Fuzzy ANP and DEA approaches for analyzing the human development and competitiveness relation

Abstract

Human development and competitiveness have a causal relation. However, the literature is not clear on which one affects the other. This study investigates the bilateral relation between human development and competitiveness. For this purpose, initially, Fuzzy Analytic Network Process (FANP) is utilized to develop a composite index based on the relative importance weights of respective human development and competitiveness drivers. By FANP, the effects of key dimensions of human development and indexes of competitiveness on each other are taken into account. Subsequently, countries’ efficiencies on converting their human development to competitiveness and inversely, competitiveness to human development is measured by Data Envelopment Analysis (DEA). Two different DEA models are developed to consider the bilateral relations. 45 countries are evaluated using both FANP and DEA models. Finally, the results are synthesized to reveal the direction of the relationship. It is found that the effect of competitiveness on human development is more significant than the effect of human development on competitiveness.

Keywords

Human development competitiveness of nations fuzzy analytic network process data envelopment analysis

1 Introduction

Human development allows the enrichment of people’s choices and opportunities [1]. It comprises the following aspects: having a long and healthy life, a decent standard of living and being knowledgeable. Competitiveness of a nation on the other hand, is the innovation capacity of a country [2]. Through productivity, it enables a country to be in a more advantageous position or to maintain its advantageous position compared to the other countries.

There exists a relationship between human development and competitiveness [3]. It has been shown that they and their growth trends are positively correlated [4, 5]. Furthermore, main purpose of progress is to reach human development [6, 7]. As competitiveness is a contributing factor to human development [8], countries can utilize their competitiveness to enhance their human development. Ülengin et al. [9] state that one of the possible key outcomes of good competitiveness management is a satisfactory level of human development. On the other hand, advancements in human development is certain to increase the competitiveness level, since more knowledgeable and healthy people in the society enhances the labor efficiency and productivity [4].

This study claims that there is bilateral relation between human development and competitiveness at national level. In order to reveal the relationship and to find out which one affects the other one more, two approaches are used: Fuzzy Analytic Network Process (FANP), and Data Envelopment Analysis (DEA).

Initially, by using FANP approach, an index to rank the countries based on their human development and competitiveness levels is developed. In this analysis, bilateral relations are considered, that is, the human development dimensions affect the competitiveness subindexes and the competitiveness subindexes affect human development dimensions. These interrelations cannot be modelled using classical multiple attribute decision making approach that have hierarchy between criteria and alternatives, whereas FANP addresses problems where all criteria and alternatives might influence each other in a network structure [26]. Therefore, in this study, FANP is preferred, as it can deal with a network of indicators of human development and competitiveness. Besides, different from classical ANP, FANP utilizes fuzzy set theory to deal with imprecise and uncertain judgments of decision makers [28]. FANP can model uncertainties in the subjective judgements of the experts, while finding the magnitudes of the effects in the complex system of human development and competitiveness.

Furthermore, DEA is utilized to find out the efficiencies of countries on converting their human development to competitiveness and competitiveness to human development. Two separate DEA models are developed. DEA is a non-parametric data-oriented approach to assess the performance of a set of decision making units (DMUs). Efficiency of DMUs are calculated based on the inputs and outputs of peer entities. In this study, as bilateral relations are considered, it is not clear which of human development and competitiveness is the input or the output. Therefore, two DEA models are developed where human development dimensions are input and competitiveness subindexes are output in the first model and the input-output relation is the opposite in the second model. DEA is employed to scrutinize the bilateral effects of human development and the competitiveness with 3-year time lags.

After the application of FANP and DEA, the results are compared to find out the direction of the significant relation between human development and competitiveness. For this purpose, correlations among the composite index of the countries found by the application of FANP and efficiencies of the countries in both DEA models are calculated.

To the best of our knowledge, this study is one of the first studies to analyze the bilateral relationship between human development and competitiveness.

Data sources in this study are Human Development Index (HDI) in United Nations Development Programme’s (UNDP) Human Development Report and Global Competitiveness Index (GCI) in World Economic Forum’s (WEF) Global Competitiveness Report. HDI assesses a country by its people’s capabilities. It presents the achievement in key dimensions of human development: A long and healthy life (LHL), being knowledgeable (BK) and a decent standard of living (DSL). GCI evaluates the countries based on policies and factors that govern productivity based on three subindexes: Basic requirements (BR), efficiency enhancers (EE) and innovation and sophistication factors (ISF). Both HDI and GCI are recognized and widely used in the literature [10 –12]. GCI subindexes and HDI dimensions are shown in Fig. 1 as part of the framework of the study.

Fig. 1

Framework of the study.

The paper is organized as follows: The literature review on human development and competitiveness is provided in Section 2. FANP and DEA models as well as their application to the human development and competitiveness relation are explained in Section 3. The results and discussions are presented in Section 4 and the paper concludes with Section 5.

2 Human development and competitiveness

The literature is limited in the context of the relationship between human development and competitiveness. Shkiotov [13] investigated world’s five largest economies for a five-year period in terms of GCI and HDI and concluded by comparing them without any mathematical methods that there is no direct relationship between national competitiveness and human development. Skorvagova and Drienikova [14] argued that the rankings of European Union member states’ national competitiveness and their Esping-Andersen’s welfare state type classes have no relation.

Conversely, Waheeduzzaman [8] has shown via correlation analysis that competitiveness has positive impact on human development. Additionally, Onyusheva [3], also utilizing correlation analysis, for the data of GCI and HDI of 144 countries on the time period 2012–13 has concluded that a relationship exists. Furthermore, Lonska and Boronenko [4] also shown that GCI and HDI growth trends are positively correlated. Similarly, Bucher [5] recognized high correlation between a country’s human development and competitiveness.

Moreover, Aiginger [15] suggested the measurement of national competitiveness by how well the country has maximized its human development level. Similarly, Aiginger [16] presented a model for measuring competitiveness via its outcome, human development. On the other hand, Ülengin et al. [17] examined the relationship between human development and competitiveness of countries by using data envelopment analysis. In addition, Ülengin et al. [5] analyzed how efficient countries were in transforming their competitiveness to human development via data envelopment analysis and based on these results identified the main factors affecting this efficiency by an artificial neural network. Ditkun et al. [18] argued that Brazil having a lower competitiveness level at the time period of 2003–13 may be related to its fixed HDI score since 2007. Moreover, Thore and Tarverdyan [19] have examined countries’ efficiency on the conversion of their sustainable competitiveness into environmental and social welfare with data envelopment analysis. Also, Tridico and Meloni [20] have argued that threats to competitiveness can be managed better with the increases in human development investments.

