Abstract
This paper presents a novel approach to identify the prediction interval associated with data using interval type-2 fuzzy logic systems with support vector regression. For such a purpose, a constrained quadratic objective function is defined which is then solved using well-established quadratic programming approaches. Not only does the output of interval type-2 fuzzy logic system replicates the measured value, but also it provides the lower bound and the upper bound for measured data values. In the proposed approach, to have more valuable information, a penalty term is added in the cost functions to have full control over the width of prediction interval. This method has been successfully applied to two benchmark identification problems. It is observed that by using the control parameter in the cost function, it is possible to obtain a narrower, yet inclusive prediction interval. Furthermore, superior prediction accuracy is obtained compared to existing methods in literature. Motivated by these results, the proposed approach is used to predict time series collected using a satellite from Urmia lake water level which resulted in high accuracy and an inclusive prediction interval. The graphical abstract presented for the paper illustrates the overall data gathering as well as data analysis made to estimate the prediction interval associated with Urmia lake water level data.
Highlights
Training such a purpose, a constrained quadratic objective function is defined which is solved using well-established quadratic programming approaches
Interval type-2 fuzzy membership functions (MFs) are a promising method to deal with such different expert knowledge which benefit from an infinite number of type-1 fuzzy MFs
Use of interval type-2 fuzzy MFs makes the structure of Interval type-2 fuzzy logic systems (IT2FLSs) more complicated, it allows them to deal with high levels of uncertainties in the system
Summary
A list of articles related to the estimation of the prediction interval associated with data are presented. Existing approaches can be placed into three major categories of classical statistical approaches, upper and lower estimation methods and other optimization-based approaches which does not include extraction of upper and lower bound of data a priori (see Fig. 1)
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