Fuzzy Statistics
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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.
Statistical Methods For Fuzzy Data
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Author : Reinhard Viertl
language : en
Publisher: John Wiley & Sons
Release Date : 2011-01-25
Statistical Methods For Fuzzy Data written by Reinhard Viertl 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 2011-01-25 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.
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.
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.
Fundamentals Of Statistics With Fuzzy Data
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Author : Hung T. Nguyen
language : en
Publisher: Studies in Fuzziness and Soft Computing
Release Date : 2006-03-20
Fundamentals Of Statistics With Fuzzy Data written by Hung T. Nguyen and has been published by Studies in Fuzziness and Soft Computing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-20 with Computers categories.
This book presents basic aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The book aims at motivating statisticians to examine fuzzy statistics to enlarge the domain of applicability of statistics in general.
Asymptotics In Statistics And Probability
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Author : Madan L. Puri
language : en
Publisher: VSP
Release Date : 2000-01-01
Asymptotics In Statistics And Probability written by Madan L. Puri and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Performance Measurement With Fuzzy Data Envelopment Analysis
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Author : Ali Emrouznejad
language : en
Publisher: Springer
Release Date : 2013-11-29
Performance Measurement With Fuzzy Data Envelopment Analysis written by Ali Emrouznejad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Technology & Engineering categories.
The intensity of global competition and ever-increasing economic uncertainties has led organizations to search for more efficient and effective ways to manage their business operations. Data envelopment analysis (DEA) has been widely used as a conceptually simple yet powerful tool for evaluating organizational productivity and performance. Fuzzy DEA (FDEA) is a promising extension of the conventional DEA proposed for dealing with imprecise and ambiguous data in performance measurement problems. This book is the first volume in the literature to present the state-of-the-art developments and applications of FDEA. It is designed for students, educators, researchers, consultants and practicing managers in business, industry, and government with a basic understanding of the DEA and fuzzy logic concepts.
The Signed Distance Measure In Fuzzy Statistical Analysis
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Author : Rédina Berkachy
language : en
Publisher: Springer Nature
Release Date : 2021-10-31
The Signed Distance Measure In Fuzzy Statistical Analysis written by Rédina Berkachy and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-31 with Computers categories.
The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called “FuzzySTs” which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.
Synergies Of Soft Computing And Statistics For Intelligent Data Analysis
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Author : Rudolf Kruse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-13
Synergies Of Soft Computing And Statistics For Intelligent Data Analysis written by Rudolf Kruse 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 2012-09-13 with Technology & Engineering categories.
In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.
Fuzzy Set Social Science
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Author : Charles C. Ragin
language : en
Publisher: University of Chicago Press
Release Date : 2000-08
Fuzzy Set Social Science written by Charles C. Ragin and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08 with Mathematics categories.
In this innovative approach to the practice of social scienceÇharles Ragin explores the use of fuzzy sets to bridge the divide between quantitive and qualitative methods. He argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible.