Discrete Fuzzy Measures

Author : Gleb Beliakov,Simon James,Jian-Zhang Wu
Publisher : Springer
Page : 245 pages
File Size : 55,5 Mb
Release : 2019-03-19
Category : Technology & Engineering
ISBN : 9783030153052

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Discrete Fuzzy Measures by Gleb Beliakov,Simon James,Jian-Zhang Wu Pdf

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.

Author : Adrian I. Ban
Publisher : Nova Publishers
Page : 280 pages
File Size : 47,7 Mb
Release : 2006
Category : Mathematics
ISBN : 1594549117

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Intuitionistic Fuzzy Measures by Adrian I. Ban Pdf

This book is the outcome of about eight years of work performed by the author largely in the field of intuitionistic fuzzy set theory and more in depth on intuitionistic fuzzy measures presented from a point of view characteristic for pure mathematics. The purpose of the book is to present a continuation of studies conducted focusing mainly on measures that evaluate intuitionistic fuzzy sets by real values and crisp sets by intuitionistic fuzzy values.

Author : Zhenyuan Wang,George J. Klir
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 42,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475753035

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Fuzzy Measure Theory by Zhenyuan Wang,George J. Klir Pdf

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 : Matsumoto Gen,Yamakawa Takeshi
Publisher : World Scientific
Page : 1064 pages
File Size : 47,7 Mb
Release : 1996-08-31
Category : Electronic
ISBN : 9789814740784

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Methodologies For The Conception, Design, And Application Of Intelligent Systems - Proceedings Of The 4th International Conference On Soft Computing (In 2 Volumes) by Matsumoto Gen,Yamakawa Takeshi Pdf

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.

Author : Anonim
Publisher : Arihant Publications India limited
Page : 1199 pages
File Size : 48,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789326194969

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by Anonim Pdf

Author : Zhenyuan Wang,George Klir
Publisher : Unknown
Page : 368 pages
File Size : 44,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475753047

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Fuzzy Measure Theory by Zhenyuan Wang,George Klir Pdf

Author : Dan E. Tamir,Naphtali D. Rishe,Abraham Kandel
Publisher : Springer
Page : 684 pages
File Size : 43,6 Mb
Release : 2015-05-23
Category : Technology & Engineering
ISBN : 9783319196831

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Fifty Years of Fuzzy Logic and its Applications by Dan E. Tamir,Naphtali D. Rishe,Abraham Kandel Pdf

This book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh’s seminal paper on “fuzzy sets,” published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh’s paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years’ anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments of Fuzzy Logic-based systems.

Author : Zhenyuan Wang,Kwong Sak Leung,Rong Yang
Publisher : World Scientific
Page : 359 pages
File Size : 54,5 Mb
Release : 2010
Category : Computers
ISBN : 9789812814685

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Nonlinear Integrals and Their Applications in Data Mining by Zhenyuan Wang,Kwong Sak Leung,Rong Yang Pdf

Ch. 1. Introduction -- ch. 2. Basic knowledge on classical sets. 2.1. Classical sets and set inclusion. 2.2. Set operations. 2.3. Set sequences and set classes. 2.4. Set classes closed under set operations. 2.5. Relations, posets, and lattices. 2.6. The supremum and infimum of real number sets -- ch. 3. Fuzzy sets. 3.1. The membership functions of fuzzy sets. 3.2. Inclusion and operations of fuzzy sets. 3.3. [symbol]-cuts. 3.4. Convex fuzzy sets. 3.5. Decomposition theorems. 3.6. The extension principle. 3.7. Interval numbers. 3.8. Fuzzy numbers and linguistic attribute. 3.9. Binary operations for fuzzy numbers. 3.10. Fuzzy integers -- ch. 4. Set functions. 4.1. Weights and classical measures. 4.2. Extension of measures. 4.3. Monotone measures. 4.4. [symbol]-measures. 4.5. Quasi-measures. 4.6. Mobius and zeta transformations. 4.7. Belief measures and plausibility measures. 4.8. Necessity measures and possibility measures. 4.9. k-interactive measures. 4.10. Efficiency measures and signed efficiency measures -- ch. 5. Integrations. 5.1. Measurable functions. 5.2. The Riemann integral. 5.3. The Lebesgue-Like integral. 5.4. The Choquet integral. 5.5. Upper and lower integrals. 5.6. r-integrals on finite spaces -- ch. 6. Information fusion. 6.1. Information sources and observations. 6.2. Integrals used as aggregation tools. 6.3. Uncertainty associated with set functions. 6.4. The inverse problem of information fusion -- ch. 7. Optimization and soft computing. 7.1. Basic concepts of optimization. 7.2. Genetic algorithms. 7.3. Pseudo gradient search. 7.4. A hybrid search method -- ch. 8. Identification of set functions. 8.1. Identification of [symbol]-measures. 8.2. Identification of belief measures. 8.3. Identification of monotone measures. 8.4. Identification of signed efficiency measures by a genetic algorithm. 8.5. Identification of signed efficiency measures by the pseudo gradient. 8.6. Identification of signed efficiency measures based on the Choquet integral by an algebraic method. 8.7. Identification of monotone measures based on r-integrals by a genetic algorithm -- ch. 9. Multiregression based on nonlinear integrals. 9.1. Linear multiregression. 9.2. Nonlinear multiregression based on the Choquet integral. 9.3. A nonlinear multiregression model accommodating both categorical and numerical predictive attributes. 9.4. Advanced consideration on the multiregression involving nonlinear integrals -- ch. 10. Classifications based on nonlinear integrals. 10.1. Classification by an integral projection. 10.2. Nonlinear classification by weighted Choquet integrals. 10.3. An example of nonlinear classification in a three-dimensional sample space. 10.4. The uniqueness problem of the classification by the Choquet integral with a linear core. 10.5. Advanced consideration on the nonlinear classification involving the Choquet integral -- ch. 11. Data mining with fuzzy data. 11.1. Defuzzified Choquet Integral with Fuzzy-Valued Integrand (DCIFI). 11.2. Classification model based on the DCIFI. 11.3. Fuzzified Choquet Integral with Fuzzy-Valued Integrand (FCIFI). 11.4. Regression model based on the CIII

