## 2 Materials and Methods
### Basic Steps of TOPSIS Method  
Constructing the evaluation matrix. For the competitiveness evaluation system of French-speaking African countries, targeting 'n' evaluation objects (26 countries) and setting a certain factor layer as'm' evaluation indicators, a data matrix can be obtained. Here, 'a\({}_{\text{ij}}\)' represents the numerical value of the 'j'th evaluation indicator for the 'i'th evaluation object.  
\[A=\left\{a_{ij}\right\}m\times n\]  
Matrix normalization. The range standardization method is used for processing. The calculation formula for positive indicators is as follows:  
\[r_{ij}=\frac{a_{ij}-\underset{1\leq j\leq n}{\text{min}}a_{ij}}{\underset{1 \leq j\leq n}{\text{max}}a_{ij}-\underset{1\leq j\leq n}{\text{min}}a_{ij}}\]  
The calculation formula for inverse indicators is as follows:  
\[r_{ij}=\frac{\underset{1\leq j\leq n}{\text{min}}a_{ij}-a_{ij}}{\underset{1 \leq j\leq n}{\text{max}}a_{ij}-\underset{1\leq j\leq n}{\text{min}}a_{ij}}\]  
In the formula, \(\underset{1\leq j\leq n}{\text{max}}a_{ij}\) and \(\underset{1\leq j\leq n}{\text{min}}a_{ij}\), respectively, represent the maximum and minimum values of the indicator a\({}_{\text{ij}}\); r\({}_{\text{ij}}\) is the evaluation value of the jth indicator for the ith evaluation object after range standardization, where each element in r\({}_{\text{ij}}\) is within the range of 0 \(\leq\) r\({}_{\text{ij}}\)\(\leq\) 1 (i = 1, 2, \(\ldots\), n; j = 1, 2, \(\ldots\), m) [40]. This results in the normalized matrix:  
\[R=\left\{r_{ij}\right\}m\times n\]  
Determining weights using the coefficient of variation method:  
\[w_{ij}=\left.\sigma_{j}\middle/\sum_{j=1}^{m}\sigma_{j},\right.\left.\sigma_{ j}=D_{j}/\overline{r_{j}}\right.\]  
\[D_{j}=\sqrt{\left[\frac{1}{n}\sum_{i=1}^{n}\left(r_{j}-\overline{r_{j}} \right)^{2}\right]},\right.\left.\overline{r_{j}}=\frac{1}{n}\sum_{i=1}^{n}r_ {ij}\]  
In the formula, w\({}_{\text{ij}}\) is the weight of each indicator, \(\sigma_{\text{j}}\) is the coefficient of variation, D\({}_{\text{j}}\) is the standard deviation, and \(\overline{r_{j}}\) is the mean value of the jth indicator.  
Calculating the Euclidean distance between the actual values of the research object's indicators and the 'ideal values' and 'negative ideal values':  
\[d^{+}=\sqrt{\sum_{j=1}^{m}w_{ij}\times\left(r_{ij}-r_{j^{+}}\right)^{2}}\]\[d^{-}=\sqrt{\sum_{j=1}^{m}w_{ij}\times\left(r_{ij}-r_{j^{-}}\right)^{2}}\]  
In the formula, r\({}_{j^{+}}\) and r\({}_{j^{-}}\), respectively, represent the maximum and minimum values of indicator j among all the standardized evaluation objects.  
Calculating the measure value C of the competitiveness indicators for each African country:  
\[C_{i}=d_{i}^{-}/\left(d_{i}^{+}+d_{i}^{-}\right)\]  
Based on the TOPSIS method, the core competitiveness, basic competitiveness, and auxiliary competitiveness levels of various French-speaking countries in Africa are ranked, and the comprehensive competitiveness of each country is calculated and summarized according to the weight of each aspect.  
The value range of the calculation result is between 0 and 1. The larger the value, the higher the competitiveness level and the stronger the competitiveness, and vice versa. Generally, comprehensive competitiveness is divided into three levels: low level, medium level, and high level. Considering the relatively backward overall development level of African countries and the actual situation of African French-speaking countries, in order to more significantly reflect the competitiveness level of each country, this study adopts a 5-stage equal interval evaluation scheme for comprehensive competitiveness to classify the core competitiveness, basic competitiveness, auxiliary competitiveness, and comprehensive competitiveness calculation results of each country [41], and according to this standard, the order of the comprehensive competitiveness of African French-speaking countries is ranked. The specific classification scheme is shown in Table 1: