Identifying Strategic Development Objectives for African Countries Using Dominance-Based Rough Set Approach: The Poverty String Theory

The objective of this article is to expose the results of a research using Dominance-based Rough Set Approach (DRSA) to help African countries and international organizations (both non-governmental organizations and governmental organizations), to identify economical, sociological, political and technological strategic objectives for international development. We hope that the results of this research will aid politicians and leaders to prioritize African countries strategic development objectives according to political, economical, sociological and technological (PEST) needs. In this study we use 23 various indicators to classify all the African countries according to the following three different categories: [A] African countries that are doing well according to the selected indicators; [B] African countries that need support to acquire category A status; [C] African countries ranked the lowest and needing special support with regard to the criterion or criteria considered. The three categories are delimited by tertiles obtained from the average ranking of countries. The chosen criteria are measured in order to provide decision rules based on this classification. These decision rules thus focus on the political, economic, sociological and technological needs of countries with respect to improve their development and classification. We strongly believe that by targeting these identified needs, this research will help the development of African countries, target and prioritize International funding, evaluate economic growth and sociological improvements. Our results, from both the correlation matrix and DRSA, clearly demonstrate that top priority should be given to analphabetism, school life and reducing the amount of adolescents pregnancies in order to improve both economically and sociologHow to cite this paper: Marin, J.-C., Trudel, B. and Zaras, K. (2018) Identifying Strategic Development Objectives for African Countries Using Dominance-Based Rough Set Approach: The Poverty String Theory. Modern Economy, 9, 1262-1286. https://doi.org/10.4236/me.2018.97082 Received: May 23, 2018 Accepted: July 23, 2018 Published: July 26, 2018 Copyright © 2018 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access


Introduction
This is the first research of a series of three articles using a systematic approach using a combination of statistics and DRSA to help specific territories identifying strategic objectives to improve their development. The first article helps to determine strategic objectives for African countries for international development. The second uses the same methodology to determine strategic objectives for potential candidate countries for the European Union, more precisely with the case of the country of Bosnia-Herzegovina. The third will help identify poverty for all United Nations countries and strategic objectives for sustainable development.
The systematic approach was first presented for a large scale project in the Northern Region of the Province of Quebec (Canada). What we are proposing is a selection of statistical data taken from different census, the World Bank and various indexes. We categorize these variables using different perspectives (Political, Economical, Sociological and Technological) and rank all selected territories (Region, Province or Country) according to these perspectives. When information is missing, we compare states by weighting the average. The last step is to use DRSA to help determine decision rules and conditions for each specific territory. These conditions become strategic objectives in order to improve the territory's development compared to others.

Literature Review
There are several decision tools to help decision makers and leaders defining strategy and courses of action. Rough set theory, developed by Pawlak [1] [2] and by Pawlak and Slowinski [3], is a mathematical tool that is used to support decision-making processes in fields such as medicine, banking, engineering, learning, location selection, pharmacology, finance, market analysis and economics [4]- [11]. It was modified by Greco, Matarazo and Slowinski [12] and renamed the "Dominance-based Rough Set Approach" (DRSA) and later Zaras developed it for mixed data (deterministic, probabilistic and fuzzy) [13]. This In this paper, a statistical analysis is presented in Section 2. In this analysis we identify the significant correlations between considered indicators classified per perspectives (PEST). After, in Section 3, we apply DRSA to classify all the African countries with regard to the perspectives (PEST) and present decision rules for each category (countries classified as: A, B and C). Section 4 will propose a strategy map for each individual country, proposing strategic objectives and performance measures to improve and monitor the sustainable development of all African countries.

