A comparative analysis of economic efficiency of mediumsized manufacturing enterprises in districts of Wielkopolska province using the hybrid approach with metric and interval-valued data

The article describes a hybrid approach to evaluating economic efficiency of medium-sized manufacturing enterprises (employing from 50 to 249 people) in districts of Wielkopolska province, using metric and interval-valued data. The hybrid approach combines multidimensional scaling with linear ordering. In the first step, multidimensional scaling is applied to obtain a visual representation of objects in a two-dimensional space. In the next step, a set of objects is ordered linearly based on the distance from the pattern (ideal) object. This approach provides new possibilities for interpreting linearly ordered results of a set of objects. Interval-valued variables characterise the objects of interests more accurately than metric data do. Metric data are atomic, i.e. an observation of each variable is expressed as a single real number. In contrast, an observation of each interval-valued variable is expressed as an interval. The analysis was based on data prepared in a two-stage process. First, a data set of observations was obtained for metric variables describing economic efficiency of medium-sized manufacturing enterprises. These unit-level data were aggregated at district level (LAU 1) and turned into two types of data: metric and interval-valued data. In the analysis of interval-valued data, two approaches are used: symbolic-to-classic, symbolic-to-symbolic. The article describes a comparative analysis of results of the assessment of economic efficiency based on metric and interval-valued data (the results of two approaches). The calculations were made with scripts prepared in the R environment.