Unlike the literature, in this study, we considered the interrelations among human development and competitiveness drivers with time lags. We did not make assumptions related to the direction of the effect between human development and competitiveness, initially. We analyzed the relations in both ways with two different models. In the last step, we compared the models’ results to find out the direction of the significant relation.

3 Methodology

The methodology consists of two approaches: FANP and DEA. The details of these methods as well as their application to the human development –competitiveness relationship is presented in this section.

In order to measure human development and competitiveness, the key dimensions of Human Development Index of UNDP Human Development Report and subindexes of Global Competitiveness Index of WEF Global Competitiveness Report are used. As given in Fig. 1, human development indicators are

A long and healthy life (LHL),

Being knowledgeable (BK),

A decent standard of living (DSL).

Competitiveness indicators are

Basic requirements (BR),

Efficiency enhancers (EE),

Innovation and sophistication factors (ISF).

Particularly for FANP, the 2015 HDI data [21] and 2015 GCI data [22] are used. These features are presented in the Appendix, Table A1. For DEA, as 3-year time lag was considered in the models, in addition to the 2015 data, 2012 data of both HDI and GCI are used as well.

In order to avoid unbalanced comparisons with respect to population or gross domestic product (GDP) (e.g., comparison of a heavily populated country vs a very lightly populated country –China vs Luxembourg), we selected 45 countries that comprise the 90% of the globe’s population or GDP [23, 24].

3.1 Fuzzy analytic network process (FANP)

Analytic network process (ANP) is a multi-criteria decision-making method developed by Saaty [25]. It addresses decisions involving interdependent decision levels and attributes such that it comprises a network in which all elements might influence each other [26]. The decision maker is required to conduct pairwise comparisons of each element in the network to any relevant other. A nine-point scale is utilized to express these judgments numerically [27]. Meanwhile, a satisfactory level of consistency ratio regarding these judgments is sought. Based on this structure, ANP assigns each alternative at question an overall priority. The best alternative has the largest overall priority.

Fuzzy ANP copes with imprecise and uncertain judgments of decision makers [28]. To that end, it utilizes the fuzzy set theory which is first introduced by Zadeh [29]. It follows the same structure as ANP. The only main difference is that pairwise comparison judgments of the decision maker are fuzzified to reflect the imprecision and uncertainty in their choices. As such, the process of getting to crisp overall priorities involves more work.

Although the fuzzy extension of ANP is discussed in the literature [30], Boran and Goztepe [31] state that FANP grants more practical results in pairwise comparison process and models the ambiguity and imprecision associated better than ANP. Sipahi and Timor [32], Kubler et al. [33], Chen et al. [30] provide review of FANP applications in the literature

Yüksel and Dağdeviren [34] reports, there are many methods in the literature tackling this process [35 –42]. According to Wicher et al. [43], FAHP/FANP methods are classified into three groups: (1) Methods using defuzzification (e.g. [44, 45]), (2) Methods using α-cuts of fuzzy sets without mathematical programming (e.g. [36–40 , 46]), and (3) Methods using mathematical programming (e.g. [41 , 47–49]). Although the methods using defizzification are easy to use, they defuzzify the inputs early in the process that may result in loss of information. The disadvantages of the methods using α-cuts are the difficulty of setting α value or if the process depends on processing of multiple α cuts, the difficulty of aggregating the solutions of several α-cuts. Methods using mathematical programming methods, on the other hand, suffer from finding local optimal solutions and non-reliable methods for approximation of the fuzzy weights.

In order to cope with the disadvantages of the methods used in the literature, we used a hybrid method that is composed of two phases. In the first phase the evaluations of the experts are transformed to fuzzy weighted supermatrix by an accepted method from the literature [50 –52]. The elements of the resulting supermatrix are represented by triangular fuzzy sets. Therefore, loss of information is prevented. Subsequently, the fuzzy global weights are calculated depending on a new method from the literature that uses a mathematical programming model [49]. In order to find a satisfactory solution, the initial conditions are defined appropriately.

We use FANP to investigate the relation between HDI dimensions and GCI subindexes respectively and for developing a composite index to assess countries in terms of both human development and competitiveness. Our network is presented in Fig. 1. Each HDI dimension is linked to each HDI dimension and each GCI subindex. The same applies to GCI subindexes.

The pairwise comparisons of the criteria with respect to their effect on the other criteria are gathered based on a designed questionnaire. The questionnaire consists of six tables as there are three criteria in both HDI and GCI clusters, the questionnaire included six tables. Sample questionnaire are presented in Appendix, Table A2 and A3. Notice that first three questions are directed to the criteria in the other cluster, while the last question asks for comparison of the criteria in the same cluster.

Two academics knowledgeable on nations’ human development and competitiveness, the indexes HDI and GCI answered the questionnaire. During the interview, their evaluations’ consistency was calculated and if the consistency ratio were to be higher than % 10, they were asked to revise their evaluations. This way, an acceptable level of consistency was acquired. Their evaluations are converted to triangular fuzzy numbers (TFN) according to Table 1. Sample fuzzy pairwise comparison matrix is presented in Table 2. The evaluations are aggregated by geometric mean.

