# Effects of the Hybrid CRITIC-VIKOR Method on Product Aspect Ranking in Customer Reviews
## 2 Literature Review and Theory
### CRITIC Weighting Method  
The CRITIC method generates objective weights for a criteria set based on the divergence in the scores of the alternatives in the decision matrix [35]. By analyzing the contrast intensity and conflict within the decision problem data, the CRITIC method derives robust and objective weights. It provides a systematic and reliable means of determining the importance of each criterion, taking into account the inherent variations and conflicts present in the decision data. It offers a more objective perspective, free from biases and subjectivity, which enhances the accuracy and validity of the criteria weighting process [30]. In particular, the contrast intensity of criterion \(j\) is measured by the standard deviation (\(\sigma_{j}\)after normalizing the performances of the alternatives. Equation (2) is employed for criteria normalization.  
\[r_{ij}=\frac{x_{ij}-x_{j}^{-}}{x_{j}^{+}-x_{j}^{-}}. \tag{2}\]  
Then, the measure of conflict (or deviation) between the corresponding criterion \(j\) and the other criteria is applied by using Equation (3)  
\[\sum_{k=1}^{n}(1-p_{jk}), \tag{3}\]  
where \(p_{jk}\) is the correlation coefficient between criteria \(j\) and \(k\), which is computed by using Equation (4):  
\[p_{jk}=\frac{\sum_{i=1}^{m}\left(r_{ij}-\overline{r_{j}}\right)\cdot\left(r_{ ik}-\overline{r_{k}}\right)}{\sqrt{\sum_{i=1}^{m}\left(r_{ij}-\overline{r_{j}} \right)^{2}\cdot\sum_{i=1}^{m}\left(r_{ik}-\overline{r_{k}}\right)^{2}}}. \tag{4}\]  
The assumption underlying this method is that interdependent criteria can potentially lead to misleading results [30]. This arises from the challenge of distinguishing decision alternatives when the criteria are similar to each other. To address this, a deviation measure is employed to assess the degree of discordance between a particular criterion and the remaining criteria, enabling a more accurate evaluation of the alternatives. Considering the interdependence among criteria and utilizing deviation measures, the proposed method offers a comprehensive and nuanced approach to criteria weighting. This helps overcome the limitations of traditional methods that may overlook the intricate relationships between criteria, ultimately leading to more reliable and meaningful rankings of product aspects.  
The amount of information emitted by criterion \(C_{j}\) is determined by composing both conflict and contrast intensity measures, as shown in Equation (5). The greater the value of \(C_{j}\), the larger the amount of information contained in criterion \(j\), and thus, the higher the relative importance of the criterion in the decision-making problem. The normalized objective weight of criterion \(j\) is calculated by using Equation (6).  
\[C_{j}=\sigma_{j}\cdot\sum_{k=1}^{n}(1-p_{jk}). \tag{5}\]  
\[w_{j}=\frac{C_{j}}{\sum_{k=1}^{n}C_{k}}. \tag{6}\]  
Previous studies have attempted to combine the CRITIC method with other subjective or objective approaches for weight assessment. For instance, [36] designed a hybrid CRITIC-VIKOR method to evaluate the ranking of initial public offerings. Moreover, [37] introduced CRITIC into COCOSO for use in a fuzzy DM environment. Additionally, [38] designed a hybrid PF CRITIC-COCOSO method for the 5G industry. To the best of our knowledge, no research has previously investigated the usability of the CRITIC approach for solving problems related to product aspect ranking.