Tackling outliers in granular box regression

Granular computing has gained increasing attention in the last decade. It is motivated by the needs for simply and robust low cost solutions in many real life applications. Addressing these needs, the main objective of granular computing is to develop efficient algorithms. Today granular computing provides a rich variety of such algorithms including methods derived from interval mathematics, fuzzy and rough sets and others. Within this framework granular box regression was proposed recently. Granular box regression uses hyper-dimensional interval numbers to establish a f.g-generalization of a function between several independent variables and one dependent variable. Since granular box regression utilizes intervals a challenge is the detection of outliers. In this paper, we propose three methods tackling outliers in granular box regression and discuss their properties. We also apply these methods to artificial as well as to real data.