# Effects of the Hybrid CRITIC-VIKOR Method on Product Aspect Ranking in Customer Reviews
## 2 Literature Review and Theory  
### Types of Criteria Weighting Tasks in MCDM  
Criteria weighting is considered an essential stage in MCDM approaches, indicating the relative importance of each participating criterion in the decision-making process. The two weighting approaches for handling a criteria set in MCDM are the subjective and objective approaches [11; 16]. Subjective weighting depends on the judgments of decision makers who assign crisp values to each criterion and rank all criteria based on experience and knowledge. Then, mathematical methods are applied to evaluate the importance of each criterion. Several subjective weighting methods have been proposed in the literature, such as the simple attribute weighting technique [17], direct rating [18], and analytical hierarchy process (AHP) [19]. AHP, a subjective weighting method based on pairwise comparisons, is often used to evaluate the preferences of decision makers regarding a set of criteria, after which these preferences undergo a ranking process. AHP allows decision makers to decompose a decision problem into a hierarchy, such as a goal level, criteria level, or subcriteria level (lowest in the hierarchy). Pairwise comparisons between the pairs of criteria on the same level are performed on a scale of 1 to 9 [19]. Although AHP has gained acceptance from many researchers, it is constrained by limitations such as uncertainties in the judgments of decision makers [20]. Furthermore, the hierarchical structure of AHP requires the criteria to be independent of one another, which is not always true in real-world applications [21]. An advanced version of the AHP method proposed by [22] is the analytical network process (ANP). In ANP, the goal, criteria, and alternatives are formulated as a network structure to process the interdependencies among the criteria during the weighting process [13]. An essential step in the ANP procedure is for the decision maker to determine in advance the relative importance of the criteria. ANP also requires many more pairwise comparisons [23]. Furthermore, in the criteria weighting process, fuzzy set theory is incorporated into the judgments of decision makers, allowing them to quantitatively express the criteria as linguistic variables (i.e., _ordinary_, _important_, and _very important_) instead of using crisp values [24; 25; 26; 27]. AHP approaches are considered expert-dependent methods because the weights are determined by a decision group of \(K\) persons [28], and the final weight \(w_{j}\) for each criterion \(j\) is obtained by aggregating the fuzzy weights provided by the decision makers, as shown in Equation (1). Additionally, fuzzy weighting approaches have inert limitations that have been derived from the traditional assumption that the evaluation criteria must be considered independently. \[w_{j}=\sum_{i=1}^{k}w_{j}^{k} \tag{1}\]  
Objective weighting is highly independent of the judgments of decision makers, and the criteria weights can be determined automatically using mathematical models that utilize the known data in the decision matrix [11; 15]. Furthermore, in contrast to subjective approaches, objective approaches are more suitable for situations in which reliable subjective weights cannot be obtained [23]. The fuzziness of human judgments can be eliminated using the aforementioned approaches. Various objective measures have been proposed to mathematically evaluate the criteria weights. Examples include the entropy method of [PERSON] [29], which computes weights based on the degree of divergence in the performance of a criterion; the equal weight method [15], which considers the criteria as having importance; the criteria importance method that uses intercriteria correlation (i.e., the CRITIC method) [30], which computes the weights of the criteria based on correlation analysis to incorporate both the contrast intensity and conflict between the criteria; and the preference selection index method [31], which is based on the degree of convergence in the performance rating of each criterion.