Author : Gia Sirbiladze
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 46,8 Mb
Release : 2012-09-25
Category : Science
ISBN : 9781461442509

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Extremal Fuzzy Dynamic Systems by Gia Sirbiladze Pdf

In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems. It begins with a thorough introduction, where the general research domain, the problems, and ways of their solutions are discussed. The book then progresses systematically by first covering the theoretical aspects before tackling the applications. In the application section, a software library is described, which contains discrete EFDS identification methods elaborated during fundamental research of the book. Extremal Fuzzy Dynamic Systems will be of interest to theoreticians interested in modeling fuzzy processes, to researchers who use fuzzy statistics, as well as practitioners from different disciplines whose research interests include abnormal, extreme and monotone processes in nature and society. Graduate students could also find this book useful.

Author : Gleb Beliakov,Humberto Bustince Sola,Tomasa Calvo
Publisher : Springer
Page : 352 pages
File Size : 52,9 Mb
Release : 2015-10-15
Category : Technology & Engineering
ISBN : 9783319247533

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A Practical Guide to Averaging Functions by Gleb Beliakov,Humberto Bustince Sola,Tomasa Calvo Pdf

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.

Author : Salvatore Greco
Publisher : Springer Science & Business Media
Page : 1063 pages
File Size : 54,5 Mb
Release : 2006-01-20
Category : Business & Economics
ISBN : 9780387230818

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Multiple Criteria Decision Analysis: State of the Art Surveys by Salvatore Greco Pdf

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.

Author : Vicenc Torra,Yasuo Narukawa
Publisher : Springer
Page : 330 pages
File Size : 41,7 Mb
Release : 2004-07-16
Category : Computers
ISBN : 9783540277743

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Modeling Decisions for Artificial Intelligence by Vicenc Torra,Yasuo Narukawa Pdf

This book constitutes the refereed proceedings of the First International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2004, held in Barcelona, Spain in August 2004. The 26 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 53 submissions. The papers are devoted to topics like models for information fusion, aggregation operators, model selection, fuzzy integrals, fuzzy sets, fuzzy multisets, neural learning, rule-based classification systems, fuzzy association rules, algorithmic learning, diagnosis, text categorization, unsupervised aggregation, the Choquet integral, group decision making, preference relations, vague knowledge processing, etc.

Author : Vicenc Torra,Yasuo Narukawa,Michio Sugeno
Publisher : Springer
Page : 207 pages
File Size : 46,6 Mb
Release : 2013-10-23
Category : Technology & Engineering
ISBN : 9783319031552

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Non-Additive Measures by Vicenc Torra,Yasuo Narukawa,Michio Sugeno Pdf

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.

Author : Peter Sinc? k,J n Vas?c? k,Kaoru Hirota
Publisher : World Scientific
Page : 475 pages
File Size : 52,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9789812387516

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Machine Intelligence by Peter Sinc? k,J n Vas?c? k,Kaoru Hirota Pdf

This book brings together the contributions of leading researchers in the field of machine intelligence, covering areas such as fuzzy logic, neural networks, evolutionary computation and hybrid systems.There is wide coverage of the subject ? from simple tools, through industrial applications, to applications in high-level intelligent systems which are biologically motivated, such as humanoid robots (and selected parts of these systems, like the visual cortex). Readers will gain a comprehensive overview of the issues in machine intelligence, a field which promises to play a very important role in the information society of the future.

Author : Linda C. van der Gaag
Publisher : Springer
Page : 546 pages
File Size : 45,5 Mb
Release : 2013-07-04
Category : Computers
ISBN : 9783642390913

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Symbolic and Quantiative Approaches to Resoning with Uncertainty by Linda C. van der Gaag Pdf

This book constitutes the refereed proceedings of the 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2013, held in Utrecht, The Netherlands, in July 2013. The 44 revised full papers presented were carefully reviewed and selected from 89 submissions. Papers come from researchers interested in advancing the technology and from practitioners using uncertainty techniques in real-world applications. The scope of the ECSQARU conferences encompasses fundamental issues, representation, inference, learning, and decision making in qualitative and numeric uncertainty paradigms.