Measuring Well-Being by TOPSIS (Tecnique for Order Preference by Similarity to Ideal Solution) Method: Empirical Evidence for Italian Regions
Isabella Carbonaro
Economics and Territory (DET), University of Rome Tor Vergata, Rome, Italy

Well-being has always been a matter of debate for researchers. From an operational perspective, however, is common to treat well-being as a multidimensional concept: each dimension represents an aspect to be described by means of different indicators able to characterize it. For each dimension composite indexes are then obtained by aggregating and weighting the relevant indicators.

This paper attempts to measure the well-being of Italian Regions using composite indexes of eleven dimensions. Zeleny's compromise solution concept and a modified TOPSIS (Tecnique for Order Preference by Similarity to Ideal Solution) method of compromise ranking (Zeleny, 1982; Hwang e Yoon, 1981) are used. TOPSIS is a methodological tool capable of handling conflicting situations between dimensions, relations between indicators and incomparable units (Antucheviciene et al,2010). The fundamental of TOPSIS is that doesn't exist in real life a “Pareto solution”; in the context of regional well-being assessment this means that is never happens that all indicators will be at their best level for the same region, even for a single dimension: a compromise solution is needed. The basic principle of TOPSIS is the following: the region that ranks best is the closest to the ideal solution and the most distant from the negative ideal solution. The ideal solution is the set of all the best values achievable by each indicator within a specific dimension (profit indicators the maximum, cost indicators the minimum); on the contrary, negative ideal solution is the set of all the worst achievable values (profit indicators the minimum, cost indicators the maximum).

In this paper TOPSIS method has been modified as regards normalization criteria and weighting system. The procedure of the Shannon's entropy (Shannon CE., Weaver W., 1947) and the Mahalanobis distance, instead of Euclidean distance, have been used.

The source of data is ISTAT (Italian National Institute of Statistics). Empirical results confirm the existence of a lot of disparities between Italian Regions in all the considered dimensions of well-being. The ranking operation provides a priority list of regions needing of urgent and strong actions in one or more dimensions to improve regional and national well-being.


Antucheviciene, J., Zavadskas, E. K., Zakarevicius, A., “Multiple criteria construction management decisions considering relations between criteria”, Baltic Journal on Sustainability, 16(1): pp. 109–125, 2010

Hwang C.L., Yoon K., Multiple Attribute Decision Making: Methods and Applications, A State of the Art Survey, Springer-Verlag, New York, 1981

Shannon CE, Weaver W., The mathematical theory of communication, The University of Illinois Press, 1947.

Zeleny, M., Multiple Criteria Decision Making,. Mc-Graw-Hill, New York, 1982.

Keywords: TOPSIS (Tecnique for Order Preference by Similarity to Ideal Solution); Compromise solution; Relations between indicators and Mahalanobis distance; Shannon's entropy

Biography: Italian. Associate Professor in Economic Statistics (SECS-S/03) at Department of Economics and Territory, University of Rome “Tor Vergata”. Member of the Italian Statistics Society (SIS), of International Association of Survey Statisticians (IASS), of the Economics, Demography and Statistics Italian Society (SIEDS) and of Espon (European Spatial Planning Observation Network) Contact Point Italy (ECP). Main activities and responsibilities: coordination of territorial data and statistical methods within Department's Projects and, more generally, supporting statistical activities. Main fields of interest: measuring well-being; construction of composite indexes of complex phenomena; construction of bilateral and multilateral spatial price indexes.