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Author: Carlo Bertoluzza Publisher: Physica ISBN: 3790818003 Category : Computers Languages : en Pages : 315
Book Description
The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories.
Author: Carlo Bertoluzza Publisher: Physica ISBN: 3790818003 Category : Computers Languages : en Pages : 315
Book Description
The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories.
Author: Reinhard Viertl Publisher: John Wiley & Sons ISBN: 0470974567 Category : Mathematics Languages : en Pages : 199
Book Description
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information. Key Features: Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data. Describes methods of increasing importance with applications in areas such as environmental statistics and social science. Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples. Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data. This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.
Author: Jonathan Lawry Publisher: Springer Science & Business Media ISBN: 3540347771 Category : Computers Languages : en Pages : 413
Book Description
The idea of soft computing emerged in the early 1990s from the fuzzy systems c- munity, and refers to an understanding that the uncertainty, imprecision and ig- rance present in a problem should be explicitly represented and possibly even - ploited rather than either eliminated or ignored in computations. For instance, Zadeh de?ned ‘Soft Computing’ as follows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologically inspired methods such as genetic algorithms. Here, however, we adopt a more straightforward de?nition consistent with the original concept. Hence, soft methods are understood as those uncertainty formalisms not part of mainstream s- tistics and probability theory which have typically been developed within the AI and decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory.
Author: Przemyslaw Grzegorzewski Publisher: Springer ISBN: 3030032019 Category : Technology & Engineering Languages : en Pages : 200
Book Description
This book discusses the problems of complexity in industrial data, including the problems of data sources, causes and types of data uncertainty, and methods of data preparation for further reasoning in engineering practice. Each data source has its own specificity, and a characteristic property of industrial data is its high degree of uncertainty. The book also explores a wide spectrum of soft modeling methods with illustrations pertaining to specific cases from diverse industrial processes. In soft modeling the physical nature of phenomena may not be known and may not be taken into consideration. Soft models usually employ simplified mathematical equations derived directly from the data obtained as observations or measurements of the given system. Although soft models may not explain the nature of the phenomenon or system under study, they usually point to its significant features or properties.
Author: Didier Dubois Publisher: Springer Science & Business Media ISBN: 3540850279 Category : Mathematics Languages : en Pages : 436
Book Description
Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.
Author: Claudio Sossai Publisher: Springer Science & Business Media ISBN: 3642029051 Category : Computers Languages : en Pages : 951
Book Description
These are the proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2009, held in Verona (Italy), July 1–3, 2009. The biennial ECSQARU conferences are a major forum for advances in the theory and practice of reasoning under uncertainty. The ?rst ECSQARU conf- ence was held in Marseille (1991), and since then it has been held in Granada (1993), Fribourg (1995), Bonn (1997), London (1999), Toulouse (2001), Aalborg (2003), Barcelona (2005) and Hammamet (2007). The 76 papers gathered in this volume were selected out of 118 submissions from 34 countries, after a rigorous review process. In addition, the conference included invited lectures by three outstanding researchers in the area: Isabelle Bloch (“Fuzzy and bipolar mathematical morphology, applications in spatial reasoning”), Petr Cintula (“From (deductive) fuzzy logic to (logic-based) fuzzy mathematics”),andDaniele Mundici(“Conditionalsandindependence inma- valued logics”). Twospecialsessionswerepresentedduringtheconference:“Conditioning,- dependence, inference” (organizedby Giulianella Coletti and BarbaraVantaggi) and “Mathematicalfuzzy logic” (organizedby Stefano Aguzzoli,Brunella Gerla, Llu´ ?s Godo, Vincenzo Marra, Franco Montagna) On the whole, the program of the conference provided a broad, rich and up-to-date perspective of the current high-level research in the area which is re?ected in the contents of this volume.
Author: Vassilis G. Kaburlasos Publisher: Springer Science & Business Media ISBN: 3540341706 Category : Computers Languages : en Pages : 245
Book Description
This research monograph proposes a unified, cross-fertilizing approach for knowledge-representation and modeling based on lattice theory. The emphasis is on clustering, classification, and regression applications. It presents novel tools and useful perspectives for effective pattern classification. The material is multi-disciplinary based on on-going research published in major scientific journals and conferences.
Author: Tsau-Young Lin Publisher: Springer Nature ISBN: 1071626280 Category : Mathematics Languages : en Pages : 936
Book Description
The first edition of the Encyclopedia of Complexity and Systems Science (ECSS, 2009) presented a comprehensive overview of granular computing (GrC) broadly divided into several categories: Granular computing from rough set theory, Granular Computing in Database Theory, Granular Computing in Social Networks, Granular Computing and Fuzzy Set Theory, Grid/Cloud Computing, as well as general issues in granular computing. In 2011, the formal theory of GrC was established, providing an adequate infrastructure to support revolutionary new approaches to computer/data science, including the challenges presented by so-called big data. For this volume of ECSS, Second Edition, many entries have been updated to capture these new developments, together with new chapters on such topics as data clustering, outliers in data mining, qualitative fuzzy sets, and information flow analysis for security applications. Granulations can be seen as a natural and ancient methodology deeply rooted in the human mind. Many daily "things" are routinely granulated into sub "things": The topography of earth is granulated into hills, plateaus, etc., space and time are granulated into infinitesimal granules, and a circle is granulated into polygons of infinitesimal sides. Such granules led to the invention of calculus, topology and non-standard analysis. Formalization of general granulation was difficult but, as shown in this volume, great progress has been made in combing discrete and continuous mathematics under one roof for a broad range of applications in data science.
Author: Sergei O. Kuznetsov Publisher: Springer ISBN: 3642218814 Category : Computers Languages : en Pages : 382
Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2011, held in Moscow, Russia in June 2011. The 49 revised full papers presented together with 5 invited and 2 tutorial papers were carefully reviewed and selected from a total of 83 submissions. The papers are organized in topical sections on rough sets and approximations, coverings and granules, fuzzy set models, fuzzy set applications, compound values, feature selection and reduction, clusters and concepts, rules and trees, image processing, and interactions and visualization.
Author: Carlo Bertoluzza
Author: Carlo Bertoluzza
Author: Reinhard Viertl
Author: Laurent, Anne
Author: Jonathan Lawry
Author: Przemyslaw Grzegorzewski
Author: Didier Dubois
Author: Claudio Sossai
Author: Vassilis G. Kaburlasos
Author: Tsau-Young Lin
Author: Sergei O. Kuznetsov