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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. Key Features: * 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.
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