Political, Economic, Sociological and Technological Indicators
The data of the 23 variables considered in this research were obtained from the World Bank, the United Nations and the International Institute for Strategic Studies [14] [15] [16] during January and March 2018 period. They were divided into four perspectives: political, economic, sociological and technological (PEST) as summarized in Table 1. Several of these indicators were selected and converted per capita to avoid biases due to the size of the population. It is important to understand that some indexes are scales where a lower score is better and others are more appropriate when the specific subject has a higher score. Table 1 demonstrates each variable divided into perspectives, their definitions and arrows showing if a higher score or lower score is more appropriate.

Statistics
Using the various databases presented earlier, we were able to calculate each indicator for the 54 African countries. It is important to mention that we also added 4 indicators for our statistical portrait: % of type of religion per country (Christianity, Islam, Buddhism, Hinduism, Irreligion, Folk religions and Judaism), oil rents (% of GDP) and finally percentages of analphabetism male and female. Those variables were not included in the overall classification. Correlation is defined as a measure of the linear relationship between variables [17]. Researching the possibility of relationship between variables will help determine the relationships between the various perspectives (PEST). Since we do only want to check for relationship, and not to invest in understanding the behavior of a variable, we limited our research to correlation, instead of regression analysis.
All correlations presented in this research are significant at the 0.01 level (2-tailed). The correlation matrix is presented in Appendix B.

Relationship between the Various Indicators
Testing for significant relationship between two indicators according to: Null Hypothesis 0: There is no relation between the two indicators.
Alternative Hypothesis 1: There is relation between the two indicators.
Then, after reviewing the data, we reject or not the null hypothesis 0. Table 2 Table 3 is a summary of all the correlations for the Economical perspective. Using the correlation matrix, it is plausible that:   Table 4 is a summary of all the correlations for the Sociological perspective. Using the correlation matrix, it is plausible that:  GNP and GNI per capita, exports of goods and services, life expectancy for women and men and all technological variables. School life is negatively correlated to ease of doing business index, all the variables related to analphabetism and adolescent fertility; 5) Urban population is positively correlated with the GNP and GNI per capita, broad money, exports of goods and services, life expectancy for women and men, academic papers per capita and mobile phones. Urban population is negatively correlated to analphabetism for men; 6) Adolescent fertility is positively correlated with the analphabetism variables. It is negatively correlated to the global competitiveness index, GNI per capita, broad money, school life in years, life expectancy for women and men, academic papers per capita, internet subscriptions and fixed telephones; 7) Homicides index is positively correlated with unemployment and negatively correlated to life expectancy for men.  Table 5 is a summary of all the correlations for the Technological perspective.

Dependency between Technological Perspective and Other Variables
Using the correlation matrix, it is plausible that:

The Dominance-Based Rough Set Approach (DRSA)
Applied to Estimate the Strategic Developmental Goals of African Countries

Description
The following section presents the application of the Dominance-based Rough Set Approach (DRSA) in order to determine the strategic objectives of each African country and improve their overall classification. Our methodology consists of the following steps: First, all the African countries are classified per perspectives in category A, B or C: Category [A] African countries that are doing well according to the selected indicators; [B] African countries that need support to acquire category A status; [C] African countries ranked the lowest and needing special support with regard to the criterion or criteria considered. Table 6 demonstrates the evaluation of the 54 African countries with respect to the four conditional criteria as determined on the basis of each perspectives (PEST) and with respect to the decisional criterion. Second, decision rules are determined for all the variables on a first time, and on a second time individually on each perspective (PEST). Third, each African country could determine and prioritize its strategic objectives with regard to their respective variables and values.

