Observations of uncertainty in measured data with time improves forecasting capability in a wide range of fields in engineering. This book provides an introduction to uncertainty forecasting based on fuzzy time series. It details descriptive, modeling, and forecasting methods for fuzzy time series. Coverage places emphasis on forecasting based on fuzzy random processes as well as forecasting involving fuzzy neuronal networks.
Author(s): Bernd Moller, Uwe Reuter
Edition: 1
Publisher: Springer
Year: 2007
Language: English
Pages: 211
Contents......Page 7
Abbrevations......Page 9
1.1 Application of Time Series for Forecasting in Engineering......Page 14
1.2 Data Uncertainty and Fuzzy Time Series......Page 18
1.3 Examples of Fuzzy Time Series......Page 20
2.1 Fuzzy Variables......Page 22
2.1.1 Classical and Incremental Discretization of Fuzzy Variables......Page 24
2.1.2 Incremental Fuzzy Arithmetic......Page 29
2.1.3 Subtraction of Fuzzy Variables......Page 31
2.1.4 Distance between Fuzzy Variables......Page 35
2.1.5 Fuzzy Functions......Page 36
2.2 Fuzzy Random Variables......Page 38
2.2.1 Classical and Incremental Discretization of Fuzzy Random Variables......Page 39
2.2.2 Fuzzy Probability Distribution Functions of Fuzzy Random Variables......Page 43
2.2.3 Characteristic Moments......Page 57
2.2.4 Monte Carlo Simulation of Fuzzy Random Variables......Page 63
2.3 Fuzzy Random Processes......Page 66
3.1 Plot of Fuzzy Time Series......Page 71
3.2 Fuzzy Component Model......Page 75
3.3 Stationary Fuzzy Time Series......Page 81
3.4 Transformation of Fuzzy Time Series Using Filters......Page 86
3.4.1 Smoothing of Fuzzy Time Series......Page 87
3.4.2 Fuzzy Difference Filter......Page 89
3.4.3 Extended Smoothing and Extended Fuzzy Difference Filter......Page 90
3.5.1 Fuzzy White-Noise Processes......Page 91
3.5.2 Fuzzy Moving Average Processes......Page 95
3.5.3 Fuzzy Autoregressive Processes......Page 97
3.5.4 Fuzzy Autoregressive Moving Average Processes......Page 98
3.5.5 Specification of Model Order......Page 101
3.5.6 Parameter Estimation......Page 108
3.6.1 The Basics of Artificial Neural Networks......Page 118
3.6.2 Multilayer Perceptron for Fuzzy Variables......Page 119
3.6.3 Backpropagation Algorithm......Page 123
3.6.4 Neural Network Architecture for Fuzzy Time Series......Page 130
3.6.5 Conditioning of the Fuzzy Data......Page 136
4.1 Underlying Concept......Page 142
4.2.1 Optimum Forecast......Page 145
4.2.2 Fuzzy Forecast Intervals......Page 148
4.2.3 Fuzzy Random Forecast......Page 152
4.3 Forecasting on the Basis of Artificial Neural Networks......Page 155
4.3.1 Optimum Forecast......Page 156
4.3.2 Fuzzy Forecast Intervals......Page 158
4.3.3 Fuzzy Random Forecast......Page 161
5.1 Model-Free Forecasting......Page 164
5.2 Model-Based Forecasting......Page 166
5.3 Applications......Page 174
5.3.1 Forecasting of Structural Actions......Page 175
5.3.2 Forecasting of Structural Responses......Page 188
References......Page 203
E......Page 208
F......Page 209
P......Page 210
W......Page 211
