## 2 Background
### Quality Assessment Indicators  
This section presents a literature review of the most commonly utilized metrics for evaluating machine translations. The review was conducted following the methodology outlined in [42], utilizing the Scopus and IEEE Xplore databases. Below, we summarize the most prevalent automatic translation evaluation metrics identified in the scientific literature. BLEU (Bilingual Evaluation Understudy Score) [43] is among the most widely adopted metrics for assessing machine translations. It is a string-based metric, meaning it evaluates the structural alignment of words between the \"hypothesis\" translation and the \"reference\" translation. Specifically, BLEU measures the precision of n-grams between the two translations. This entails comparing contiguous sequences of n words to determine how many match those in the reference translation--beginning with single-word sequences and progressing to multi-word sequences up to the maximum defined n-grams. Furthermore, BLEU incorporates a length penalty to account for discrepancies in word count, penalizing excessively short translations through a \"brevity penalty\". The BLEU score for a translation is computed as follows:  
\[\text{BLEU}=BP\times\exp\left(\sum_{n=1}^{N}w_{n}\cdot\log p_{n}\right)\]  
where \(w_{n}\) represents the weight of each n-gram, \(p_{n}\) is the precision of the n-grams, and \(BP\) is the brevity penalty, which is defined as  
\[BP= \begin{cases}1&\text{if }c>r\\ \exp\left(1-\frac{r}{c}\right)&\text{if }c\leq r\end{cases} \]  
where \(c\) is the length of the hypothesis translation and \(r\) is the length of the reference translation. The BLEU score ranges from 0 to 1, with values closer to 1 indicating a higher degree of similarity to the reference translation and, consequently, better translation quality. However, BLEU has certain limitations, including its inability to account for context or semantic fluency, which may hinder its capacity to fully capture human translation quality. GLEU (Google Bilingual Evaluation Understudy Score) [44] is a string-based metric developed by Google that introduces key modifications to address issues related to the excessive use of common n-grams. Unlike BLEU, GLEU evaluates both the correct n-grams present in the translation and the incorrect ones absent in the reference translations, thereby offering a more balanced and appropriate assessment for machine learning-generated translations, particularly those produced by neural network-based machine translation systems. Similar to BLEU, GLEU relies on n-grams; however, in this case, the score is derived by computing the Precision and Recall of the translations as follows:  
\[\text{Precision}=\frac{\text{common n-grams}}{\text{total n-grams in the hypothesis}}=\frac{\alpha}{\beta_{H}} \tag{1}\]  
\[\text{Recall}=\frac{\text{common n-grams}}{\text{total n-grams in the reference}}=\frac{\alpha}{\beta_{R}} \tag{2}\]  
The final score assigned to the translation is the minimum between precision and recall:  
\[\text{GLEU}=\min\left(\frac{\alpha}{\beta_{H}},\frac{\alpha}{\beta_{R}} \right)=\frac{\alpha}{\max(\beta_{H},\beta_{R})} \tag{3}\]The result of applying this metric always falls within the range of 0 to 1, with higher values indicating better translation quality. Similar to BLEU, this metric relies exclusively on the string input it receives, meaning it does not assess the semantics or fluency of translations. CHRF (Character n-gram F-score) [45] is a string-based metric designed to address the limitations of previous evaluation methods. Instead of computing n-grams based on whole words, as BLEU does, CHRF evaluates the match of character n-grams. This characteristic makes CHRF particularly effective for morphologically rich languages and in scenarios where translated words may exhibit minor variations or spelling errors.