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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Part I

FUZZY INFORMATION

Fuzzy information is a special kind of information and information is an omnipresent word in our society. But in general there is no precise definition of information.

However, in the context of statistics which is connected to uncertainty, a possible definition of information is the following: Information is everything which has influence on the assessment of uncertainty by an analyst. This uncertainty can be of different types: data uncertainty, nondeterministic quantities, model uncertainty, and uncertainty of a priori information.

Measurement results and observational data are special forms of information. Such data are frequently not precise numbers but more or less nonprecise, also called fuzzy. Such data will be considered in the first chapter.

Another kind of information is probabilities. Standard probability theory is considering probabilities to be numbers. Often this is not realistic, and in a more general approach probabilities are considered to be so-called fuzzy numbers.

The idea of generalized sets was originally published in Menger (1951) and the term ‘fuzzy set’ was coined in Zadeh (1965).

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