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Statistical Methods for Fuzzy Data

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ISBN-10: 0470699450

ISBN-13: 9780470699454

Edition: 2010

Authors: Reinhard Viertl

List price: $72.50
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Description:

Fuzzy logic provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. This book explains the basics of fuzzy logic and the use of statistical methods for fuzzy data sets.
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Book details

List price: $72.50
Copyright year: 2010
Publisher: John Wiley & Sons, Limited
Publication date: 1/28/2011
Binding: Hardcover
Pages: 268
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.144
Language: English

Preface
Fuzzy Information
Fuzzy data
One-dimensional fuzzy data
Vector-valued fuzzy data
Fuzziness and variability
Fuzziness and errors
Problems
Fuzzy numbers and fuzzy vectors
Fuzzy numbers and characterizing functions
Vectors of fuzzy numbers and fuzzy vectors
Triangular norms
Problems
Mathematical operations for fuzzy quantities
Functions of fuzzy variables
Addition of fuzzy numbers
Multiplication of fuzzy numbers
Mean value of fuzzy numbers
Differences and quotients
Fuzzy valued functions
Problems
Descriptive Statistics for Fuzzy Data
Fuzzy samples
Minimum of fuzzy data
Maximum of fuzzy data
Cumulative sum for fuzzy data
Problems
Histograms for fuzzy data
Fuzzy frequency of a fixed class
Fuzzy frequency distributions
Axonometric diagram of the fuzzy histogram
Problems
Empirical distribution functions
Fuzzy valued empirical distribution function
Fuzzy empirical fractiles
Smoothed empirical distribution function
Problems
Empirical correlation for fuzzy data
Fuzzy empirical correlation coefficient
Problems
Foundations of Statistical Inference with Fuzzy Data
Fuzzy probability distributions
Fuzzy probability densities
Probabilities based on fuzzy probability densities
General fuzzy probability distributions
Problems
A law of large numbers
Fuzzy random variables
Fuzzy probability distributions induced by fuzzy random variables
Sequences of fuzzy random variables
Law of large numbers for fuzzy random variables
Problems
Combined fuzzy samples
Observation space and sample space
Combination of fuzzy samples
Statistics of fuzzy data
Problems
Classical Statistical Inference for Fuzzy Data
Generalized point estimators
Estimators based on fuzzy samples
Sample moments
Problems
Generalized confidence regions
Confidence functions
Fuzzy confidence regions
Problems
Statistical tests for fuzzy data
Test statistics and fuzzy data
Fuzzy p-values
Problems
Bayesian Inference and Fuzzy Information
Bayes' theorem and fuzzy information
Fuzzy a priori distributions
Updating fuzzy a priori distributions
Problems
Generalized Bayes' theorem
Likelihood function for fuzzy data
Bayes' theorem for fuzzy a priori distribution and fuzzy data
Problems
Bayesian confidence regions
Bayesian confidence regions based on fuzzy data
Fuzzy HPD-regions
Problems
Fuzzy predictive distributions
Discrete case
Discrete models with continuous parameter space
Continuous case
Problems
Bayesian decisions and fuzzy information
Bayesian decisions
Fuzzy utility
Discrete state space
Continuous state space
Problems
Regression Analysis and Fuzzy Information
Classical regression analysis
Regression models
Linear regression models with Gaussian dependent variables
General linear models
Nonidentical variances
Problems
Regression models and fuzzy data
Generalized estimators for linear regression models based on the extension principle
Generalized confidence regions for parameters
Prediction in fuzzy regression models
Problems
Bayesian regression analysis
Calculation of a posteriori distributions
Bayesian confidence regions
Probabilities of hypotheses
Predictive distributions
A posteriori Bayes estimators for regression parameters
Bayesian regression with Gaussian distributions
Problems
Bayesian regression analysis and fuzzy information
Fuzzy estimators of regression parameters
Generalized Bayesian confidence regions
Fuzzy predictive distributions
Problems
Fuzzy Time Series
Mathematical concepts
Support functions of fuzzy quantities
Distances of fuzzy quantities
Generalized Hukuhara difference
Descriptive methods for fuzzy time series
Moving averages
Filtering
Linear filtering
Nonlinear filters
Exponential smoothing
Components model
Model without seasonal component
Model with seasonal component
Difference filters
Generalized Holt-Winter method
Presentation in the frequency domain
More on fuzzy random variables and fuzzy random vectors
Basics
Expectation and variance of fuzzy random variables
Covariance and correlation
Further results
Stochastic methods in fuzzy time series analysis
Linear approximation and prediction
Remarks concerning Kalman filtering
Appendices
List of symbols and abbreviations
Solutions to the problems
Glossary
Related literature
References
Index