Assessment of the Sustainability of Countries at Worldwide

For the quantification and ranking of sustainablility reliable indicators are needed in the economic, social and environmental areas. For this, decision-making methods have been used to identify and rank the most important indicators. However, it is important to know which method to use, since this choice can modify the result. Therefore, two methods of multi-criteria decision making were evaluated: Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and TOPSIS with Hierarchical Analytical Process (AHP). It was observed a difference between the methods tested, where the TOPSIS-AHP method presented better performance as a function of the weights assigned by the specialists. The research results demonstrated which countries have a more balanced sustainable development in environmental, social and economic levels together. In this case, the three most sustainable countries are Switzerland, Sweden and Norway. Additionally this research shows which countries are more sustainable taking into account each indicator separately. It is expected that the results provide a basis in decision-making and it contribute to the best choices in all aspects of sustainability.


Introduction
Economic growth with the rational use of environmental resources and less social inequality is one of the premises of sustainable development.In this sense, countries seek to achieve this goal through the most diverse political, social, economic and environmental measures (Brundtland, 1985).Thus, assessing and quantifying sustainability in countries shows the overall situation of sustainable development.For this, sustainable development indicators (SDIs), which are important parameters used in the study of sustainability are used (Ciegs Ramanauskiene & Startiene, 2015).SDIs can be obtained for different countries around the world, allowing comparisons and establishing ordering ranks for sustainability models (Wass et al., 2014).Human Development Index (HDI), Sustainable Economic Welfare Index (SEWI), Genuine Progress Index (GPI) and the Ecological Footprint (EF) are indicators that show the degree of development of a country or region (Weidmann et al., 2015).Each indicator has variables which assume different values in different countries (Rametsteiner, Pülzl, Alkan-Olsson & Frederiksen, 2011;Shields, Solar & Martin 2002).Therefore, it is necessary to select and hierarchize the variables to use them in the ranking of SDIs.Once the variables have been established it is possible to prioritize the indicators by the degree of importance, where in the evaluation and quantification of sustainability, the SDIs define the position that a country occupies in relation to the level of sustainability (Spangenberg, Pfahl & Deller, 2002).SDI are used to collect, process and use information in order to make better decisions, drive more intelligent policy choices, measure progress and monitor feedback mechanisms in all pillars of sustainability.SDI is also used as an interaction between values and objectives, policy and science to increase the precision of the evaluation / quantification of various sustainability issues at different times (short, medium or long term) and spaces (international, national, regional, municipal or local) (Ramos & Caeiro, 2010).In indicators economic, social and environmental have been chosen because of their importance for the establishment of sustainable development.Besides that, it is important to know what are the main variables for sustainability in the indicators and whether they differ between countries.As there are several SDIs, the definition and prioritization of indicators is an important step in the analysis and comparison of sustainability.Some approaches have been used to determine variables and indicators.Among these techniques, the use of decision-making models has been used (Egilmez Gumus & Kucukvar, 2015).
Order Preference by Similarity to Ideal Solution (TOPSIS) and Analytic Hierarchic Process (AHP), generally used separately to classify sustainability at the sectorial level (Ertugrul & Karakaçoglu, 2009).However, these methods have been little used for SDIs analysis at the global level and interaction among SDIs.In addition, the use of TOPSIS-AHP together is still little explored in this type of analysis.Thus, this study aims to use different methods of multicriteria decision to define and prioritize variables into SDIs, also between the SDIs and through this, to achieve the ranking of the sustainability of the countries around the world.It measure sustainability performance through global metrics, compare rankings, using different decision-making methods, and verify differences and imbalances between degrees of sustainability among selected countries.In addition, the effectiveness of the TOPSIS-AHP model was tested for the ranking and prioritization of SDIs.In this context, three indicators were defined (economic, social and environmental) subdivided into 19 sustainability variables for 175 countries in the period 2013 and 2014 in order to assess and compare whether there is a sustainable development of these countries in the economic, social and environmental dimensions, when environmental conditions deteriorate every year.
The questions that guide the construction of this text were the following: Based on economic, social and environmental indicators, which countries are considered the most sustainable in the world?Is there a differentiation in the ranking between countries when analyzing the indicators separately?What are the main variables that impact differentiation for sustainability?Also, in order to corroborate with this general objective, the specific objectives are: To measure sustainability performance through global metrics, compare rankings, using different decision-making methods, and verify differences and imbalances between degrees of sustainability among selected countries.This article is organized as follows.This first section presents the introduction to the research, its context, the research question, and objectives.The next section presents the research methodology.The following section presents the results that were obtained and discusses the findings.Finally, the last section presents the most important conclusions and contributions of this work, along with implications for future research and for practice.