Table 1
Fuzzy dominance scale for pairwise comparative judgment

Classical Numerical scale Linguistic Triangular Fuzzy scale

1 Just equal (1, 1, 1)

2 Equal to moderate (1, 2, 3)

3 Moderate dominance (2, 3, 4)

4 Moderate to strong (3, 4, 5)

5 Strong dominance (4, 5, 6)

6 Strong to very strong (5, 6, 7)

7 Very strong dominance (6, 7, 8)

8 Very strong to absolute (7, 8, 9)

9 Absolute dominance (8, 9, 9)

Classical Numerical scale	Linguistic	Triangular Fuzzy scale
1	Just equal	(1, 1, 1)
2	Equal to moderate	(1, 2, 3)
3	Moderate dominance	(2, 3, 4)
4	Moderate to strong	(3, 4, 5)
5	Strong dominance	(4, 5, 6)
6	Strong to very strong	(5, 6, 7)
7	Very strong dominance	(6, 7, 8)
8	Very strong to absolute	(7, 8, 9)
9	Absolute dominance	(8, 9, 9)

Table 2

Sample fuzzy pairwise comparison matrix for cluster HDI with respect to their effect on BR

Factors	LHL	BK	DSL
LHL	(1,1,1)	(0.25, 0.33, 0.5)	(0.71, 1, 1.41)
BK	(2, 3, 4)	(1,1,1)	(0.45, 0.71, 1)
DSL	(0.71, 1, 1.41)	(1, 1.41, 2.24)	(1,1,1)

In this study FANP is applied in two phases. In the first phase, the aggregated evaluations of the experts are transformed into a fuzzy supermatrix using the normalization method proposed by Wang and Elhag [50], Wang et al. [51]. In the second phase, the fuzzy weights of the indicators of human development and competitiveness are derived based on the fuzzy supermatrix by a mathematical programming model suggested in Chen and Huang [49].

FANP –Phase 1.

The fuzzy supermatrix is formed using the normalization method proposed by Wang and Elhag [50], Wang et al. [51] as suggested in Asan et al. [52]. Let ${\tilde{c}}_{i_{n_{i}, n_{k}}}^{j_{m_{j}}} = (l_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}, m_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}, u_{i_{n_{i}, n_{k}}}^{j_{m_{j}}})$ , where ${\tilde{c}}_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}$ denotes an aggregated fuzzy pairwise comparison of elements n_i and n_k in cluster i∈ { 1 (HDI dimensions) , 2 (GCI subindexes) } with respect to element m_j in cluster j∈ { 1 (HDI dimensions) , 2 (GCI subindexes) } and $l_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}, m_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}, u_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}$ reflect the lower, mid-, upper value of this comparison respectively. For cluster i, j = 1, n_i, n_k, m_j∈ { 1 (LHL) , 2 (BK) , 3 (DSL) }, whereas for cluster i, j = 2, n_i, n_k, m_j∈ { 1 (BR) , 2 (EE) , 3 (ISF) }. Additionally, let ${\tilde{s}}_{i_{n_{i}}}^{j_{m_{j}}} = (l_{i_{n_{i}}}^{j_{m_{j}}}, m_{i_{n_{i}}}^{j_{m_{j}}}, u_{i_{n_{i}}}^{j_{m_{j}}})$ where ${\tilde{s}}_{i_{n_{i}}}^{j_{m_{j}}}$ is the fuzzy local priority of element n_i in cluster i with respect to element m_j in cluster j (i.e., the values of fuzzy supermatrix). Then, every ${\tilde{s}}_{i_{n_{i}}}^{j_{m_{j}}}$ is calculated with Equations (1), (2) and (3) [44, 45]. The resulting fuzzy supermatrix for our case is given in Table 3 by applying these equations.

–

Fuzzy supermatrix

Factors	LHL	BK	DSL	BR	EE	ISF
LHL	(1,1,1)	(0.54, 0.61, 0.71)	(0.80, 0.83, 0.86)	(0.16, 0.22, 0.32)	(0.11, 0.16, 0.25)	(0.12, 0.15, 0.20)
BK	(0.41, 0.5, 0.59)	(1,1,1)	(0.14, 0.17, 0.20)	(0.31, 0.45, 0.56)	(0.49, 0.64, 0.73)	(0.63, 0.71, 0.76)
DSL	(0.41, 0.5, 0.59)	(0.29, 0.39, 0.46)	(1,1,1)	(0.23, 0.33, 0.46)	(0.14, 0.20, 0.32)	(0.11, 0.14, 0.19)
BR	(0.20, 0.27, 0.36)	(0.17, 0.23, 0.31)	(0.31, 0.44, 0.58)	(1,1,1)	(0.45, 0.55, 0.67)	(0.8, 0.83, 0.86)
EE	(0.38, 0.49, 0.58)	(0.42, 0.54, 0.63)	(0.27, 0.41, 0.53)	(0.71, 0.78, 0.82)	(1,1,1)	(0.14, 0.17, 0.2)
ISF	(0.19, 0.24, 0.32)	(0.17, 0.23, 0.32)	(0.11, 0.15, 0.24)	(0.18, 0.22, 0.29)	(0.33, 0.45, 0.55)	(1,1,1)

$l_{i_{n_{i}}}^{j_{m_{j}}} = \frac{\sum_{n_{k} = 1}^{3} l_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}}{\sum_{n_{k} = 1}^{3} l_{i_{n_{i}, n_{k}}}^{j_{m_{j}}} + \sum_{n_{l} \neq n_{i}}^{3} \sum_{n_{k} = 1}^{3} u_{i_{n_{l}, n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (1) $m_{i_{n_{i}}}^{j_{m_{j}}} = \frac{\sum_{n_{k} = 1}^{3} m_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}}{\sum_{n_{l} = 1}^{3} \sum_{n_{k} = 1}^{3} m_{i_{n_{l}, n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (2) $u_{i_{n_{i}}}^{j_{m_{j}}} = \frac{\sum_{n_{k} = 1}^{3} u_{i_{n_{i}, n_{k}}}^{j_{m_{j}}}}{\sum_{n_{k} = 1}^{3} u_{i_{n_{i}, n_{k}}}^{j_{m_{j}}} + \sum_{n_{l} \neq n_{i}}^{3} \sum_{n_{k} = 1}^{3} l_{i_{n_{l}, n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (3)

The weighted fuzzy supermatrix $\tilde{Π}$ is formulated by processing the fuzzy supermatrix. Let ${\tilde{s}}_{i_{n_{i}}}^{* j_{m_{j}}} = (l_{i_{n_{i}}}^{* j_{m_{j}}}, m_{i_{n_{i}}}^{* j_{m_{j}}}, u_{i_{n_{i}}}^{* j_{m_{j}}})$ be the values of fuzzy weighted supermatrix. Then, every ${\tilde{s}}_{i_{n_{i}}}^{* j_{m_{j}}}$ is calculated by Equations (4), (5) and (6). The weighted fuzzy supermatrix for our study is presented in Table 4.