Formulation of the Multi-Criteria Problems
The first issue was the ranking of the 54 countries on the basis of the 23 criteria measured by 23 indicators. Next, the same was done for each perspective on the basis respective criteria. It can be represented using the AXE model, where: A is a finite set of countries a i for i = 1, 2, …, 54. X is a finite set of criteria X k for k = 1, 2 ,…, 23 or X kj for k j = 1, 2,…, nj for each perspective j. E is the set of evaluations measured by indicators e ik with respect to criterion X k or indicators e ikj with respect to criterion X kj for each perspective j.
The ranking of countries was obtain using the weighted average rank method, in which the countries are ranked from the most to the least preferable in terms of each indicator in relation to each criterion. Next, we calculate for each country the weighted average rank in order to obtain the ranking of the countries with respect to a given perspective and overall. (In this study the weights of indicators are assumed equal.) For each perspective j, the weighted average of country i, where: w k is the weight of criterion k and w kj for perspective j; r ki is a rank of country i with respect to criterion k and r kij for perspective j.
Then, with the obtained classifications of 54 countries, overall and for each perspective, we have to group into three categories A, B and C, each containing 18 countries. The final overall classification of the 54 African countries according to the four perspectives is presented in Table 6.

Geographical Analysis of the Overall Classification Decision Table
When analysis the overall classification presented in Table 6, most countries listed in category C seem to be geographically in contact with one another (Sier-

The Decision Rules
The calculations were performed using 4eMka2 software, developed by the intelligent decision support systems laboratory (IDSS) at the computing science institute of the Poznan University of Technology. In the same manner we can obtain strategies for each perspective individually.  The same we can say about countries which belong to the class C. Rule 7 dictates that for those which GPN per capita is at least equal to 820$ is strategic objective which allow to classify this country to the class B at least.
For the sociological perspective, according to rules 8, 9 and 10, we can conclude that if in the country, the value of life expectancy women is at least equal to 68.71 years or homicide is at most equal to 1.85 and urban population is at least equal to 35.74% or analphabetism is at most equal to 11.5% and homicides is at most equal to 2.175 then this country is in the class A.
The same we can say about countries which belong to the class C. Rules 11,12 and 13 dictate that for those which life expectancy men is at least equal to 59.66 years or school life is at least equal to 12 years and life expectancy men is at least equal to 59.13 years or analphabetism is at most equal to 13.1% and life expectancy men is at least equal to 58.59 years are strategic objectives which will allow to classified this country to the class B at least.

Strategic Decision-Making
This section demonstrates how to apply the decision rules for each country in order to develop strategic objectives and performance measures based on the data provided by the decision rules. Each country categorized overall as [C] (African countries ranked the lowest and needing special support with regard to the criterion or criteria considered) are provided with targets based on the decision rules that apply. In order to improve strategically, each country in category C must be interested in the decision rules listed in category B (Decision ≥ B) in the overall evaluation described in Table 7. For countries in category B, they must be interested in the decision rules listed in category A (Decision ≥ A). Table 9 describes all the strategic objectives and targets for all the countries classified in category C. Table 10 describes all the strategic objectives and targets for all the countries classified in category B. All countries may decide to evaluate each perspective individually and apply the same process to determine more specific strategic objectives in order to improve their socio-economic situation.
Appendix C shows all the strategic objectives for the various perspectives.

Poverty String Phenomenon
With the help of the statistical data, we classified all the African countries in tions may now target their investments and know precisely where the development is required and by how much it is required to be improved or reduced.
When analyzing the African map in Appendix A and all the classification results, we can clearly observe that most countries in category C are, in majority, geographically touching one another. The opposite is the same as wealth seems to be also grouped. Therefore, it seems that both wealth and poverty spread like

Limitations of the Research
This research did not include environmental statistics for each country or cultural indicators such as religion percentages. Since most countries in category C are along the same latitude, climate may play an important role and impact poverty.

Future Research
The original data collection included the percentages of all the different religions within each African country. The researchers understand the sensitivity of the topic discussed in this paragraph. The purpose was to integrate religion since it affects greatly the culture of a nation, its history, laws and traditions. Understanding the importance of religion in all aspect of international relations, politics and sociology, we propose that further research, with the help of sociologists, is needed to study the correlations found between the various PEST indicators and the various religion indicators found in all the African countries.

Appendix C
Strategic Objectives for the four perspectives (PEST) All Perspectives Objectives (