Materials and Methods
For this research, the database of the World Bank and the United Nations Development Programme (UNDP) were was used as variables of indicators for implementing global sustainability assessments.The research was based on use of two methods of Multicriteria Support: TOPSIS and AHP.TOPSIS is a method which has been widely used with a variety of goals in various areas of knowledge (Behzadian, Otaghsara, Yazdani & Ignatius, 2012).The basic principle of TOPSIS is to choose an alternative that is as close as possible to the positive ideal solution and as far as possible to the negative ideal solution.The ideal solution is formed by taking the best values achieved by the alternatives during the evaluation for each decision criterion, while the negative ideal solution is composed similarly, by taking the worst values.The application of TOPSIS method can be described as a series of successive steps which begin with the implementation of an original data matrix, which uses value criteria for each alternative, and then TOPSIS turns this original matrix into a matrix considered standardised (Bulgurcu, 2012).This technique has three steps.The first one concerns the calculation of the positive ideal solutions A* and negative ideal solutions A', as follows Eqs.(1-2): Positive ideal solution: A* = {v1*, ..., vn*}, where Negative ideal solution: A' = {v1 ..., vn'}, where Where: J and J' respectively represent the positive or negative variables.
The second step is the calculation of Euclidean distances, i.e., calculating the separation measure.This calculation of Euclidean distances between the benefits is then given by Eqs.(3-4): The separation of the positive ideal alternative: Similarly, the separation of the negative ideal alternative: With i = 1, …, m.The weights were used with values of wi = 1.
The third step of the TOPSIS method is the calculation of the relative proximity in relation to the ideal solution, as follows (Eq.5): Finally, after the completion of these TOPSIS steps the ranking is drawn up so that the data closest to the ideal solution is designated as the first place in the rankings and so on.The other method used was the AHP created in 1971 which is considered to be a multi-criteria method that permits the analysis of qualitative variables in a decision process (Aragonés-Beltrán, Chaparro-González, Pastor-Ferrando, & Pla-Rubio, 2014).
AHP develops a pair-wise comparison matrix on the basis of the criteria, and creates multiple square decision matrices, in which for each criteria and each alternative, a priority value is associated over the others under analysis, from a fundamental preference scale, the Saaty comparison scale (Table 1).If activity i receives one of the different designations above zero, when compared to activity j, then j has the reciprocal value when compared with i.

Rational
Reasons arising from the scale If the consistency has to be forced to obtain numerical values n, to complete the matrix Source: SAATY, T. L. (1991).
In order to put into practice and analyze the judgments, it is necessary to form n-square matrices and their related eigenvectors.Equation 6 is used to demonstrate the relationship between the decision matrix and the eigenvector row, which is equivalent to the importance of one of the criteria, or of one of the alternatives classified into one of the criteria.λ is the eigenvalues, and A is a square decision matrix of order m.
Equation 7 is used to calculate the amount of judgments required for each array. (7) Each judgment matrix must have its weighted matrix calculated by dividing the elements of the column of the matrix by the sum of the same elements.Next step is to calculate the priority vector (standardized weights), which is possible through averaging the elements of each row.The standard weight indicates which of the criteria or alternatives is the most important.After that, Consistency Index (CI) is calculated with reference to the maximum eigenvalues (λ max) obtained and the number of elements analyzed (n).Maximum eigenvalues is calculated by multiplying the matrix of judgments by the vector of priorities; this result is then divided by the vector of priorities (Saaty, 2008).
One of the most crucial points in the AHP method is checking the consistency of judgments made by experts in the pair wise comparisons.For a judgment to be consistent it must present reason of consistency (RC) below 10%, if the RC is higher than this it is necessary that the experts redo their analysis so that it can be used to create a priority scale.Equation 4 is used to calculate the CR, which takes into account the IC and the random consistency index (RI) (Eq.8).RI is determined by the number of elements as shown in Table 2.The SDIs and variables were chosen through the analysis of sustainable development carried out by the World Bank, PNUD and OECD whose data were obtained from European Union Statistics Office (Eurostat) and relevant (Luzzati & Gucciardi, 2015;Bohringer & Jochem, 2007;Distaso, 2007;Jingzhu & Opschoor, 1999).Tables 3, 4 and 5 detail the variables selected for each indicator of sustainable development and the scale of the positive ideal solution (the higher the better | and j the lower the better) used for the application of the TOPSIS method.Renewable fuels and waste comprise solid biomass, liquid biomass, biogas, industrial waste and municipal waste, measured as a percentage of total energy consumption.