Table 4

Weighted fuzzy supermatrix ( $\tilde{Π}$ )

Factors	LHL	BK	DSL	BR	EE	ISF
LHL	(0.06, 0.09, 0.13)	(0.05, 0.08, 0.11)	(0.10, 0.15, 0.20)	(0.05, 0.07, 0.12)	(0.03, 0.05, 0.09)	(0.04, 0.05, 0.07)
BK	(0.12, 0.16, 0.21)	(0.13, 0.18, 0.22)	(0.09, 0.14, 0.18)	(0.10, 0.15, 0.20)	(0.15, 0.21, 0.26)	(0.20, 0.24, 0.26)
DSL	(0.06, 0.08, 0.12)	(0.05, 0.08, 0.12)	(0.03, 0.05, 0.09)	(0.07, 0.11, 0.16)	(0.04, 0.07, 0.12)	(0.04, 0.05, 0.06)
BR	(0.29, 0.33, 0.39)	(0.16, 0.20, 0.26)	(0.24, 0.28, 0.32)	(0.29, 0.33, 0.39)	(0.14, 0.18, 0.24)	(0.25, 0.28, 0.30)
EE	(0.13, 0.17, 0.21)	(0.29, 0.33, 0.39)	(0.04, 0.06, 0.07)	(0.21, 0.26, 0.30)	(0.28, 0.33, 0.40)	(0.05, 0.06, 0.07)
ISF	(0.13, 0.17, 0.21)	(0.09, 0.13, 0.17)	(0.29, 0.33, 0.38)	(0.05, 0.07, 0.11)	(0.10, 0.15, 0.20)	(0.31, 0.33, 0.36)

$l_{i_{n_{i}}}^{* j_{m_{j}}} = \frac{l_{i_{n_{i}}}^{j_{m_{j}}}}{l_{i_{n_{i}}}^{j_{m_{j}}} + \sum_{a = 1}^{2} \sum_{\begin{matrix} n_{k} = 1 \\ i_{n_{k}} \neq i_{n_{i}} \end{matrix}}^{3} u_{a_{n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (4) $m_{i_{n_{i}}}^{* j_{m_{j}}} = \frac{m_{i_{n_{i}}}^{j_{m_{j}}}}{\sum_{a = 1}^{2} \sum_{n_{k} = 1}^{3} m_{a_{n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (5) $u_{i_{n_{i}}}^{* j_{m_{j}}} = \frac{u_{i_{n_{i}}}^{j_{m_{j}}}}{u_{i_{n_{i}}}^{j_{m_{j}}} + \sum_{a = 1}^{2} \sum_{\begin{matrix} n_{k} = 1 \\ i_{n_{k}} \neq i_{n_{i}} \end{matrix}}^{3} l_{a_{n_{k}}}^{j_{m_{j}}}}, \forall i, j, n_{i}, m_{j}$ (6)

NP –Phase 2.

Based on the weighted fuzzy supermatrix, the fuzzy global weights $\tilde{w} = (w^{l}, w^{m}, w^{u})$ are calculated using the methodology proposed in Chen and Huang [49]. Their methodology involves solving the FANP by inverse matrix, which is extended from solving the ANP by inverse matrix. However, with this method, unlike ANP, FANP requires a non-trivial non-linear optimization model to be solved to compute the inverse matrix.

Let I be the identity matrix, e = [1, 1, …, 1] and set $\tilde{P} = {\tilde{Π}}^{T}$ . The aim is to find ${\tilde{G}}^{- 1}$ which satisfies $\tilde{G} {\tilde{G}}^{- 1} = \tilde{I}$ where $\tilde{G} = (I - \tilde{P} + {ee}^{T})$ . Then, the fuzzy global weights are each column sum of ${\tilde{G}}^{- 1}$ .

Let ${\tilde{G}}^{- 1}$ be a matrix that is composed of triangular fuzzy numbers $({\tilde{G}}_{ij}^{l^{- 1}}, {\tilde{G}}_{ij}^{m - 1}, {\tilde{G}}_{ij}^{u - 1})$ , ${\tilde{G}}^{l - 1}$ the matrix of ${\tilde{G}}_{ij}^{l^{- 1}}$ values, ${\tilde{G}}^{m - 1}$ the matrix of ${\tilde{G}}_{ij}^{m - 1}$ values, and ${\tilde{G}}^{u - 1}$ the matrix of ${\tilde{G}}_{ij}^{u^{- 1}}$ values. Initially, ${\tilde{G}}^{m - 1}$ is calculated as follows: ${\tilde{G}}^{m - 1} = {(I - {\tilde{P}}^{m} + {ee}^{T})}^{- 1}$ (7)

In order to calculate ${\tilde{G}}^{l - 1}$ and ${\tilde{G}}^{u - 1}$ the following non-linear optimization problem similar to Chen and Huang [49] is solved: $min \sum_{i = 1}^{n} \sum_{j = 1}^{n} {\tilde{G}}_{ij}^{u^{- 1}} - {\tilde{G}}_{ij}^{l^{- 1}}$ (8)

subject to: $(I - R + {ee}^{T}) {\tilde{G}}^{u - 1} \geq I + ɛ$ (9) $(I - R + {ee}^{T}) {\tilde{G}}^{l - 1} ⩽ I - ɛ$ (10) ${\tilde{P}}^{l} ⩽ R ⩽ {\tilde{P}}^{u}$ (11) ${\tilde{G}}^{l - 1} ⩽ {\tilde{G}}^{m - 1} ⩽ {\tilde{G}}^{u - 1}$ (12)

${\tilde{G}}^{l - 1}$ , ${\tilde{G}}^{u - 1}$ , $R \in ℝ^{nxn}$ are matrices of decision variables. n reflects the number of criteria considered. The objective function (Equation (8)) minimizes the spread of the resulting ${\tilde{G}}^{- 1}$ . In Equations (9) and (10), ɛ parameter is added to relax the strict inequalities. In Equation (11), the values of R is bounded between ${\tilde{P}}^{l}$ and ${\tilde{P}}^{u}$ . Equation (12) is added to guarantee the results are triangular fuzzy numbers.

