Good day bras, I wanna show you something about Fuzzy Randomness. I hope someone could understand.
Oh, maybe it may be relevant, I can't understand whut I'm goin' to talk about.
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.
1 REMARKS ON UNCERTAINTY
Modeling of data uncertainty in engineering problems as random variables or random processes becomes problematic when the preconditions of the underlying theory are not satisfied, e.g. when the reproduction conditions during the generation of sample elements do not remain constant or if the single element is uncertain. Such uncertain data have additional uncertainty besides the property of randomness.
Fuzzy randomness is a generalized uncertainty model to describe samples with uncertainty of the single sample element. If uncertainty is interpreted as fuzziness, this model combines randomness and fuzziness. Basic terms and definitions related to fuzzy randomness have been introduced, iter alia, by Kwakernaak (1978, 1979), Puri and Ralescu (1986), Wang and Zang (1992). The formal description of fuzzy randomness chosen by these authors is not suitable for formulating the uncertainty encountered in nonlinear structural analysis, e.g. in the nonlinear finite element method. A suitable form of representation for numerical engineering problems may be obtained on the basis of alfa -discretization by Möller and Beer (2004). A formal description for fuzzy random variables and fuzzy random functions is dealt with in Sects. 2 and 3. The extension to time series with fuzzy data and applications of time series are shown in Sects. 4 and 5. Further applications of fuzzy randomness on engineering problems may be found in Möller and Beer (2004), in Möller et al. (2005) and in Sickert et al. (2005).
Ok, this is the theoretical aspect, if any of you bras wanna learn something about practical one, write a comment.