Support Vector Regression for Multi-objective Parameter Estimation of Interval Type-2 Fuzzy Systems
Support Vector Regression for Multi-objective Parameter Estimation of Interval Type-2 Fuzzy Systems
复制标题
区间2型模糊系统多目标参数估计的支持向量回归
DOI：
10.1007/978-981-15-3290-0_8
复制
发表时间：
2020
期刊：
影响因子：
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通讯作者：
Ahmadieh Khanesar M.
中科院分区：
文献类型：
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作者：
Ahmadieh Khanesar M.
提出了一种基于支持向量回归的区间二型模糊系统多目标参数估计方法。这样的预测区间涵盖了数据的未来值，这在某些任务中非常有用。更窄但包含性更强的预测区间是更可取的，并且包含更多的信息，因为它避免了数据的保守下限和上限。早期的基于支持向量回归的区间型2模糊系统的参数估计方法没有控制这个宽度，而是专注于预测精度。在该工作中，为了控制这样的预测区间，引入多目标成本函数，该多目标成本函数除了与预测精度相对应的项之外还包括与预测区间的宽度相对应的加权项。用于预测区间宽度的权重提供了预测精度和预测区间宽度之间的折衷。成本函数是制定一个约束的二次目标函数的问题，可以使用良好的二次规划方法来解决。该方法成功地应用于混沌Mackey-Glass时间序列的预测，可以观察到该方法能够通过适当选择加权参数来控制预测区间。例如，混沌Mackey-Glass时间序列的预测相对于现有的支持向量回归估计算法，在保持预测精度的同时，预测区间的绝对值之和可能减少70%。这是当前方法优于文献中先前方法的主要益处。
This paper presents a support vector regression-based multi-objective parameter estimation method for interval type-2 fuzzy systems, which deals with prediction interval rather than its crisp output value. Such a prediction interval covers future values of data which is quite useful in some tasks. A narrower yet inclusive prediction interval is more desirable and contains more information, as it avoids conservative lower and upper limits for data. Earlier support vector regression-based estimation approaches for the parameters of interval type-2 fuzzy systems do not have control over this width and instead focus on prediction accuracy. In this work, to control such a prediction interval, a multi-objective cost function is introduced that other than a term corresponding to prediction accuracy includes a weighted term corresponding to width of prediction interval. The weight used for the width of prediction interval provides a trade-off between prediction accuracy and width of prediction interval. The cost function is formulated in terms of a constrained quadratic objective function problem which can be solved using well established quadratic programming approaches. The proposed method is successfully applied to the prediction of the chaotic Mackey-Glass time series, where it can be observed that the proposed method is capable of controlling prediction interval through appropriate selection of weighting parameter. For instance, the prediction of the chaotic Mackey-Glass time series is done with probable 70% decrease in sum of absolute value of prediction interval with respect to the existing support vector regression estimation algorithm while maintaining the prediction accuracy. This is the main benefit of the current approach over previous approaches in the literature.