Non Additive Measures

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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 : 207 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 207 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.

Non-Additive Measures

Author : Vicenç Torra
Publisher :
ISBN 13 : 9783319031569
Total Pages : 212 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Non-Additive Measures by : Vicenç Torra

Download or read book Non-Additive Measures written by Vicenç Torra and published by . This book was released on 2013-11-30 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Additivations of Non-Additive Measures

Author : Itzhak Gilboa
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (636 download)

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Book Synopsis Additivations of Non-Additive Measures by : Itzhak Gilboa

Download or read book Additivations of Non-Additive Measures written by Itzhak Gilboa and published by . This book was released on 1985 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-additive Measures and Random Processes

Author :
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.:/5 (932 download)

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Book Synopsis Non-additive Measures and Random Processes by :

Download or read book Non-additive Measures and Random Processes written by and published by . This book was released on 2003 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

DAX Patterns

Author : Marco Russo
Publisher : SQLBI Corp.
ISBN 13 : 1735365211
Total Pages : 514 pages
Book Rating : 4.7/5 (353 download)

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Book Synopsis DAX Patterns by : Marco Russo

Download or read book DAX Patterns written by Marco Russo and published by SQLBI Corp.. This book was released on 2020-08-10 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pattern is a general, reusable solution to a frequent or common challenge. This book is the second edition of the most comprehensive collection of ready-to-use solutions in DAX, that you can use in Microsoft Power BI, Analysis Services Tabular, and Power Pivot for Excel. The book includes the following patterns: Time-related calculations, Standard time-related calculations, Month-related calculations, Week-related calculations, Custom time-related calculations, Comparing different time periods, Semi-additive calculations, Cumulative total, Parameter table, Static segmentation, Dynamic segmentation, ABC classification, New and returning customers, Related distinct count, Events in progress, Ranking, Hierarchies, Parent-child hierarchies, Like-for-like comparison, Transition matrix, Survey, Basket analysis, Currency conversion, Budget.

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.

Theory of Charges

Author : K.P.S. Bhaskara Rao
Publisher : Academic Press
ISBN 13 : 0080874282
Total Pages : 327 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Theory of Charges by : K.P.S. Bhaskara Rao

Download or read book Theory of Charges written by K.P.S. Bhaskara Rao and published by Academic Press. This book was released on 1983-05-10 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Charges

Advances in the Theory of Probabilistic and Fuzzy Data Scientific Methods with Applications

Author : József Dombi
Publisher : Springer Nature
ISBN 13 : 303051949X
Total Pages : 201 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Advances in the Theory of Probabilistic and Fuzzy Data Scientific Methods with Applications by : József Dombi

Download or read book Advances in the Theory of Probabilistic and Fuzzy Data Scientific Methods with Applications written by József Dombi and published by Springer Nature. This book was released on 2020-08-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the advanced soft computational and probabilistic methods that the authors have published over the past few years. It describes theoretical results and applications, and discusses how various uncertainty measures – probability, plausibility and belief measures – can be treated in a unified way. It also examines approximations of four notable probability distributions (Weibull, exponential, logistic and normal) using a unified probability distribution function, and presents a fuzzy arithmetic-based time series model that provides an easy-to-use forecasting technique. Lastly, it proposes flexible fuzzy numbers for Likert scale-based evaluations. Featuring methods that can be successfully applied in a variety of areas, including engineering, economics, biology and the medical sciences, the book offers useful guidelines for practitioners and researchers.

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.

Planning Based on Decision Theory

Author : Giacomo Della Riccia
Publisher : Springer
ISBN 13 : 3709125308
Total Pages : 170 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Planning Based on Decision Theory by : Giacomo Della Riccia

Download or read book Planning Based on Decision Theory written by Giacomo Della Riccia and published by Springer. This book was released on 2014-05-04 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Planning of actions based on decision theory is a hot topic for many disciplines. Seemingly unlimited computing power, networking, integration and collaboration have meanwhile attracted the attention of fields like Machine Learning, Operations Research, Management Science and Computer Science. Software agents of e-commerce, mediators of Information Retrieval Systems and Database based Information Systems are typical new application areas. Until now, planning methods were successfully applied in production, logistics, marketing, finance, management, and used in robots, software agents etc. It is the special feature of the book that planning is embedded into decision theory, and this will give the interested reader new perspectives to follow-up.