According to the solution of the optimization model, the lower and upper values of the fuzzy global weights are calculated as follows: $w_{i}^{l} = \sum_{k = 1}^{n} {\tilde{G}}_{ki}^{l^{- 1}}, i = 1, \dots, n$ (13) $w_{i}^{m} = \sum_{k = 1}^{n} {\tilde{G}}_{ki}^{m^{- 1}}, i = 1, \dots, n$ (14) $w_{i}^{u} = \sum_{k = 1}^{n} {\tilde{G}}_{ki}^{u^{- 1}}, i = 1, \dots, n$ (15)

In the optimization model, the objective function is linear, but the first two constraints (Equations (9) and (10)) are non-linear. Therefore, there is no guaranteed method to acquire a global optimal solution to this problem. In this particular application, generalized reduced gradient method is utilized to solve the problem, where ɛ = 10^-2 and the initial solution to G was ${\tilde{G}}^{m}$ , initial solutions to both ${\tilde{G}}_{ij}^{l^{- 1}}$ , ${\tilde{G}}_{ij}^{u^{- 1}}$ were ${\tilde{G}}_{ij}^{m^{- 1}}$ , since the global optimal solution is expected to be around ${\tilde{G}}^{m}$ and ${\tilde{G}}_{ij}^{m^{- 1}}$ as the aim is to reduce the spread from ${\tilde{G}}_{ij}^{m^{- 1}}$ . The resulting ${\tilde{G}}^{- 1}$ matrix is presented in Table 5.

Table 5

Resulting ${\tilde{G}}^{- 1}$ matrix

L	BK	DSL	BR	EE	ISF
LHL	(1.09, 1.10, 1.10)	(–0.18, –0.18, –0.18)	(–0.09, –0.09, –0.09)	(–0.28, –0.28, –0.28)	(–0.17, –0.17, –0.17)	(–0.21, –0.21, –0.21)
BK	(–0.06, –0.06, –0.06)	(1.03, 1.03, 1.03)	(–0.15, –0.15, –0.15)	(–0.3, –0.3, –0.3)	(–0.15, –0.15, –0.15)	(–0.22, –0.22, –0.22)
DSL	(0.05, 0.05, 0.05)	(–0.35, –0.35, –0.35)	(1.12, 1.12, 1.13)	(–0.2, –0.2, –0.2)	(–0.2, –0.2, –0.2)	(–0.26, –0.26, –0.26)
BR	(–0.29, –0.29, –0.29)	(–0.18, –0.18, –0.18)	(–0.2, –0.2, –0.2)	(1.05, 1.06, 1.06)	(–0.02, –0.02, –0.02)	(–0.21, –0.21, –0.21)
EE	(–0.32, –0.32, –0.32)	(–0.08, –0.08, –0.08)	(–0.27, –0.27, –0.27)	(–0.11, –0.11, –0.11)	(1.04, 1.04, 1.04)	(–0.1, –0.1, –0.1)
ISF	(–0.32, –0.32, –0.32)	(–0.05, –0.05, –0.05)	(–0.29, –0.29, –0.29)	(0.02, 0.02, 0.02)	(–0.3, –0.3, –0.3)	(1.12, 1.12, 1.12)

The ${\tilde{G}}^{- 1}$ matrix is processed based on Equations (13), (14) and (15) to acquire the fuzzy global weights (second column of Table 6). However, the crisp global weights are required to evaluate the countries. The crisp values of fuzzy global weights are computed by Equation (16) [53] and presented in the third column of Table 6.

Table 6

Fuzzy and crisp global weights

Criteria	Fuzzy global weights	Crisp global weights
Long and healthy life	(0.15, 0.164, 0.169)	0.162
Knowledge	(0.186, 0.199, 0.206)	0.198
A decent standard of living	(0.122, 037, 0.142)	0.135
Basic requirements	(0.167, 0.18, 0.187)	0.179
Efficiency enhancers	(0.187, 0.201, 0.207)	0.199
Innovation and	(0.108, 0.118, 0.127)	0.118
sophistication

$w_{i} = \frac{w_{i}^{l} + 2 w_{i}^{m} + w_{i}^{u}}{4}, i = 1, \dots, n$ (16)

Finally, the country scores are calculated with the crisp global weights. The criteria data of the selected 45 countries are from the 2015 HDI data [21] and 2015 GCI data [22]. For the calculation of countries’ scores, GCI subindexes and HDI dimensions data are standardized to [0,1] interval. FANP scores are presented in Table 7.

Table 7

Countries: Score (rank)