↑
The choice of obtaining the selected indicators was based on available data of 2013 and 2014, and for the countries that did not have specific data for these periods, it was calculated as an average of previous years as of 2009 to characterize a reality closer to the present time.Thus, 175 countries were selected for the study.Some countries for which no data was available for some variables in economic, social and environmental indicators were displayed in the table index as zero and their indices were not considered in the application of the TOPSIS method.
In the TOPSIS method, the score for the criteria assumed that m were the countries and n the variables of the indicators, where the matrix was formed by m x n.The variables n can assume positive and negative values.Initially, a standardized matrix was built from on data from the 175 countries surveyed, some variables of certain countries were not available in the database, so the next steps of the method was done according to the data available for each country.Firstly, for weighted standardized decision matrix the weights were considered with the same value (= 1).It was necessary to determine the positive and negative ideal solution.In this case, the scale shown in tables 3, 4 and 5 was used and it was defined which variable should be calculated by "the higher value the better" or "the smaller value the better" to obtain the positive and negative ideal solutions.From there separation measures for each alternative were calculated.Standardized values of 19 variables were separated and calculated the positive and negative ideal alternative.Then the relative proximity was calculated to the ideal solution Ci*, sum of the ideal solutions and negative solutions already obtained.Thereby, it was possible to obtain the ranking of the countries taking into account each of its variables.
The use of AHP served for evaluation of the indicators and variables of sustainability, which are part of the model proposed.The structuring of the model for the AHP application was the following: 1 -Sustainability assessment of countries worldwide; 2 -Economic, Social and Environmental SIDs; 3 -Variables of each indicator (Figure 1).

Applic
The result countries.
(Table 6).Compared with Japan, ranked second, China has almost double the value of the indicator.It was observed that the difference in the value of the economic indicators between the first ten and the last ten is not very large, with the exception of China and Venezuela.Unlike the economic indicator, the social indicator shows a large difference between the top ten and ten last countries.This is evident when we compare Belgium, which occupies the tenth position with Botswana occupying the hundred and sixty sixth.Thereby, the social indicator of Belgium was 3.25 times higher than Botswana.In the environmental indicator the first five positions were occupied by African countries, while India, China and the USA occupied the last, penultimate and antepenultimate position respectively.
These countries were behind Cambodia, Nepal, Angola, Haiti, Ecuador, among others.However, when comparing the general indicator, we observed that the countries with the highest economic indicators remained in the top ten.China and Japan were first and second, respectively, in the general rank, just as they had been in the economic rank, while Venezuela was last in the two ranks.

Application of AHP Method
The AHP method assigns weights to each indicator and the variables that compose them (Table 7).The environmental indicator was the most important to sustainability with almost 50% of the total weight, while social and economic were second and third respectively.As a result, the variables of the environmental indicator were the most important, with emphasis on Forest area (10.03%),Fresh water withdrawal (9.36%) and CO 2 emissions (7.91%) which were the first three in the rank of intra and inter-indicator comparison.For the social indicator the intra-indicator Total health expenditure has large weight followed by Public expenditure on education and HDI while in inter-indicator ranking these variables occupied fourth, sixth and seventh positions.The economic indicator had the least weight in sustainability.Among its variables GDP per capita, GDP growth and Inflation were the most important within the economic indicator.However, because of the low weight of the indicator, these variables occupied the tenth, eleventh and fifteenth positions among all the variables.

Application of TOPSIS-AHP Method
With the TOPSIS-AHP method it was allowed to insert the weights of the indicators and their variables in the TOPSIS analysis, creating the weighted ranks for the countries.When we compared the two methods in relation to the rank of the countries for the general indicator, changes were observed (Table 8).The upper countries had an average value of 0.674 for the social indicator, while last countries had a value of 0.106 which represents a value 6 times higher for the top countries.Among the countries with the highest social indicator, Norway, United States, Switzerland, Denmark, Australia, Netherlands, Luxembourg, Sweden, Austria and Belgium achieved the best performances among the 175 countries in TOPSIS and TOPSIS-AHP, there the top five positions remained unchanged, while the Netherlands lost three positions and Luxembourg one; Sweden and Austria win two.There was no entry or exit in the group of ten countries with the highest social indicator.On the contrary, in the countries with the lowest social indicator, the change in TOPSIS has led to the exit of seven countries from the last positions, besides promoting the inversion of Mauritania and Lesotho in the last and penultimate positions.These two countries and Sudan remain in the last positions in both methods.
In the social indicators European continent was featured with eight countries among the top ten.In fact, social policies and greater state participation in various sectors of European society contribute to more social investments in relation to other economic ones.The few differences observed between the methods are due to the lower weight of this indicator for TOPSIS-AHP.However, for the countries at the bottom of the ranking, the weighting of the social variables changed the order of the countries.Unlike TOPSIS, in the TOPSIS-AHP method, it took occupation of the last ten positions only by African countries.In fact, most countries in the African continent have a lower standard of living, with economic crises, high infant mortality rates and consequently lower welfare level and social sustainability, especially in the variables evaluated.The use of the different methods also significantly modified the rank of countries as per the environmental indicator, especially among the ten best placed countries (Table 11).
experts, the other results were stable and without much oscillation.This result can also be considered as a starting point for the global analysis, since it reveals strengths and weaknesses of each country.The greatest difficulty in assessing sustainability is the challenge of exploring and analyzing a holistic system (Hardi & Zdan, 2000).For this author, a holistic view does not only require a vision of the complex economic, social and ecological systems, but also the interaction between these systems.

