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.
by Charles Darwin
by Henry David Thoreau
by Andrew Reinhard
by Reinhard Scheer
by Reinhard W. Hoffmann
by Mark Twain
by Charles Dickens
by Frederick Douglass
by Alexis de Tocqueville
by Elizabeth Gaskell
by Carlo Collodi