Grażyna Dehnel , Marek Walesiak

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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.


medium-sized enterprise, metric data, interval-valued data, multidimensional scaling, composite measures


C38, C43, C63, C88, R12


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