Sustainable development of territorial units: MCDM approach with optimal tail selection.

• The positional TOPSIS, combined with different optimal tail selection methods of the variable distribution, is proposed to assess the sustainable development of territorial units. • The cluster compactness measure is proposed to evaluate the classification results of the positional TOPSIS with the optimal tail selection of variable distribution. • The automated Eye-Ball method and the Guillou and Hall's method enable correct identification of extreme values of variables describing the economic, social, and environmental development of municipalities. • The positional TOPSIS with selected optimal tail selection methods enable correct classification of the municipalities and assessment of their sustainable development in terms of levels and statuses. In the face of accelerating climate change, economic instability and limited resources, it is essential to find indicators that better measure the sustainable development of territorial units. Despite ambiguous definitions of sustainable development, numerous studies describe quantitative indicators of sustainable development. Main methodological problems include data availability and their use, spatial and time scales, selection of indicators, and their aggregation. Usually, analysts and decision-makers apply well known conventional methods that have numerous limitations. These methods in many cases cause excessive simplification of the real phenomena and relations between their determinants. Moreover, variables describing the development of territorial units (especially the environmental pillar) are often characterized by strong asymmetry or extreme observations. Even a single outlier for a given territorial unit may significantly affect the analysis and the resulting conclusions. The objective of this paper is to present the application potential of a Multi-Criteria Decision Making (MCDM) approach with an optimal tail selection to assess the sustainable development of territorial units. The proposed approach is based on the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and different methods of optimal tail selection of variable distribution. The Oja's spatial median and the optimal tail selection methods are used to reduce the impact of strong asymmetry and extreme values of variables. Moreover, the measure of cluster compactness is proposed for the evaluation of the proposed method. The proposed approach was used to assess the sustainable development of municipalities in Poland in 2018. We found that the automated Eye-Ball method and the Guillou and Hall's method enabled correct identification of extreme values of variables describing the economic, social, and environmental development of municipalities. This made it possible to distinguish the types of sustainable development level and its pillars and enabled to provide the statuses of the sustainable development level of the examined municipalities with respect to other municipalities in Poland. [Display omitted] [ABSTRACT FROM AUTHOR]