Discrete Fuzzy Measures

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Discrete Fuzzy Measures

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Author : Gleb Beliakov
language : en
Publisher: Springer
Release Date : 2019-03-19

Discrete Fuzzy Measures written by Gleb Beliakov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Computers categories.

This book addresses computer scientists, IT specialists, mathematicians, knowledge engineers and programmers, who are engaged in research and practice of multicriteria decision making. Fuzzy measures, also known as capacities, allow one to combine degrees of preferences, support or fuzzy memberships into one representative value, taking into account interactions between the inputs. The notions of mutual reinforcement or redundancy are modeled explicitly through coefficients of fuzzy measures, and fuzzy integrals, such as the Choquet and Sugeno integrals combine the inputs. Building on previous monographs published by the authors and dealing with different aspects of aggregation, this book especially focuses on the Choquet and Sugeno integrals. It presents a number of new findings concerning computation of fuzzy measures, learning them from data and modeling interactions. The book does not require substantial mathematical background, as all the relevant notions are explained. It is intended as concise, timely and self-contained guide to the use of fuzzy measures in the field of multicriteria decision making.

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Author :
language : en
Publisher: Arihant Publications India limited
Release Date :

written by and has been published by Arihant Publications India limited this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Generalized Measure Theory

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Author : Wang Zhenyuan
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-27

Generalized Measure Theory written by Wang Zhenyuan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-27 with Mathematics categories.

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.

Non Additive Measures

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Author : Vicenc Torra
language : en
Publisher: Springer
Release Date : 2013-10-23

Non Additive Measures written by Vicenc Torra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-23 with Technology & Engineering categories.

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.

Methodologies For The Conception Design And Application Of Intelligent Systems Proceedings Of The 4th International Conference On Soft Computing In 2 Volumes

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Author : Gen Matsumoto
language : en
Publisher: World Scientific
Release Date : 1996-08-31

Methodologies For The Conception Design And Application Of Intelligent Systems Proceedings Of The 4th International Conference On Soft Computing In 2 Volumes written by Gen Matsumoto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-31 with categories.

IIZUKA '96, the 4th International Conference on Soft Computing, emphasized the integration of the components of soft computing to promote the research work on post-digital computers and to realize the intelligent systems. At the conference, new developments and results in soft computing were introduced and discussed by researchers from academic, governmental, and industrial institutions.This volume presents the opening lectures by Prof. Lotfi A. Zadeh and Prof. Walter J. Freeman, the plenary lectures by seven eminent researchers, and about 200 carefully selected papers drawn from more than 20 countries. It documents current research and in-depth studies on the conception, design, and application of intelligent systems.

Fuzzy Measures And Integrals

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Author : Michel Grabisch
language : en
Publisher: Physica
Release Date : 2000-01-24

Fuzzy Measures And Integrals written by Michel Grabisch and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-24 with Business & Economics categories.

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.

A Practical Guide To Averaging Functions

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Author : Gleb Beliakov
language : en
Publisher: Springer
Release Date : 2015-10-15

A Practical Guide To Averaging Functions written by Gleb Beliakov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-15 with Technology & Engineering categories.

This book offers an easy-to-use and practice-oriented reference guide to mathematical averages. It presents different ways of aggregating input values given on a numerical scale, and of choosing and/or constructing aggregating functions for specific applications. Building on a previous monograph by Beliakov et al. published by Springer in 2007, it outlines new aggregation methods developed in the interim, with a special focus on the topic of averaging aggregation functions. It examines recent advances in the field, such as aggregation on lattices, penalty-based aggregation and weakly monotone averaging, and extends many of the already existing methods, such as: ordered weighted averaging (OWA), fuzzy integrals and mixture functions. A substantial mathematical background is not called for, as all the relevant mathematical notions are explained here and reported on together with a wealth of graphical illustrations of distinct families of aggregation functions. The authors mainly focus on practical applications and give central importance to the conciseness of exposition, as well as the relevance and applicability of the reported methods, offering a valuable resource for computer scientists, IT specialists, mathematicians, system architects, knowledge engineers and programmers, as well as for anyone facing the issue of how to combine various inputs into a single output value.

Multiple Criteria Decision Analysis State Of The Art Surveys

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Author : Salvatore Greco
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-20

Multiple Criteria Decision Analysis State Of The Art Surveys written by Salvatore Greco and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-20 with Business & Economics categories.

Multiple Criteria Decision Analysis: State of the Art Surveys provides survey articles and references of the seminal or state-of-the-art research on MCDA. The material covered ranges from the foundations of MCDA, over various MCDA methodologies (outranking methods, multiattribute utility and value theories, non-classical approaches) to multiobjective mathematical programming, MCDA applications, and software. This vast amount of material is organized in 8 parts, with a total of 25 chapters. More than 2000 references are listed.

Neural Nets Wirn09

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Author : Bruno Apolloni
language : en
Publisher: IOS Press
Release Date : 2009

Neural Nets Wirn09 written by Bruno Apolloni and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.

This book reports the proceedings of WIRN09, the 19th Italian Workshop of the Italian Society for Neural Networks (SIREN). Neural networks explore thought mechanisms that efficient computational tools and a representative physics of our brain share together and that ultimately produce the loops of our thoughts. The general approach is to see how these loops run and which tracks they leave.

Multiple Criteria Decision Analysis

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Author : Salvatore Greco
language : en
Publisher: Springer
Release Date : 2016-02-18

Multiple Criteria Decision Analysis written by Salvatore Greco and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-18 with Business & Economics categories.

In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.