measure, Integration & Real Analysis by : Sheldon Axler

Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Measure theory and Integration

Author : G De Barra
Publisher : Elsevier
ISBN 13 : 0857099523
Total Pages : 240 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Measure theory and Integration by : G De Barra

Download or read book Measure theory and Integration written by G De Barra and published by Elsevier. This book was released on 2003-07-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text approaches integration via measure theory as opposed to measure theory via integration, an approach which makes it easier to grasp the subject. Apart from its central importance to pure mathematics, the material is also relevant to applied mathematics and probability, with proof of the mathematics set out clearly and in considerable detail. Numerous worked examples necessary for teaching and learning at undergraduate level constitute a strong feature of the book, and after studying statements of results of the theorems, students should be able to attempt the 300 problem exercises which test comprehension and for which detailed solutions are provided. Approaches integration via measure theory, as opposed to measure theory via integration, making it easier to understand the subject Includes numerous worked examples necessary for teaching and learning at undergraduate level Detailed solutions are provided for the 300 problem exercises which test comprehension of the theorems provided

Modeling Decisions for Artificial Intelligence

Author : Vincenc Torra
Publisher : Springer
ISBN 13 : 3642415504
Total Pages : 309 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Modeling Decisions for Artificial Intelligence by : Vincenc Torra

Download or read book Modeling Decisions for Artificial Intelligence written by Vincenc Torra and published by Springer. This book was released on 2014-07-08 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 10th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2013, held in Barcelona, Spain, in November 2013. The 24 papers presented in this volume were carefully reviewed and selected from 40 submissions. They deal with the theory and tools for modeling decisions, as well as applications that encompass decision making processes and information fusion techniques.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author : Melvin Fitting
Publisher : Physica
ISBN 13 : 3790817694
Total Pages : 374 pages
Book Rating : 4.7/5 (98 download)

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Book Synopsis Beyond Two: Theory and Applications of Multiple-Valued Logic by : Melvin Fitting

Download or read book Beyond Two: Theory and Applications of Multiple-Valued Logic written by Melvin Fitting and published by Physica. This book was released on 2013-06-05 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

Encyclopaedia of Mathematics, Supplement III

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Artificial Intelligence: Theory and Applications

Author : Endre Pap
Publisher : Springer Nature
ISBN 13 : 3030727114
Total Pages : 353 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Artificial Intelligence: Theory and Applications by : Endre Pap

Download or read book Artificial Intelligence: Theory and Applications written by Endre Pap and published by Springer Nature. This book was released on 2021-07-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an up-to-date collection, in AI and environmental research, related to the project ATLAS. AI is used for gaining an understanding of complex research phenomena in the environmental sciences, encompassing heterogeneous, noisy, inaccurate, uncertain, diverse spatio-temporal data and processes. The first part of the book covers new mathematics in the field of AI: aggregation functions with special classes such as triangular norms and copulas, pseudo-analysis, and the introduction to fuzzy systems and decision making. Generalizations of the Choquet integral with applications in decision making as CPT are presented. The second part of the book is devoted to AI in the geo-referenced air pollutants and meteorological data, image processing, machine learning, neural networks, swarm intelligence, robotics, mental well-being and data entry errors. The book is intended for researchers in AI and experts in environmental sciences as well as for Ph.D. students.