Prediction interval construction using interval type-2 fuzzy logic systems

This study proposes a novel non-parametric method for construction of prediction intervals (PIs) using interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLSs). The key idea in the proposed method is to treat the left and right end points of the type-reduced set as the lower and upper bounds of a PI. This allows us to construct PIs without making any special assumption about the data distribution. A new training algorithm is developed to satisfy conditions imposed by the associated confidence level on PIs. Proper adjustment of premise and consequent parameters of IT2 TSK FLSs is performed through the minimization of a PI-based objective function, rather than traditional error-based cost functions. This new cost function covers both validity and informativeness aspects of PIs. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Quantitative measures are applied for assessing the quality of PIs constructed using IT2 TSK FLSs. The demonstrated results for four benchmark case studies with homogenous and heterogeneous noise clearly show the proposed method is capable of generating high quality PIs useful for decision-making.