Conclusion
Comparing the two methods, it was evident that TOPSIS-AHP was more judicious due to the weights attributed to the qualitative variables by the specialists.However, because all the experts were from environmental areas, there was a bias towards higher importance of environmental variables in sustainability.Accordingly, AHP test showed that the environmental indicator is the most important for assessing sustainability at the expense of economic and social indicators.However, for a less biased analysis it would be necessary the opinion of experts from the three areas evaluated.In this way, there could be more debate about the weights of the economic and social areas for composition of matrix with weights.The largest discrepancy observed among SDI methods in relation to the other indicators was related to the fact that SDI is the sum of economic, social and environmental indicators.When there is strong correlation between the economic, social and environmental indicators, only one indicator cannot be held responsible for the global degradation.In fact, the three indicators together play a key role in improving the sustainability of countries and need to develop together.However, TOPSIS-AHP was a consistent method for ranking countries in the perspective of sustainability.This is a starting point for the overall analysis as it reveals the strengths and weaknesses of each country.Indeed, these results are a stimulus for developing countries to increasingly improve the issue of sustainable development and for other countries to seek the causes of their sustainability weaknesses in order to correct them.In addition, results of this study warn the governance of countries so that they can carry out effective measures in pursuit of a truly sustainable development, not focusing on only one of the indicators described in this work.In addition, we can consider that one implication for those responsible for guiding the countries' growth is the effective perception of the impact generated by the neglect of sustainability.Moreover, the purpose of using economic, social and environmental indicators in this study, although much discussed in recent years, is to present more current information on global sustainability, since we suffer daily with the impact generated, and it is possible to identify them in our daily lives.We can see the need for these economic, social and environmental pillars to be studied more and more in an integrated way, and no longer separated into categories, so that a sustainable assessment can be obtained and the deficient pillar corrected for balance.With that, we hope to contribute to the growth of actions and innovations where sustainable development is a priority, making it stronger for a truly sustainable planet.Accordingly, with the result and knowledge obtained in the development of this study, the following future works are suggested: • Identify the possibility of introducing new indicators and new variables that have not been evaluated in these studies; • Conduct a comparative study from time to time to present the countries that are really seeking sustainability; • One suggestion to continue this research is to carry out new studies using other methods of decision making;

•
We suggest applying AHP to other expert groups from different areas so that the main variables can be searched and identified from different points of view.

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Specifically for Brazil, the same study could be carried out considering the States and Municipalities, so that politicians can be attentive to sustainability in the economic, social and environmental trinomial.
last.The difference between the economic indicator between China and the other countries is high.

Table 2 .
Random Consistency Index (RI)Once completed the judgments, it is necessary to synthesize the priorities, and this can be achieved in two ways: Individual judgment aggregation (IJA) and individual priority aggregation (IPA) (Zu & Xu 2014).

Table 3 .
Economic indicatorsInflation measured by the consumer price index reflects the annual percentage change in the cost to the average consumer of acquiring a basket of goods and services that may be fixed or changed at specified intervals, such as yearly.GDP is the sum of gross value added by all resident producers in the economy plus any taxes on products and minus any subsidies not included in the value of the products.
Total reserves include monetary gold holdings, special drawing rights, reserves of IMF members held by the IMF and holdings of foreign exchange under the control of monetary authorities.The gold component of these reserves is valued at year-end (December 31) London prices.Data are in current US dollars.↑Table 4. Social Indicators

Table 5 .
Environmental indicators

Table 7 .
Rank of indicators and variables for intra-indicator and inter-indicator based on percentage of general weight to sustainability

Table 8 .
Comparative rank of TOPSIS and TOPSIS-AHP for top ten and last ten countries on general (sum of previous three) indicators

Table 10 .
Comparative rank of TOPSIS and TOPSIS-AHP for top ten and last ten countries on social indicators