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