Country	HDI	GCI	FANP	DEA-1-HDItoGCI	DEA-2-GCItoHDI
Algeria	0.749 (26)	3.967 (35)	0.391 (34)	0.806 (43)	1 (1–16)
Argentina	0.822 (20)	3.793 (37)	0.479 (26)	0.759 (44)	1 (1–16)
Australia	0.936 (3)	5.149 (12)	0.847 (10)	0.964 (23)	1 (1–16)
Austria	0.903 (12)	5.118 (14)	0.799 (12)	0.925 (29)	0.98 (25)
Bangladesh	0.592 (39)	3.763 (38)	0.253 (40)	0.902 (33)	0.939 (29)
Belgium	0.913 (10)	5.201 (11)	0.822 (11)	0.939 (28)	0.988 (22)
Brazil	0.757 (25)	4.078 (33)	0.469 (28)	0.897 (35)	0.912 (33)
Canada	0.92 (7–8)	5.308 (9)	0.857 (8)	0.995 (14)	0.991 (18)
China	0.743 (28–29)	4.889 (17)	0.589 (20)	1 (1–12)	0.896 (37)
Colombia	0.742 (30)	4.278 (30)	0.481 (25)	0.894 (36)	0.91 (34)
Egypt	0.691 (34)	3.66 (41)	0.327 (38)	0.813 (42)	0.907 (35)
Ethiopia	0.451 (45)	3.745 (39)	0.137 (45)	1 (1–12)	1 (1–16)
France	0.898 (13–14)	5.128 (13)	0.798 (13)	0.947 (27)	0.989 (21)
Germany	0.933 (4)	5.529 (3)	0.899 (2)	1 (1–12)	1 (1–16)
India	0.627 (38)	4.311 (27)	0.382 (36)	0.999 (13)	0.817 (43)
Indonesia	0.686 (35)	4.522 (20)	0.476 (27)	0.985 (16)	0.81 (45)
Italy	0.876 (16)	4.458 (22)	0.658 (18)	0.834 (41)	1 (1–16)
Japan	0.905 (11)	5.466 (5)	0.855 (9)	1 (1–12)	1 (1–16)
Kenya	0.578 (40)	3.851 (36)	0.292 (39)	1 (1–12)	0.85 (39)
Mexico	0.767 (24)	4.294 (29)	0.514 (24)	0.891 (37)	0.933 (30)
Morocco	0.655 (37)	4.165 (32)	0.39 (35)	0.973 (18)	0.93 (31)
Netherlands	0.926 (6)	5.505 (4)	0.893 (4)	0.987 (15)	0.985 (23)
Nigeria	0.527 (43)	3.46 (43)	0.154 (44)	1 (1–12)	0.829 (42)
Norway	0.948 (1)	5.406 (8)	0.897 (3)	0.97 (19)	1 (1–16)
Pakistan	0.551 (41)	3.445 (44)	0.189 (41)	0.963 (24)	1 (1–16)
Peru	0.745 (27)	4.21 (31)	0.466 (29)	0.891 (38)	0.922 (32)
Philippines	0.693 (32)	4.391 (24)	0.456 (30)	0.973 (17)	0.834 (41)
Poland	0.855 (18)	4.493 (21)	0.641 (19)	0.907 (32)	1 (1–16)
Russia	0.813 (21)	4.439 (23)	0.58 (21)	0.923 (30)	1 (1–16)
Saudi Arabia	0.854 (19)	5.066 (15)	0.7 (16)	0.969 (21)	0.99 (19)
South Africa	0.692 (33)	4.386 (25)	0.456 (31)	1 (1–12)	0.868 (38)
South Korea	0.898 (13–14)	4.987 (16)	0.781 (15)	0.952 (26)	0.985 (24)
Spain	0.885 (15)	4.587 (19)	0.697 (17)	0.889 (39)	1 (1–16)
Sweden	0.929 (5)	5.435 (6)	0.881 (6)	0.969 (22)	0.99 (20)
Switzerland	0.942 (2)	5.759 (1)	0.95 (1)	1 (1–12)	1 (1–16)
Tanzania	0.528 (42)	3.569 (42)	0.168 (42)	0.911 (31)	0.816 (44)
Thailand	0.741 (31)	4.642 (18)	0.543 (22)	0.97 (20)	0.899 (36)
Turkey	0.783 (22)	4.372 (26)	0.535 (23)	0.901 (34)	0.952 (28)
Uganda	0.505 (44)	3.661 (40)	0.163 (43)	1 (1–12)	0.841 (40)
Ukraine	0.743 (28–29)	4.033 (34)	0.449 (32)	0.886 (40)	0.962 (26)
UAE	0.86 (17)	5.24 (10)	0.795 (14)	1 (1–12)	1 (1–16)
UK	0.918 (9)	5.434 (7)	0.865 (7)	1 (1–12)	0.998 (17)
USA	0.92 (7–8)	5.613 (2)	0.882 (5)	1 (1–12)	1 (1–16)
Venezuela	0.775 (23)	3.301 (45)	0.333 (37)	0.682 (45)	1 (1–16)
Vietnam	0.684 (36)	4.301 (28)	0.421 (33)	0.961 (25)	0.961 (27)

3.2 DEA model

DEA is a popular non-parametric data-oriented approach to assess the performance of a set of peer entities. Liu et al. [54], Emrouznejad and Yang [55] review various DEA applications in the literature. Cook and Seiford [56] report the DEA models in the literature as: constant returns to scale (CRS) [57], variable returns to scale (VRS) [58], additive [59], slacks-based measures [60], the Russell measure [61] and other non-radial models. Furthermore, Liu et al. [62] state that bootstrapping and two-stage analysis, undesirable factors, cross-efficiency and ranking, network DEA, dynamic DEA and slacks-based measure are the recent research fronts in the DEA methodology.

This study uses DEA to compare the countries based on their performance on converting human development to competitiveness and competitiveness to human development. Therefore, two DEA structures are designed: 1) DEA-1-HDItoGCI; INPUT: HDI dimensions, OUTPUT: GCI subindexes, 2) DEA-2-GCItoHDI; INPUT: GCI subindexes, OUTPUT: HDI dimensions.

Countries operate at different scales. Additionally, the overall goal in this study’s scope is output enhancement instead of input reduction. Thus, an output-oriented variable returns to scale (VRS) model is fitting for this study. Suppose that there are n decision making units (DMUs), where each DMU_j, j = 1, 2, ... , n has the observed values x_ij of inputs (i = 1, 2, …, m) and y_rj of outputs (r = 1, 2, …, s). Then, the VRS model in its output-oriented envelopment form is formulated as: $max Φ_{0} + ɛ (\sum_{i = 1}^{m} s_{i}^{-} + \sum_{r = 1}^{s} s_{r}^{+})$ $s . t . \sum_{j = 1}^{n} x_{ij} Λ_{j} + s_{i}^{-} = x_{i 0}, i = 1, 2, \dots, m$ $\sum_{i = 1}^{m} y_{ij} Λ_{j} - s_{r}^{+} = Φ y_{r 0}, r = 1, 2, \dots, s$ $\sum_{j = 1}^{n} Λ_{j} = 1$ (17) $Λ_{j} \geq 0, j = 1, 2, \dots, n$ $s_{i}^{-} \geq 0, \forall i$ $s_{r}^{+} \geq 0, \forall r$ where $s_{i}^{-}$ are slack and $s_{r}^{+}$ are excess variables. ɛ > 0 is a non-Archimedean element defined to be smaller than any positive real number. A specific DMU₀ is efficient if Φ₀ = 1 and $s_{i}^{-} = s_{r}^{+} = 0$ . DMU₀ is weakly efficient if Φ₀ = 1 and either $s_{i}^{-} \neq 0$ or $s_{r}^{+} \neq 0$ . Otherwise, DMU₀ is inefficient.

In this study, countries are the DMUs. The DEA models use the same data used in the FANP model. The minor difference is that a 3-year time lag is considered to incorporate the possible time delays in the conversions. As such, DEA-1’s inputs are 2012 HDI dimensions and its outputs are 2015 GCI subindexes, whereas DEA-2’s inputs are 2012 GCI subindexes and its outputs are 2015 HDI dimensions. Accordingly, previously selected 45 countries’ 2012 and 2015 HDI and GCI data [21, 22] are used. The models are then solved using the CPLEX solver in the General Algebraic Modeling System (GAMS). The DEA results are given in Table 7’s last two columns.

