## 3 Group Decision-Making with Consensus Based on Subjectivity and Sentiment Analysis
### Preference Extraction  
After initialising the decision-making process and obtaining the data, our method must apply sentiment analysis to obtain the experts' preferences for each of the alternatives. The reliability of the obtained preferences will also be calculated. This whole process is carried out through the following steps:  
1. Obtain the sentiment score: Once we have selected the relevant texts from each of the experts, sentiment analysis must be applied for each of them. To do this, we will use functions from the R Syuzhet package [37]. This package provides four sentiment  
Figure 4: Post elements. Figure 5: Example of a post in the social network X.  
dictionaries and a method to access the robust sentiment extraction tool developed in the Stanford NLP group. In addition, it allows the use of a dictionary that associates words with ten different emotions (anger, anticipation, disgust, fear, joy, sadness, surprise, trust, negative and positive) (see Figure 6). For our research we will only consider positive and negative, since our aim is to determine whether the expert is for or against each of the alternatives. 2. Obtain the polarity of the post: In this step, the method obtains the polarity of a post \(tw\), i.e., the positive or negative degree \(S_{tw}\) obtained from expert survey from the alternative of \(tw\) sensitive. The following expression is used: \[S_{tw}=\frac{N_{ptw}-N_{ntw}}{N_{ptw}+N_{ntw}}\] (3) where \(N_{ptw}\) refers to the number of positive words contained in \(tw\) and \(N_{ntw}\) the number of negative words. The result of this process is a numerical value in the range \([-1,1]\). The closer the result is to the value \(1\), the more evident the positivity of the post will be. Conversely, the closer the result is to \(-1\), the greater the disagreement with the alternative described. Finally, all those values close to \(0\) would imply that the expert has a neutral attitude towards the alternative, neither in favour nor against it. In Figure 7, a post analysis example result is shown graphically. The score for each post, as mentioned above, is in the range of \([-1,1]\), where \(1\) represents very positive polarity and \(-1\) very negative. Once the preference has been extracted, we change the domain of the value from the interval \([-1,1]\) to the interval \([0,1]\). To do this, we apply the following expression: \[P_{tw}=\frac{S_{tw}+1}{2}\] (4)
3. Calculating the reliability of preferences: Once the preference value has been obtained, we can calculate its associated reliability. For this, as we have already mentioned, we will analyse the number of positive and negative words associated with each alternative. Therefore, if the alternative has many more positive words than negative words associated with it or vice versa, this will mean that the reliability is high. Conversely, if the expert rates the alternative with a similar amount of positivity and negativity, then the expert's opinion regarding the alternative is unclear. Once the preference and its associated reliability value are obtained, we can create the Z-number representing the preference. For a clearer and more user-friendly representation of preferences that allows a more convenient analysis of expert opinion, we will use linguistic labels to represent each calculated preference value. We will associate each preference value with a linguistic label using the conversion described in the Table 1. Once the linguistic label representing the preference value has been obtained, the associated reliability value is calculated. To accomplish this, we use the following expression: \[Z=\left|\frac{N_{ptw}-N_{ntw}}{N_{ttw}}\right|\] (5) where \(N_{ptw}\) is the number of positive words, \(N_{ntw}\) the number of negative words and \(N_{ttw}=N_{ptw}+N_{ntw}\). The more extreme, i.e., the closer it is to \(1/-1\), either positive or negative, the more polarised the expression is and, therefore, the clearer the expert's positivity and negativity.