Support Vector Regression for Multi-objective Parameter Estimation of Interval Type-2 Fuzzy Systems

Abstract

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.