Statistical Methods For Fuzzy Data

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Statistical Methods for Fuzzy Data

Reinhard Viertl
Statistical Methods for Fuzzy Data Book PDF

Author : Reinhard Viertl
Publisher : John Wiley & Sons
Page : 199 pages
File Size : 54,8 Mb
Release : 2011-01-25
Category : Mathematics
ISBN : 9780470974568

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Statistical Methods for Fuzzy Data by Reinhard Viertl Pdf

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

Hans Bandemer,Wolfgang Näther
Fuzzy Data Analysis Book PDF

Author : Hans Bandemer,Wolfgang Näther
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401125062

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Fuzzy Data Analysis by Hans Bandemer,Wolfgang Näther Pdf

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.

Fundamentals of Statistics with Fuzzy Data

Hung T. Nguyen,Berlin Wu
Fundamentals of Statistics with Fuzzy Data Book PDF

Author : Hung T. Nguyen,Berlin Wu
Publisher : Springer
Page : 196 pages
File Size : 52,6 Mb
Release : 2009-09-02
Category : Mathematics
ISBN : 3540819983

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Fundamentals of Statistics with Fuzzy Data by Hung T. Nguyen,Berlin Wu Pdf

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.

Fundamentals of Statistics with Fuzzy Data

Hung T. Nguyen,Berlin Wu
Fundamentals of Statistics with Fuzzy Data Book PDF

Author : Hung T. Nguyen,Berlin Wu
Publisher : Springer
Page : 0 pages
File Size : 42,5 Mb
Release : 2006-02-28
Category : Mathematics
ISBN : 9783540316978

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Fundamentals of Statistics with Fuzzy Data by Hung T. Nguyen,Berlin Wu Pdf

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.

Fuzzy Statistical Inferences Based on Fuzzy Random Variables

Gholamreza Hesamian
Fuzzy Statistical Inferences Based on Fuzzy Random Variables Book PDF

Author : Gholamreza Hesamian
Publisher : CRC Press
Page : 313 pages
File Size : 52,8 Mb
Release : 2022-02-24
Category : Mathematics
ISBN : 9781000539776

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Fuzzy Statistical Inferences Based on Fuzzy Random Variables by Gholamreza Hesamian Pdf

This book presents the most commonly used techniques for the most statistical inferences based on fuzzy data. It brings together many of the main ideas used in statistical inferences in one place, based on fuzzy information including fuzzy data. This book covers a much wider range of topics than a typical introductory text on fuzzy statistics. It includes common topics like elementary probability, descriptive statistics, hypothesis tests, one-way ANOVA, control-charts, reliability systems and regression models. The reader is assumed to know calculus and a little fuzzy set theory. The conventional knowledge of probability and statistics is required. Key Features: Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data. The book is suitable for students and researchers in statistics, social science, engineering, and economics, and it can be used at graduate and P.h.D level.

The Signed Distance Measure in Fuzzy Statistical Analysis

Rédina Berkachy
The Signed Distance Measure in Fuzzy Statistical Analysis Book PDF

Author : Rédina Berkachy
Publisher : Springer Nature
Page : 356 pages
File Size : 51,7 Mb
Release : 2021-10-31
Category : Computers
ISBN : 9783030769161

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The Signed Distance Measure in Fuzzy Statistical Analysis by Rédina Berkachy Pdf

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 Modeling, Analysis and Management of Fuzzy Data

Carlo Bertoluzza,Maria A. Gil,Dan A. Ralescu
Statistical Modeling Analysis and Management of Fuzzy Data Book PDF

Author : Carlo Bertoluzza,Maria A. Gil,Dan A. Ralescu
Publisher : Physica
Page : 315 pages
File Size : 43,6 Mb
Release : 2012-11-02
Category : Computers
ISBN : 9783790818000

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Statistical Modeling, Analysis and Management of Fuzzy Data by Carlo Bertoluzza,Maria A. Gil,Dan A. Ralescu Pdf

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.

Combining Soft Computing and Statistical Methods in Data Analysis

Christian Borgelt,Gil González Rodríguez,Wolfgang Trutschnig,María Asunción Lubiano,María Angeles Gil,Przemyslaw Grzegorzewski,Olgierd Hryniewicz
Combining Soft Computing and Statistical Methods in Data Analysis Book PDF

Author : Christian Borgelt,Gil González Rodríguez,Wolfgang Trutschnig,María Asunción Lubiano,María Angeles Gil,Przemyslaw Grzegorzewski,Olgierd Hryniewicz
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 42,9 Mb
Release : 2010-10-12
Category : Technology & Engineering
ISBN : 9783642147463

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Combining Soft Computing and Statistical Methods in Data Analysis by Christian Borgelt,Gil González Rodríguez,Wolfgang Trutschnig,María Asunción Lubiano,María Angeles Gil,Przemyslaw Grzegorzewski,Olgierd Hryniewicz Pdf

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.

