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B Möller, M Beer, and U Reuter (2005)
Theoretical Basics of Fuzzy Randomness - Application to Time Series with Fuzzy Data
In: Safety and Reliability of Engineering Systems and Structures - Proceedings of the 9th Int. Conference on Structural Safety and Reliability, edited by G. Augusti and G.I. Schueller and M. Ciampoli. Millpress, Rotterdam, pages 1701--1707.
The paper introduces the uncertainty model fuzzy randomness. Using
fuzzy random variables and fuzzy random functions it is possible to
mathematically describe uncertainty characterized by fuzzy randomness.
Fuzzy randomness arises when random variables – e.g. as a result of
changing boundary conditions – cannot be observed with exactness.
Fuzzy random variables may also be interpreted as fuzzified random
variables, as the random event can only be observed in an uncertain
manner. If the fuzzy random function is solely dependent on time, a
fuzzy random process is obtained. Fuzzy random processes can be used
for modeling time series with fuzzy data. Analysis and forecast of
time series with fuzzy data is demonstrated by way of an example.
