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Description and analysis of fuzzy information. Statistical methods for fuzzy data. (Beschreibung und Analyse unscharfer Information. Statistische Methoden für unscharfe Daten.) (German) Zbl 1101.62003
Wien: Springer (ISBN 3-211-23877-8/pbk). xvi, 129 p. (2006).
This small book presents an introduction into the description and analysis of fuzzy data. Quality and imprecision of data are discussed and methods for modelling imprecise data by fuzzy numbers are proposed. The fuzziness of the data is transferred into fuzziness of the decisions, e.g., into fuzzy point estimation, fuzzy confidence intervals and fuzzy tests. The reader should be familiar with elementary classical stochastic models and statistical procedures. A number of exercises enables the reader to train the practical use of the methods.
Contents: 1. Uncertainty and information. 1.1 Fuzzy information and fuzzy data. 1.2 Stochastics and Fuzziness.
2. Mathematical description of fuzziness. 2.1 Basics in mathematics. 2.1 Fuzzy numbers. 2.3 Fuzzy vectors. 2.4 Combination of fuzzy observations. 2.5 Functions of fuzzy variables. 2.6 Fuzzy functions. 2.7 Fuzzy probability distributions.
3. Descriptive statistics with fuzzy data. 3.1 Histograms for fuzzy data. 3.2 Empirical distribution functions for fuzzy data. 3.3 Emprical quantiles with fuzzy data. 3.4 Extreme values of fuzzy observations.
4. Statistical inference with fuzzy data. 4.1 Sample functions with fuzzy data. 4.2 Estimation of parameters. 4.3 Fuzzy confidence regions for parameters. 4.4 Statistical tests with fuzzy data.
5. Bayesian analysis with fuzzy information. 5.1 Basics in Bayesian statistics. 5.2 Fuzzy prior distributions. 5.3 Generalized Bayes theorem. 5.4 Fuzzy predictive densities. 5.5 Bayesian decisions based on fuzzy information.
Solutions of exercises. References. Index.

MSC:
62-07 Data analysis (statistics) (MSC2010)
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
03E72 Theory of fuzzy sets, etc.
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