DEA’s discrimination performance worsens if the number of DMUs are less than the number of inputs and outputs [63]. Our study does not suffer from this, since we consider a total of 6 inputs and outputs while each model has 45 DMUs. Moreover, index data might cause problems for DEA; however, it is acceptable if all the data is of index type [64]. In our study, both input and output features are indexes. As such, our case is admissible.

4 Results and discussion

Weighted fuzzy supermatrix midvalues (Table 4) show that both “being knowledgeable” and “a decent standard of living” have the most impact on “long and healthy life” followed by “efficiency enhancers”. “Being knowledgeable” is mostly affected by “long and healthy life” with “efficiency enhancers” as its secondary most impactful factor. A decent standard of living” is mostly influenced by “long and healthy life”. Furthermore, “basic requirements” is mostly affected by “efficiency enhancers” and secondarily by “being knowledgeable”. “Being knowledgeable” and “basic requirements” influence “efficiency enhancers” the most. “Basic requirements” followed by “being knowledgeable” have the most impact on “innovation and sophistication factors”.

Based on the crisp global global weights (Table 6), the most significant criteria in human development and competitiveness relation are “knowledge” dimension of HDI and “efficiency enhancers” of GCI. On the other hand, “a decent standard of living” and “innovation and sophistication” have the least impact. The criteria “long and healthy life” and “basic requirements” are observed to have mediocre impact compared to the others. In general, both human development dimensions and competitiveness subindexes clusters are not observed to be dominating the other.

Furthermore, average FANP score of countries is 0.569 with a minimum of 0.137 and a maximum of 0.95. Top 20% of countries have a score higher than 0.855, whereas the lowest 20% of countries have scores below 0.33. Switzerland, Germany and Norway are the top 3 performers while Ethiopia, Nigeria and Uganda are the worst.

Also, FANP, HDI and GCI rankings are compared. Table 7, first to third columns, shows selected countries’ FANP, HDI and GCI rankings respectively. The absolute difference between FANP and HDI ranking has an average of 2.73 with minimum 0 and maximum 14, whereas the absolute difference average between FANP and GCI rankings is 3.1 with the difference being minimum 0 and maximum 11. With FANP, 2 countries’ rankings were worsened in comparison to both HDI and GCI, whereas for 2 countries it was improved. Additionally, Fig. 2 shows the rankings of the countries in HDI and GCI based on their FANP rankings. Overall, it is observed that ranking based on FANP score is consistent with the HDI and GCI rankings.

Fig. 2

FANP ranks vs HDI and GCI ranks.

According to the DEA results (Table 7), in DEA-1-HDItoGCI model China, Ethiopia, Germany, Japan, Kenya, Nigeria, South Africa, Switzerland, Uganda, United Arab Emirates (UAE), United Kingdom (UK) and United States of America (USA) are found to be efficient. Therefore, 73% of countries are inefficient. Overall, the average efficiency is 0.94 with a minimum of 0.68. Upper 80% of countries have more than 0.890 efficiency score. India (0.9993) and Canada (0.995) have efficiency scores of almost 1. It should be noted that a DMU is efficient if it has a minimum input value for any input feature or a maximum output value for any output feature [65]. In this case, it is observed that Nigeria and Ethiopia have minimum values in inputs whereas Switzerland and USA have maximum values of output. On the other hand, the efficient countries form reference sets for the inefficient ones as elements of efficient frontier. Efficient countries being an element of multiple reference sets is an indicator of good DMU performance [66]. In that regard however, Ethiopia (20), USA (18) and Switzerland (16) perform well in comparison to Nigeria (4). Additionally, Japan (1), Germany (0) and Kenya (0) have the lowest performance in the context of reference sets.

In DEA-2-GCItoHDI model; Algeria, Argentina, Australia, Ethiopia, Germany, Italy, Japan, Norway, Pakistan, Poland, Russia, Spain, Switzerland, UAE, USA and Venezuela are efficient. Inefficient countries are 64% of the whole group. Minimum efficiency is 0.81 and the average is 0.95. Top 80% of countries are above 0.896. UK (0.998), Canada (0.991), Saudi Arabia (0.9904) and Sweden (0.9901) are the closest to efficiency score of 1. It is to be noted that Pakistan and Algeria have minimum values in input features while Germany, Japan and Norway have maximum values in output features. Algeria (12) and Norway (6) performs well regarding the reference sets while Pakistan (2), Japan (2) have low values. Germany (0) however, is in no reference set like Ethiopia (0).

In both DEA models, there are no weakly efficient countries. Countries are either efficient or inefficient. Germany, Japan, UAE and USA are efficient in both models, whereas 51% of countries are inefficient in both.

Lowest ranked countries (e.g. Ethiopia) and highest ranked countries (e.g. Switzerland and Norway) in FANP are efficient in the DEA models. This stems from the fact that very low (or very high) inputs and outputs may result in high efficiency. However, DEA-1 and DEA-2 results may differ heavily when the country’s HDI and GCI rankings are apart. For example, Venezuela’s GCI is very low compared to its HDI, therefore, it is efficient in DEA-2. However, in DEA-1 where GCI is the input, its ranking is very low.

In the next step, FANP results, DEA model results and HDI, GCI scores are compared. Their correlations are examined (Table 8). Correlations between FANP results and HDI and GCI are very high as expected. In comparison to DEA-1, DEA-2-GCItoHDI is more correlated to FANP results, HDI and GCI. Therefore, DEA-2 model can be acknowledged as more accurate and reliable, since the countries’ efficiency scores on the conversion of their GCI to HDI is more related to their combined human development and competitiveness score (i.e., FANP result). Thus, it is favorable to recognize that converting GCI to HDI is more crucial for the countries than the reverse. The effect of competitiveness on human development is more significant than the effect of human development on competitiveness. Therefore, the countries can enhance their human development by improving their competitiveness level.

