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.
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.
Table of Contents
- Title Page
Part I: Fuzzy Information
- 1: Fuzzy data
- 2: Fuzzy numbers and fuzzy vectors
- 3: Mathematical operations for fuzzy quantities
Part II: Descriptive Statistics for Fuzzy Data
- 4: Fuzzy samples
- 5: Histograms for fuzzy data
- 6: Empirical distribution functions
- 7: Empirical correlation for fuzzy data
Part III: Foundations of Statistical Inference With Fuzzy Data
- 8: Fuzzy probability distributions
- 9: A law of large numbers
- 10: Combined fuzzy samples
Part IV: Classical Statistical Inference for Fuzzy Data
- 11: Generalized point estimators
- 12: Generalized confidence regions
- 13: Statistical tests for fuzzy data
Part V: Bayesian Inference and Fuzzy Information
- 14: Bayes' theorem and fuzzy information
- 15: Generalized Bayes' theorem
- 16: Bayesian confidence regions
- 17: Fuzzy predictive distributions
- 18: Bayesian decisions and fuzzy information
Part VI: Regression Analysis and Fuzzy Information
- 19: Classical regression analysis
- 20: Regression models and fuzzy data
- 21: Bayesian regression analysis
- 22: Bayesian regression analysis and fuzzy information
Part VII: Fuzzy time series
- 23: Mathematical concepts
- 24: Descriptive methods for fuzzy time series
- 25: More on fuzzy random variables and fuzzy random vectors
- 26: Stochastic methods in fuzzy time series analysis
Part VIII: Appendices
- A1: List of symbols and abbreviations
- A2: Solutions to the problems
- A3: Glossary
- A4: Related literature
- Title: Statistical Methods for Fuzzy Data
- Release date: March 2011
- Publisher(s): Wiley
- ISBN: 9780470699454