Fuzzy Data Analysis

Hans Bandemer,Wolfgang Nather
Fuzzy Data Analysis Book PDF

Author : Hans Bandemer,Wolfgang Nather
Publisher : Unknown
Page : 360 pages
File Size : 45,9 Mb
Release : 1992-06-30
Category : Electronic
ISBN : 9401125074

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Fuzzy Data Analysis by Hans Bandemer,Wolfgang Nather Pdf

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.

Statistical Methods for QTL Mapping

Zehua Chen
Statistical Methods for QTL Mapping Book PDF

Author : Zehua Chen
Publisher : CRC Press
Page : 944 pages
File Size : 52,9 Mb
Release : 2013-11-01
Category : Mathematics
ISBN : 9780415669863

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Statistical Methods for QTL Mapping by Zehua Chen Pdf

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.

Fuzzy Statistics

James J. Buckley
Fuzzy Statistics Book PDF

Author : James J. Buckley
Publisher : Springer
Page : 166 pages
File Size : 55,6 Mb
Release : 2013-11-11
Category : Technology & Engineering
ISBN : 9783540399193

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Fuzzy Statistics by James J. Buckley Pdf

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 Survival Data Analysis

Elisa T. Lee,John Wenyu Wang
Statistical Methods for Survival Data Analysis Book PDF

Author : Elisa T. Lee,John Wenyu Wang
Publisher : John Wiley & Sons
Page : 389 pages
File Size : 41,5 Mb
Release : 2013-09-23
Category : Mathematics
ISBN : 9781118593059

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Statistical Methods for Survival Data Analysis by Elisa T. Lee,John Wenyu Wang Pdf

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.

Granular, Fuzzy, and Soft Computing

Tsau-Young Lin,Churn-Jung Liau,Janusz Kacprzyk
Granular Fuzzy and Soft Computing Book PDF

Author : Tsau-Young Lin,Churn-Jung Liau,Janusz Kacprzyk
Publisher : Springer Nature
Page : 936 pages
File Size : 53,9 Mb
Release : 2023-03-29
Category : Mathematics
ISBN : 9781071626283

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Granular, Fuzzy, and Soft Computing by Tsau-Young Lin,Churn-Jung Liau,Janusz Kacprzyk Pdf

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.

Fuzzy Statistical Decision-Making

Cengiz Kahraman,Özgür Kabak
Fuzzy Statistical Decision Making Book PDF

Author : Cengiz Kahraman,Özgür Kabak
Publisher : Springer
Page : 356 pages
File Size : 40,6 Mb
Release : 2016-07-15
Category : Technology & Engineering
ISBN : 9783319390147

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Fuzzy Statistical Decision-Making by Cengiz Kahraman,Özgür Kabak Pdf

This book offers a comprehensive reference guide to fuzzy statistics and fuzzy decision-making techniques. It provides readers with all the necessary tools for making statistical inference in the case of incomplete information or insufficient data, where classical statistics cannot be applied. The respective chapters, written by prominent researchers, explain a wealth of both basic and advanced concepts including: fuzzy probability distributions, fuzzy frequency distributions, fuzzy Bayesian inference, fuzzy mean, mode and median, fuzzy dispersion, fuzzy p-value, and many others. To foster a better understanding, all the chapters include relevant numerical examples or case studies. Taken together, they form an excellent reference guide for researchers, lecturers and postgraduate students pursuing research on fuzzy statistics. Moreover, by extending all the main aspects of classical statistical decision-making to its fuzzy counterpart, the book presents a dynamic snapshot of the field that is expected to stimulate new directions, ideas and developments.

Statistics with Vague Data

Rudolf Kruse,Klaus Dieter Meyer
Statistics with Vague Data Book PDF

Author : Rudolf Kruse,Klaus Dieter Meyer
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400939431

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Statistics with Vague Data by Rudolf Kruse,Klaus Dieter Meyer Pdf

This monograph is an attempt to unify existing works in the field of random sets, random variables, and linguistic random variables with respect to statistical analysis. It is intended to be a tutorial research compendium. The material of the work is mainly based on the postdoctoral thesis (Ha bilitationsschrift) of the first author and on several papers recently published by both authors. The methods form the basis of a user-friendly software tool which supports the statistical inferenee in the presence of vague data. Parts of the manuscript have been used in courses for graduate level students of mathematics and eomputer scienees held by the first author at the Technical University of Braunschweig. The textbook is designed for readers with an advanced knowledge of mathematics. The idea of writing this book came from Professor Dr. H. Skala. Several of our students have significantly contributed to its preparation. We would like to express our gratitude to Reinhard Elsner for his support in typesetting the book, Jorg Gebhardt and Jorg Knop for preparing the drawings, Michael Eike and Jiirgen Freckmann for implementing the programming system and Giinter Lehmann and Winfried Boer for proofreading the manuscript. This work was partially supported by the Fraunhofer-Gesellschaft. We are indebted to D. Reidel Publishing Company for making the pub lication of this book possible and would especially like to acknowledge the support whieh we received from our families on this project.