Real-time fuzzy regression analysis: A convex hull approach

In this study, we present an enhancement of fuzzy regression analysis with regard to its aspect of real-time processing. Let us recall that fuzzy regression generalizes the concept of classical (numeric) regression in the sense of bringing additional capabilities that allow the model to deal with fuzzy (granular) data. We show that a convex hull method provides a useful vehicle to reduce computing time, which becomes of particular relevance in case of real-time data analysis. Our objective is to develop an efficient real-time fuzzy regression analysis based on the use of convex hull, specifically a Beneath-Beyond algorithm. In this algorithm, the re-construction of convex hull edges depends on incoming vertices while a re-computing procedure can be realized in real-time. We demonstrate the use of the developed enhancement to application to unit performance assessment and air pollution data. An important role of convex hull is contrasted with the limitations of linear programming used in the "standard" regression.