A dynamic approach to relative taxonomy and robust measures of central tendency

A Measurement of Social Cohesion in Poland’s NUTS2 Regions in the Period 2010–2019 by Applying Dynamic Relative Taxonomy to Interval-Valued Data

“…The average similarity of a given relativized observation with respect to other relativized observations of the j-th variable for each column of matrix (6) was calculated using the arithmetic mean or one of the robust measures of central tendency: median, trimmed mean, winsorized mean, and biweight mean. The corresponding formulas can be found in Section 3.1 of the article by Walesiak, Dehnel, and Dudek [25]. The same formulas can also be found in [51,52,73].…”

“…A wide range of policy measures and their effects reflects the multidimensional character of social cohesion, which requires a complex process of measurement and assessment. The proposed method of relative taxonomy in its dynamic version [25] can be used to assess the level of social cohesion in a given object (region) and in a given year relative to the level observed in all objects (regions) over the entire reference period, i.e., between 2010 and 2019. By making use of interval-valued data, it is possible to assess objects not only at the regional level but also at a lower level of territorial aggregation, taking into account spatial variation across districts that make up each region.…”

“…Studies concerning multi-criteria decision making (MCDM) make use of non-compensatory methods (see [21][22][23]). An overview of compensatory and partially compensatory aggregate measures applied to different types of data can be found in Walesiak and Dehnel [24]; Walesiak, Dehnel, and Dudek [25]. Many different concepts and applications for ranking sets of objects based on aggregate measures have been developed, including classic data matrix (an aggregate measure that accounts for the pattern of development [26]; aggregate measures accounting for the pattern and the anti-pattern of development [27]; the TOPSIS measure [28]); ordinal data (an aggregate measure in the form of GDM2 distance measure from the pattern of development [29]); fuzzy numbers (for example, fuzzy TOPSIS [30]; an interval-valued intuitionistic fuzzy synthetic measure (I-VIFSM) based on Hellwig's approach [31]); the conditions of spatial dependence [32]; combining multidimensional scaling with ranking sets of objects for classical data [33]; aggregate measures with a penalty function [34,35]; aggregate measures with the adjustment to the surroundings of a given object [36]; an iterative approach to ranking sets of objects, whereby in each iteration the highest ranked object receives the next position in the ranking and is eliminated from the set of objects [37]; and an aggregate measure covering special cases of a generalized mean (or power mean of order r): minimum, harmonic mean, geometric mean, arithmetic mean, quadratic mean, cubic mean, and maximum [38].…”

“…This article focuses on the method of relative taxonomy proposed by Wydymus [48] and its dynamic modification [24]. This approach was extended by Walesiak, Dehnel, and Dudek [25] to include robust measures of central tendency. Both approaches were developed with respect to classic, metric data.…”

Progress on SDG 7 achieved by EU countries in relation to the target year 2030: A multidimensional indicator analysis using dynamic relative taxonomy

“…In the dynamic version, values of the j -th variable in formula ( 5 ) is relativised based on a matrix of data from all periods. This approach was extended by [ 22 ] to include robust measures of central tendency. Geometric mean was used in steps 6 and 7 of the dynamic relative taxonomy procedure (c.f.…”