Statistical Methods For Fuzzy Data
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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 Data Analysis
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Author : Hans Bandemer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fuzzy Data Analysis written by Hans Bandemer 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.
Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.
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.
Combining Soft Computing And Statistical Methods In Data Analysis
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Author : Christian Borgelt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-12
Combining Soft Computing And Statistical Methods In Data Analysis written by Christian Borgelt 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 2010-10-12 with Technology & Engineering categories.
Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.
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.
Statistical Methods For Non Precise Data
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Author : Reinhard Viertl
language : en
Publisher: CRC Press
Release Date : 1995-11-29
Statistical Methods For Non Precise Data written by Reinhard Viertl and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-29 with Mathematics categories.
The formal description of non-precise data before their statistical analysis is, except for error models and interval arithmetic, a relatively young topic. Fuzziness is described in the theory of fuzzy sets but only a few papers on statistical inference for non-precise data exist. In many cases, for example when very small concentrations are being measured, it is necessary to describe the imprecision of data. Otherwise, the results of statistical analysis can be unrealistic and misleading. Fortunately, there is a straightforward technique for dealing with non-precise data. The technique - the generalized inference method - is explained in Statistical Methods for Non-Precise Data. Anyone who understands elementary statistical methods and simple stochastic models will be able to use this book to understand and work with non-precise data. The book includes explanations of how to cope with non-precise data in different practical situations, and makes an excellent graduate level text book for students, as well as a general reference for scientists and practitioners. Features
Statistical Methods And Applications From A Historical Perspective
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Author : Fabio Crescenzi
language : en
Publisher: Springer
Release Date : 2014-06-19
Statistical Methods And Applications From A Historical Perspective written by Fabio Crescenzi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-19 with Mathematics categories.
The book showcases a selection of peer-reviewed papers, the preliminary versions of which were presented at a conference held 11-13 June 2011 in Bologna and organized jointly by the Italian Statistical Society (SIS), the Institute national Institute of Statistics (ISTAT) and the Bank of Italy. The theme of the conference was "Statistics in the 150 years of the Unification of Italy." The celebration of the anniversary of Italian unification provided the opportunity to examine and discuss the methodological aspects and applications from a historical perspective and both from a national and international point of view. The critical discussion on the issues of the past has made it possible to focus on recent advances, considering the studies of socio-economic and demographic changes in European countries.
Statistical Methods For Qtl Mapping
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Author : Zehua Chen
language : en
Publisher: CRC Press
Release Date : 2013-11-01
Statistical Methods For Qtl Mapping written by Zehua Chen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-01 with Mathematics categories.
While numerous advanced statistical approaches have recently been developed for quantitative trait loci (QTL) mapping, the methods are scattered throughout the literature. Statistical Methods for QTL Mapping brings together many recent statistical techniques that address the data complexity of QTL mapping. After introducing basic genetics topics and statistical principles, the author discusses the principles of quantitative genetics, general statistical issues of QTL mapping, commonly used one-dimensional QTL mapping approaches, and multiple interval mapping methods. He then explains how to use a feature selection approach to tackle a QTL mapping problem with dense markers. The book also provides comprehensive coverage of Bayesian models and MCMC algorithms and describes methods for multi-trait QTL mapping and eQTL mapping, including meta-trait methods and multivariate sequential procedures. This book emphasizes the modern statistical methodology for QTL mapping as well as the statistical issues that arise during this process. It gives the necessary biological background for statisticians without training in genetics and, likewise, covers statistical thinking and principles for geneticists. Written primarily for geneticists and statisticians specializing in QTL mapping, the book can also be used as a supplement in graduate courses or for self-study by PhD students working on QTL mapping projects.
Statistical Methods For Survival Data Analysis
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Author : Elisa T. Lee
language : en
Publisher: John Wiley & Sons
Release Date : 2013-09-23
Statistical Methods For Survival Data Analysis written by Elisa T. Lee 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 2013-09-23 with Mathematics categories.
Praise for the Third Edition “. . . an easy-to read introduction to survival analysis which covers the major concepts and techniques of the subject.” —Statistics in Medical Research Updated and expanded to reflect the latest developments, Statistical Methods for Survival Data Analysis, Fourth Edition continues to deliver a comprehensive introduction to the most commonly-used methods for analyzing survival data. Authored by a uniquely well-qualified author team, the Fourth Edition is a critically acclaimed guide to statistical methods with applications in clinical trials, epidemiology, areas of business, and the social sciences. The book features many real-world examples to illustrate applications within these various fields, although special consideration is given to the study of survival data in biomedical sciences. Emphasizing the latest research and providing the most up-to-date information regarding software applications in the field, Statistical Methods for Survival Data Analysis, Fourth Edition also includes: Marginal and random effect models for analyzing correlated censored or uncensored data Multiple types of two-sample and K-sample comparison analysis Updated treatment of parametric methods for regression model fitting with a new focus on accelerated failure time models Expanded coverage of the Cox proportional hazards model Exercises at the end of each chapter to deepen knowledge of the presented material Statistical Methods for Survival Data Analysis is an ideal text for upper-undergraduate and graduate-level courses on survival data analysis. The book is also an excellent resource for biomedical investigators, statisticians, and epidemiologists, as well as researchers in every field in which the analysis of survival data plays a role.
Proceedings Of The Issek94 Workshop On Mathematical And Statistical Methods In Artificial Intelligence
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Author : G. Della Riccia
language : en
Publisher: Springer
Release Date : 2014-05-04
Proceedings Of The Issek94 Workshop On Mathematical And Statistical Methods In Artificial Intelligence written by G. Della Riccia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Computers categories.
In recent years it has become apparent that an important part of the theory of Artificial Intelligence is concerned with reasoning on the basis of uncertain, incomplete or inconsistent information. Classical logic and probability theory are only partially adequate for this, and a variety of other formalisms have been developed, some of the most important being fuzzy methods, possibility theory, belief function theory, non monotonic logics and modal logics. The aim of this workshop was to contribute to the elucidation of similarities and differences between the formalisms mentioned above.