Prediction interval methodology based on fuzzy numbers and its extension to fuzzy systems and neural networks

Abstract

Prediction interval modelling has been proposed in the literature to characterize uncertain phenomena and provide useful information from a decision-making point of view. In most of the reported studies, assumptions about the data distribution are made and/or the models are trained at one step ahead, which can decrease the quality of the interval in terms of the information about the uncertainty modelled for a higher prediction horizon. In this paper, a new prediction interval modelling methodology based on fuzzy numbers is proposed to solve the abovementioned drawbacks. Fuzzy and neural network prediction interval models are developed based on this proposed methodology by minimizing a novel criterion that includes the coverage probability and normalized average width. The fuzzy number concept is considered because the affine combination of fuzzy numbers generates, by definition, prediction intervals that can handle uncertainty without requiring assumptions about the data distribution. The developed models are compared with a covariance-based prediction interval method, and high-quality intervals are obtained, as determined by the narrower interval width of the proposed method. Additionally, the proposed prediction intervals are tested by forecasting up to two days ahead of the load of the Huatacondo microgrid in the north of Chile and the consumption of the residential dwellings in the town of Loughborough, UK. The results show that the proposed models are suitable alternatives to electrical consumption forecasting because they obtain the minimum interval widths that characterize the uncertainty of this type of stochastic process. Furthermore, the information provided by the obtained prediction interval could be used to develop robust energy management systems that, for example, consider the worst-case scenario.

Intelligent modeling of rheological and thermophysical properties of nanoencapsulated PCM slurry

“…The ACO R algorithm keeps track of k best solutions in a matrix S k×n , called the Solution Archive (SA). Each single row in this archive is made of the vector of model parameters and the value of the corresponding objective function f ( s ) obtained after running the flow simulation 38 . The algorithm sorts the remaining models in the archive according to their determination value (Figure 2).…”

Uncertainty-Aware Forecasting of Renewable Energy Sources

“…In [9], Takagi Sugeno (T-S) fuzzy models are utilised and by following the principles in [10] and upperlower prediction interval bounds -based on a given percentage value-are provided by utilising the covariance of data. Thereafter, a new prediction interval modelling methodology based on fuzzy numbers is proposed [11] which generate the size of prediction intervals based on a given percentage value. Fuzzy Set (FS) theory was introduced by Zadeh [12] and is applied to Fuzzy Logic Systems (FLSs) which are considered as explainable and robust systems for capturing and handling uncertainty in decision making applications.…”

A Granular Computing-Based Hybrid Hierarchical Method for Construction of Long-Term Prediction Intervals for Gaseous System of Steel Industry

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