Assessing Euro 2020 Strategy Using Multi-criteria Decision Making Methods: VIKOR and TOPSIS

Abstract

The European Union (EU) 2020 Strategy aims at forming the conditions for smart, sustainable and inclusive growth targets. Assessment of the EU countries’ situation is of vital importance in attaining the EU 2020 Strategy. This paper presents an impartial evaluation of the performance of 27 EU member countries in terms of each EU 2020 Strategy. For the basis of the evaluation, we propose an effective and easily practicable measure for ranking and monitoring the countries according to their performance by using the VIKOR and the TOPSIS methods, multi-criteria decision making (MCDM) methods, which allows for the integration of the 22 indicators, and be capable of considering such a broad spectrum of criteria including various economic, financial, demographic, educational and innovational. Our study provides a comparative analysis of the above-two methods. The contribution of the study to the literature is that these methods can be applied for assessing countries in terms of the EU 2020 Strategy which have the multi–dimensionality targets. The results point out new EU member countries such as Slovenia and Romania have attained higher scores than many of the 15 EU countries.

Appendix

The k-means or hard c-means clustering is one of the unsupervised learning algorithms, and a set of statistical methods for determining new structure when investigating data sets (Flynt and Dean 2016). The algorithm is based on a constrained optimization problem with the locally minimum of the objective function $J\left( {U, v} \right)$, where U is the partition matrix and the parameter v is the cluster centers. That constrained problem follows a simple way to classify a given data set on the assumption that where the number of clusters namely c, is known (Ross 2010; Velmurugan 2014). In the method the k-partition space and the objective function as following:

$$M_{c} = \left\{ {U | \chi_{ik} \in \left\{ {0,1} \right\}, \mathop \sum \limits_{i = 1}^{c} \chi_{ik} = 1, 0 < \mathop \sum \limits_{k = 1}^{n} \chi_{ik} < n} \right\},$$

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$$J\left( {U, v} \right) = \mathop \sum \limits_{k = 1}^{n} \mathop \sum \limits_{i = 1}^{c} \chi_{ik} \left( {d_{ik} } \right)^{2} ,$$

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where $d_{ik} ,$ is chosen distance measure between k. data point $\varvec{x}_{k}$ and i. cluster center $v_{i}$.

$$d_{ik} = d\left( {\varvec{x}_{k} - v_{i} } \right) = \varvec{x}_{k} - v_{i} = \left[ {\mathop \sum \limits_{j = 1}^{m} \left( {\varvec{x}_{kj} - v_{ij} } \right)^{2} } \right]^{1/2} ,$$

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$$v_{ij} = \frac{{\mathop \sum \nolimits_{k = 1}^{n} \chi_{ik} x_{kj} }}{{\mathop \sum \nolimits_{k = 1}^{n} \chi_{ik} }}.$$

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The optimization method is composed of the following steps (Ross 2010):

Step 1 :

$2 \le c \le n$, and initialize the $U$ matrix. $U_{0} \in M_{c}$

Step 2 :

Calculate the cluster center $\left\{ {v_{i}^{\left( r \right)} } \right\}, \left( {r = 0, 1, \ldots } \right)$ and the distance $\left\{ {d_{ik}^{\left( r \right)} } \right\}$ between data point and cluster center

Step 3 :

Update the $U^{\left( r \right)}$ matrix for the $r.$ step, $U^{\left( r \right)}$, as follows:

$$\chi_{ik}^{{\left( {r + 1} \right)}} = \left\{ {\begin{array}{*{20}c} {1, d_{ik}^{\left( r \right)} = min\left\{ {d_{jk}^{\left( r \right)} } \right\} for all j \in c} \\ {0, otherwise} \\ \end{array} } \right.$$

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Step 4 :

If $U^{{\left( {r + 1} \right)}} - U^{\left( r \right)} \le \varepsilon$ stop; otherwise set $r = r + 1$ and return to step 2