## 4 Methodology
Table 3 shows how the raw information of the dataset is transformed into the form of triangular fuzzy numbers (TFNs) as a good alternative for handling this vague information. The TFNs consist of three parameters (\(a\), \(b\), \(c\)), with \(b\) being the most likely value and \(a\) and \(c\) being the minimum and maximum values, respectively. Thus, the first step in the methodology was to transform the responses into TFNs according to the default values shown in the table. Then, in the second step, mean TFNs were calculated for each segment of analysis, which covers diverse segmentation variables \(p\) (country, opinion on governmental intervention, firm size and stakeholders) and various categories \(s\) that correspond to each of them (e.g., Cyprus or Bulgaria for the country; and consumers or producers for the stakeholders' segments). Moreover, the mean TFNs were calculated separately according to the type of information \(q\) that should be included in the EU ecolabel for FAPs (e.g., environmental issues only, social and ethical issues apart from environmental issues, animal welfare issues apart from environmental issues, etc.). In this context, the mean TFN (\(\widetilde{A}\)) for a category \(s\) that corresponds to the segmentation variable \(p\) and is related to an issue \(q\) can be calculated as the mean of the TFN responses of the individuals 1 to \(n\) that are a part of that particular segment of analysis, as shown in Equation (1). \[\widetilde{A}=(a_{s,p,q},b_{s,p,q},c_{s,p,q})=(\frac{\sum\limits_{i=1}^{n}a_{s, p,q}}{n},\frac{\sum\limits_{i=1}^{n}b_{s,p,q}}{n},\frac{\sum\limits_{i=1}^{n}c_{s, p,q}}{n}) \tag{1}\]  
where \(s\): 1,..., \(s\); \(p\): 1,..., \(p\) and \(q\): 1,..., \(q\). In the third step, we clarified the TFN information matrix obtained in the previous step through a defuzzification process that transforms each of the elements of the matrix into crisp values (CVs). The CVs were calculated according to Equation (2) for simplicity and objectivity [57] and indicate the level of acceptance for the inclusion of a particular issue \(q\) in a hypothetical EU ecolabel by each category \(s\) that belongs to a segment \(p\). \[CV_{s,p,q}=\frac{a_{s,p,q}+2\times b_{s,p,q}+c_{s,p,q}}{4} \tag{2}\]  
where \(s\): 1,..., \(s\); \(p\): 1,..., \(p\) and \(q\): 1,..., \(q\). The fourth step consisted of determining the ideal (\(CV_{q}^{+}\)) and negative ideal (\(CV_{q}^{-}\)) solutions per issue \(q\), as the maximum and minimum CVs of all the segments of analysis, \begin{table}
\begin{tabular}{c c} \hline \hline
**Linguistic Terms** & **Fuzzy Number** \\ \hline I strongly disagree (1) & (0, 0, 30) \\ I disagree (2) & (20, 30, 40) \\ I do not know (3) & (30, 50, 70) \\ I agree (4) & (60, 70, 80) \\ I strongly agree (5) & (70, 100, 100) \\ \hline \hline \end{tabular} Source: Own elaboration.  
\end{table} 
Table 3: Triangular fuzzy numbers. Default values of linguistic terms. as shown in Equation (3). While the ideal solution maximizes the level of acceptance on the inclusion of each particular issue \(q\), the negative ideal solution minimizes it. \[CV_{q}=\left\{CV_{1,1,q},\ldots,CV_{s,p,q}\right\}\]  
where  
\[CV_{q}^{+}=\max_{q}(CV_{q})\text{ and }CV_{q}^{-}=\min_{q}(CV_{q}) \tag{3}\]  
where \(s\): \(1,\ldots,s\); \(p\): \(1,\ldots,p\) and \(q\): \(1,\ldots,q\). The fifth step, as shown in Equation (4), was to calculate the Euclidean distances of each category \(s\) of the segment of analysis \(p\) with respect to the ideal solutions. Because \(q=1\) represents the inclusion of environmental issues only, the CVs associated with it were not considered in the estimation of the synthetic indicator (SI). This way, the SI represents the level of acceptance for the inclusion of other issues apart from the environmental issues in the EU ecolabel; thus, a value closer to 1 would indicate a higher acceptance to include more issues apart from the environmental issues in the ecolabel for that segment of analysis, while the values closer to 0 indicate the opposite.