O'Reilly logo

Statistical Methods for Fuzzy Data by Reinhard Viertl

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 1

a. Recreation time after an illness, quality of life data, amount of CO2 released to the environment in 1 year, position of a plane on a radar screen, hardness of a metal, height of a tree.

b. Stochastic uncertainty is due to variability of quantities, and probability distributions are the mathematical descriptions of this variability. It models the uncertainty of a quantity before it is observed. After the corresponding experiment is performed, the value of the quantity is a number or vector. Contrary to this, fuzziness is the imprecision of the outcomes of experiments after the experiment was performed. In the case of one-dimensional stochastic quantities this data uncertainty is described by fuzzy numbers.

c. The reading of a digital measurement device gives a number with finite many decimals. The resulting number contains no information on the remaining infinite number of decimals which determine a real number. Therefore, precisely speaking, the reported value is not a real number but the set of all real numbers between the real number which is obtained if all remaining decimals are equal to zero, and the real number which is obtained if all remaining decimals are equal to 9. This is an interval [x; ].

d. All these pictures are color intensity pictures representing ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required