Additive Representations of Non-additive Measures and the Choquet Integral

Author : Itzhak Gilboa
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (266 download)

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Book Synopsis Additive Representations of Non-additive Measures and the Choquet Integral by : Itzhak Gilboa

Download or read book Additive Representations of Non-additive Measures and the Choquet Integral written by Itzhak Gilboa and published by . This book was released on 1992 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Additive and Nonadditive Measures of Entropy

Author : M. Behara
Publisher : New Age International
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Additive and Nonadditive Measures of Entropy by : M. Behara

Download or read book Additive and Nonadditive Measures of Entropy written by M. Behara and published by New Age International. This book was released on 1990 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Unified Theory Of Measures Of Entropy Is Presented In This Research Monograph. After Covering Basic Materials On The Shannon And The Renyi Entropies, Which Are Additive Measures And Their Characterizations, The Monograph Focusses On Nonadditive Measures Of Entropy. Novel Techniques For The Systematic Discovery Of All Possible Entropy Measures Are Described. Geometric Entropies, Such As Parabolic Entropy, Are Derived From Geometric Configurations.When Subjected To Axioms Of Information Measures, On The Other Hand, Algebraic And Transcendental Functions Give Rise To Algebraic And Transcendental Entropies Respectively. Characterizations Of The Nonadditive Entropies Are Given By The Method Of Functional Equations While Properties Of All Entropies Are Studied In Detail. The Application Of Entropy In Coding Theory Is Extended To Parametric Entropies, Both Additive And Nonadditive, Because Of Their Superior Sensitivity Over The Shannon Entropy, A Nonparametric Measure.

Vector Measures

Author : N. Dinculeanu
Publisher : Elsevier
ISBN 13 : 1483222659
Total Pages : 446 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Vector Measures by : N. Dinculeanu

Download or read book Vector Measures written by N. Dinculeanu and published by Elsevier. This book was released on 2014-07-21 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs in Pure and Applied Mathematics, Volume 95: Vector Measures focuses on the study of measures with values in a Banach space, including positive measures with finite or infinite values. This book is organized into three chapters. Chapter I covers classes of sets, set functions, variation and semi-variation of set functions, and extension of set functions from a certain class to a wider one. The integration of vector functions with respect to vector measures is reviewed in Chapter II. In Chapter III, the regular measures on a locally compact space and integral representation of the dominated operations on the space of continuous functions with compact carrier are described. This volume is intended for specialists, researchers, and students interested in vector measures.

The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence

Author : John Toland
Publisher : Springer Nature
ISBN 13 : 303034732X
Total Pages : 104 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence by : John Toland

Download or read book The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence written by John Toland and published by Springer Nature. This book was released on 2020-01-03 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,λ)* with Lq(X,L,λ), where 1/p+1/q=1, as long as 1 ≤ p∞. However, iL/isub∞/sub(X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures./ppThis book provides a reasonably elementary account of the representation theory of iL/isub∞/sub(X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in iL/isub∞/sub(X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given./ppWith a clear summary of prerequisites, and illustrated by examples including iL/isub∞/sub(bR/bsupn/sup) and the sequence space il/isub∞/sub, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.

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

Regular Non-Additive Multimeasures. Fundaments and Applications

Author : Alina Gavriluţ
Publisher : Springer Nature
ISBN 13 : 3031111001
Total Pages : 166 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Regular Non-Additive Multimeasures. Fundaments and Applications by : Alina Gavriluţ

Download or read book Regular Non-Additive Multimeasures. Fundaments and Applications written by Alina Gavriluţ and published by Springer Nature. This book was released on 2022-10-07 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to be an exhaustive study on regularity and other properties of continuity for different types of non-additive multimeasures and with respect to different types of topologies. The book is addressed to graduate and postgraduate students, teachers and all researchers in mathematics, but not only. Since the notions and results offered by this book are closely related to various notions of the theory of probability, this book will be useful to a wider category of readers, using multivalued analysis techniques in areas such as control theory and optimization, economic mathematics, game theory, decision theory, etc. Measure and integration theory developed during the early years of the 20th century is one of the most important contributions to modern mathematical analysis, with important applications in many fields. In the last years, many classical problems from measure theory have been treated in the non-additive case and also extended in the set-valued case. The property of regularity is involved in many results of mathematical analysis, due to its applications in probability theory, stochastic processes, optimal control problems, dynamical systems, Markov chains, potential theory etc.