Fuzzy Probability And Statistics
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Fuzzy Probabilities
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Author : James J. Buckley
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-11
Fuzzy Probabilities written by James J. Buckley 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 2005-03-11 with Mathematics categories.
In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.
Fuzzy Statistics
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Author : James J. Buckley
language : en
Publisher: Springer
Release Date : 2013-11-11
Fuzzy Statistics written by James J. Buckley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Technology & Engineering categories.
1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chapter 3 we construct a fuzzy estimator for the mean of a normal distribution assuming the variance is known. More details on fuzzy estimation are in Chapter 3 and then after Chapter 3, Chapters 4-11 can be read independently. Part three, Chapters 12- 20, are on fuzzy hypothesis testing. For example, in Chapter 12 we consider the test Ho : /1 = /10 verses HI : /1 f=- /10 where /1 is the mean of a normal distribution with known variance, but we use a fuzzy number (from Chapter 3) estimator of /1 in the test statistic. More details on fuzzy hypothesis testing are in Chapter 12 and then after Chapter 12 Chapters 13-20 may be read independently. Part four, Chapters 21-27, are on fuzzy regression and fuzzy prediction. We start with fuzzy correlation in Chapter 21. Simple linear regression is the topic in Chapters 22-24 and Chapters 25-27 concentrate on multiple linear regression. Part two (fuzzy estimation) is used in Chapters 22 and 25; and part 3 (fuzzy hypothesis testing) is employed in Chapters 24 and 27. Fuzzy prediction is contained in Chapters 23 and 26. A most important part of our models in fuzzy statistics is that we always start with a random sample producing crisp (non-fuzzy) data.
Fuzzy Probability And Statistics
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Author : James J. Buckley
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-21
Fuzzy Probability And Statistics written by James J. Buckley 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 2006-02-21 with Computers categories.
This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.
Statistical Methods For Fuzzy Data
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Author : Reinhard Viertl
language : en
Publisher: Wiley
Release Date : 2011-02-14
Statistical Methods For Fuzzy Data written by Reinhard Viertl and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-14 with Mathematics categories.
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.
A First Course In Fuzzy Logic
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Author : Hung T. Nguyen
language : en
Publisher: CRC Press
Release Date : 2005-10-06
A First Course In Fuzzy Logic written by Hung T. Nguyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-06 with Computers categories.
A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world a
Mathematics Of Fuzzy Sets
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Author : Ulrich Höhle
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematics Of Fuzzy Sets written by Ulrich Höhle 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 2012-12-06 with Mathematics categories.
Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.
Introduction To Pattern Recognition
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Author : Menahem Friedman
language : en
Publisher: World Scientific
Release Date : 1999
Introduction To Pattern Recognition written by Menahem Friedman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computers categories.
This book is an introduction to pattern recognition, meant for undergraduate and graduate students in computer science and related fields in science and technology. Most of the topics are accompanied by detailed algorithms and real world applications. In addition to statistical and structural approaches, novel topics such as fuzzy pattern recognition and pattern recognition via neural networks are also reviewed. Each topic is followed by several examples solved in detail. The only prerequisites for using this book are a one-semester course in discrete mathematics and a knowledge of the basic preliminaries of calculus, linear algebra and probability theory.
Fuzzy Logic With Engineering Applications
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Author : Timothy J. Ross
language : en
Publisher: John Wiley & Sons
Release Date : 2005-04-08
Fuzzy Logic With Engineering Applications written by Timothy J. Ross and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-08 with Technology & Engineering categories.
Fuzzy logic refers to a large subject dealing with a set of methods to characterize and quantify uncertainty in engineering systems that arise from ambiguity, imprecision, fuzziness, and lack of knowledge. Fuzzy logic is a reasoning system based on a foundation of fuzzy set theory, itself an extension of classical set theory, where set membership can be partial as opposed to all or none, as in the binary features of classical logic. Fuzzy logic is a relatively new discipline in which major advances have been made over the last decade or so with regard to theory and applications. Following on from the successful first edition, this fully updated new edition is therefore very timely and much anticipated. Concentration on the topics of fuzzy logic combined with an abundance of worked examples, chapter problems and commercial case studies is designed to help motivate a mainstream engineering audience, and the book is further strengthened by the inclusion of an online solutions manual as well as dedicated software codes. Senior undergraduate and postgraduate students in most engineering disciplines, academics and practicing engineers, plus some working in economics, control theory, operational research etc, will all find this a valuable addition to their bookshelves.
Introduction To Type 2 Fuzzy Logic Control
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Author : Jerry Mendel
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-16
Introduction To Type 2 Fuzzy Logic Control written by Jerry Mendel and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-16 with Technology & Engineering categories.
An introductory book that provides theoretical, practical, and application coverage of the emerging field of type-2 fuzzy logic control Until recently, little was known about type-2 fuzzy controllers due to the lack of basic calculation methods available for type-2 fuzzy sets and logic—and many different aspects of type-2 fuzzy control still needed to be investigated in order to advance this new and powerful technology. This self-contained reference covers everything readers need to know about the growing field. Written with an educational focus in mind, Introduction to Type-2 Fuzzy Logic Control: Theory and Applications uses a coherent structure and uniform mathematical notations to link chapters that are closely related, reflecting the book’s central themes: analysis and design of type-2 fuzzy control systems. The book includes worked examples, experiment and simulation results, and comprehensive reference materials. The book also offers downloadable computer programs from an associated website. Presented by world-class leaders in type-2 fuzzy logic control, Introduction to Type-2 Fuzzy Logic Control: Is useful for any technical person interested in learning type-2 fuzzy control theory and its applications Offers experiment and simulation results via downloadable computer programs Features type-2 fuzzy logic background chapters to make the book self-contained Provides an extensive literature survey on both fuzzy logic and related type-2 fuzzy control Introduction to Type-2 Fuzzy Logic Control is an easy-to-read reference book suitable for engineers, researchers, and graduate students who want to gain deep insight into type-2 fuzzy logic control.
Statistical Reasoning With Imprecise Probabilities
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Author : Peter Walley
language : en
Publisher: Springer
Release Date :
Statistical Reasoning With Imprecise Probabilities written by Peter Walley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
When I started writing this book, my mind was full of ignorance and uncertainty, particularly about how best to deal with ignorance and uncertainty. Much of the ignorance and uncertainty remains, now that the book is finished, but it is organized more coherently. I see that as progress. As the title indicates, the book is about methods of reasoning and statistical inference using imprecise probabilities. The methods are based on a behavioural interpretation of probability and principles of coherence. The idea for such a book originated in 1982, after I had written two long reports on the mathematics and elicitation of upper and lower probabilities. My experience in teaching and applying the existing theories of statistical inference had convinced me that each of them was inadequate. The Bayesian theory is inadequate, despite its great virtues of coherence, because it requires all probability assessments to be precise yet gives little guidance on how to make them. It seemed natural to investigate whether the Bayesian theory could be modified by admitting imprecise probabilities as models for partial ignorance. Is it possible to reconcile imprecision with coherence, vagueness with rationality? Fortunately the ans wer is yes! The basic ideas of the book appeared in the two technical reports (1981, 1982). The coherence principles for conditional probabilities and statistical models were worked out in New Zealand, in 1983.