Table 8

Correlations

	HDI	GCI	DEA-1-HDItoGCI	DEA-2-GCItoHDI
FANP	0.956	0.956	0.254	0.594
HDI		0.836	–0.024	0.671
GCI			0.491	0.458
DEA-1-HDItoGCI				–0.206

Finally, we investigated the DEA-2-GCItoHDI results to develop guidance for the inefficient countries. The efficient frontiers are presented for each inefficient country, which consists of specific efficient countries. In this sense, a set of efficient countries are provided as possible role models for an inefficient country. Additionally, the scenario, in which the inefficient countries were to be efficient, is analyzed. This way, their potential human development levels they would achieve by efficiency are revealed. Inefficient countries were projected into the efficient frontier based on their computed efficiencies, slacks in DEA-2 model and current output values, i.e. their HDI [67]. These findings are presented in Table 9. For instance, Turkey is an inefficient country according to DEA-2 model with a score of 0.952. Its efficient frontier is Algeria, Italy, UAE and Venezuela. In the 2015 data, its current HDI dimension values are 0.854 (LHL), 0.683 (BK), 0.822 (DSL) with the composite index HDI being 0.783. The country is projected into the efficient frontier with the slack values in output-related constraints in addition to the efficiency score and output values. That is, if it were to be efficient it would improve its HDI dimension values to 0.898 (LHL), 0.750 (BK) and 0.864 (DSL), which translates to 5.09%, 9.75% and 5.09% of respective improvements. Additionally, potential composite HDI index through geometric mean is computed to be 0.834 with these improvements [68]. As a result, an advancement of 6.5% is possible in terms of human development. It is observed that average possible improvement in such a way is 15.9% with a minimum of 0.8% and a maximum of 48.5%. Sweden, France and UK have the least improvement potential, whereas Tanzania, Nigeria and Uganda have the most.

Table 9

Efficient frontiers and potential improvements in human development

Country	Efficient frontier	Current HDI	Potential HDI	Change in %
Austria	Australia, Italy, Norway, Switzerland	0.903	0.921	2.0%
Bangladesh	Algeria, Italy, Venezuela	0.592	0.789	33.3%
Belgium	Argentina, Australia, Italy, Norway, USA	0.913	0.924	1.2%
Brazil	Italy, Venezuela	0.757	0.850	12.3%
Canada	Australia, Italy, Norway, Spain, Switzerland	0.920	0.928	0.9%
China	Algeria, Spain	0.743	0.878	18.2%
Colombia	Algeria, Italy, Venezuela	0.742	0.831	12.0%
Egypt	Algeria, Italy, Venezuela	0.691	0.798	15.5%
France	Australia, Italy, Japan, Spain, Switzerland	0.898	0.908	1.1%
India	Italy, Venezuela	0.627	0.832	32.7%
Indonesia	Algeria, Italy, UAE, Venezuela	0.686	0.848	23.6%
Kenya	Italy, Venezuela	0.578	0.781	35.1%
Mexico	Algeria, Italy, Venezuela	0.767	0.847	10.4%
Morocco	Algeria, Italy, Spain	0.655	0.822	25.5%
Netherlands	Australia, Norway, Switzerland	0.926	0.940	1.5%
Nigeria	Pakistan, Venezuela	0.527	0.740	40.4%
Peru	Algeria, Italy, Spain, Venezuela	0.745	0.820	10.1%
Philippines	Argentina, Italy, Spain, Venezuela	0.693	0.837	20.8%
Saudi Arabia	Algeria, Norway, Russia, UAE, Venezuela	0.854	0.876	2.6%
South Africa	Argentina, USA, Venezuela	0.692	0.840	21.4%
South Korea	Australia, Japan, Spain	0.898	0.913	1.7%
Sweden	Australia, Italy, Norway, Switzerland	0.929	0.938	1.0%
Tanzania	Italy, Venezuela	0.528	0.784	48.5%
Thailand	Algeria, Italy, Spain	0.741	0.853	15.1%
Turkey	Algeria, Italy, UAE, Venezuela	0.783	0.834	6.5%
Uganda	Pakistan, Venezuela	0.505	0.686	35.8%
Ukraine	Argentina, Australia, Poland, Russia	0.743	0.831	11.8%
UK	Argentina, Australia, USA	0.918	0.925	0.8%

5 Conclusion

The bilateral relationship between human development and competitiveness is studied. FANP is used to investigate the bilateral effects between competitiveness and human development indicators. Two DEA models are developed and compared to find out which one is more appropriate. The results of both models are compared to investigate the direction of the relationship. We found that the effect of competitiveness on human development is more significant than the effect of human development on competitiveness. We conclude that competitiveness affects human development.

This study presents a composite index of human development and competitiveness, which is the result of the FANP. A new FANP approach is used, which is composed of two methods in the literature. In the first phase of the approach, the pairwise comparisons of the decision makers are transformed to weighted fuzzy supermatrix based on the proposed methodology of Wang and Elhag [50] suggested in Asan et al. [52]. Subsequently, the fuzzy supermatrix is processed using Chen and Huang’s [49] mathematical programming model to find the limiting distribution that gives the fuzzy global weights i.e. the importance weights of the criteria. The proposed approach does not defuzzify the inputs in the supermatrix. The results are provided as fuzzy sets such that it enables to model the uncertainties in the decision makers’ evaluations without losing information.

Moreover, the efficiency scores of countries on their success on converting competitiveness to human development and converting human development to competitiveness are calculated by using two different DEA models. When the results of FANP and DEA model are compared, it is revealed that the DEA model, where competitiveness is input and human development is output (i.e., DEA-2-GCItoHDI), is more similar to FANP result. Therefore, it is concluded that DEA-2 model is more accurate and reliable. Thus, the effect of competitiveness on the human development is more significant.

The results of FANP and DEA-2 provide useful information to compare the countries. In addition to the classical rankings and scorings (such as HDI, GCI, GDP per capita etc.), these two indices can guide the policy makers on their decisions to enhance the development of their countries.

A limitation is that the models use single year data. As future work, FANP can be applied to panel data to analyze the countries’ progress. To that end, DEA model with window analysis can be developed. Moreover, countries’ progress can be tracked with cluster analysis to examine the patterns. On the other hand, FANP model results are sensitive to the pairwise comparison judgments due to the subjectivity of the experts. Although it is acceptable to use index data in DEA if both input and output data are indexes, DEA models specific to interval data can be utilized in the future studies.

Footnotes

Appendix

Investigated countries and their respective HDI dimension and GCI subindex scores are given in Table A1.

The expert evaluations are acquired by questionnaire. Two samples are presented in Table A2 and A3. The numerical scale is translated to importance measures as: 1 (equal importance), 3 (moderately important), 5 (strongly more important), 7 (very strongly more important), 9 (extremely more important).

Acknowledgments

This study is supported by Istanbul Technical University, BAP. Project ID: SGA-2017-40636.

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