By Bernd Möller
Observations of uncertainty in measured facts with time improves forecasting power in quite a lot of fields in engineering. This publication presents an advent to uncertainty forecasting according to fuzzy time sequence. It information descriptive, modeling, and forecasting equipment for fuzzy time sequence. insurance locations emphasis on forecasting in accordance with fuzzy random procedures in addition to forecasting related to fuzzy neuronal networks.
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Extra resources for E Uncertainty Forecasting in Engineering
47) The requirement according to Eq. 47) also represents a boundary condition for the description and modeling of fuzzy time series. 12. As an abbreviated notation of a sum of fuzzy variables x ˜1 ❵ x ˜2 ❵ ... ❵ x ˜k , the lα rα -summation operator according to Eq. 48) is introduced. x ˜1 ❵ x ˜2 ❵ ... 3 Subtraction of Fuzzy Variables The introduced lα rα -subtraction according to Eq. 39) is now compared with the HUKUHARA difference presented in  as well as the subtraction according the extension principle (see [5, 36, 71]), and the different properties are discussed.
The realizations ∆xαi l and ∆xαi r of the random lα rα -increments ∆Xαi l and ∆Xαi r , respectively, correspond to the lα rα -increments aαi l and aαi r of a fuzzy element a ˜ of F ♣Aq with a specific probability. This probability is expressed by the probability P ♣F ♣Aqq. 38. , ∆X2n is defined as the 2n-dimensional probability distribution function lr FX˜ ♣x ˜q in the coordinate system of the increments according to Eq. , ∆x2n are the lα rα -increments of the fuzzy variable x ˜. These form the coordinates in the coordinate system of the increments.
47) also represents a boundary condition for the description and modeling of fuzzy time series. 12. As an abbreviated notation of a sum of fuzzy variables x ˜1 ❵ x ˜2 ❵ ... ❵ x ˜k , the lα rα -summation operator according to Eq. 48) is introduced. x ˜1 ❵ x ˜2 ❵ ... 3 Subtraction of Fuzzy Variables The introduced lα rα -subtraction according to Eq. 39) is now compared with the HUKUHARA difference presented in  as well as the subtraction according the extension principle (see [5, 36, 71]), and the different properties are discussed.