# Sustainable Treatment Techniques for Emerging Pollutants--The Case of Personal Hygiene Products
## 2 Materials and Methods
### Modified Saaty Method  
The modified Saaty methodology is a decision theory method that combines quantitative and qualitative criteria. It compares the different choices made by policy makers for each criterion, comparing the criterion with each choice in a similar way. To accomplish this, it uses a preference table with values ranging from 1 (nothing preferred) to 9 (very preferred) [30]. The use of the sine and cosine functions are usually used in the modified Saaty method in order to observed the behavior of the variable, as is demonstrated in Equations (1) and (2):  
\[\mu_{\text{A}}(\text{V}_{\text{o}})=\cos\left(\frac{\pi}{2}\times\frac{\text{V }_{\text{o}}-\text{V}_{\text{min}}}{\text{V}_{\text{max}}-\text{V}_{\text{min} }}\right)0\leq\mu_{\text{A}}(\text{V}_{\text{o}})\leq 1 \tag{1}\]  
\[\mu_{\text{A}}(\text{V}_{\text{o}})=\sin\left(\frac{\pi}{2}\times\frac{\text{V }_{\text{o}}-\text{V}_{\text{min}}}{\text{V}_{\text{max}}-\text{V}_{\text{min }}}\right)0\leq\mu_{\text{A}}(\text{V}_{\text{o}})\leq 1 \tag{2}\]  
where \(\mu_{\text{A}}\) (V\({}_{\text{o}}\)) is the behavior of the variable, A is the criterion or variable that is represented, (V\({}_{\text{o}}\)) is the original value, (V\({}_{\text{min}}\)) is the minimum value and (V\({}_{\text{max}}\)) is the maximum value. \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**PCPs** & **Toxic Components** & **Environmental Impact** \\ \hline Feminine Sanitary & Aldehydes, Alkanes, Halohydrocarbons, Terpenes, Ketones, PAHs & They generate toxic and mutagenic waste, produce cancer at the time of postuse exposure [80]. \\ \hline Deodorants & Heavy metals & They are bioaccumulative, cause several diseases [81]. \\ \hline Disposable Masks & Microplastics & When receiving UV rays, they release chemical substances that cause adverse effects on the marine ecosystem [82]. \\ \hline Condoms & Parabens (Methylparaben, Propylparaben and Octylparaben) & Endocrine disturbances. Both estrogenic and antiandrogenic effects [83]. \\ \hline Fragrances & Musk Xylene, Musk Ketone, Galaxolide & Musk causes endocrine disruption in aquatic biota and galaxolide is bioaccumulative [84, 85]. \\ \hline Soap, shampoo, detergent, toothpaste, sunscreen and deodorant & Triclosan (TCS, 5-chloro-2-(2,4-dichlorophenoxyoxy)phenol) & Alters the composition of benthic bacteria. Toxic for algae species, it presents endocrine disruption in fish [86]. \\ \hline Sunscreen & Octocrylene Oxybenzene & Benzophenones cause DNA alteration, bleaching and death of corals and reefs [86]. \\ \hline Hair dyes & Triclosan (TCS, 5-chloro-2-(2,4-dichlorophenoxyoxy)phenol) & Dye residues accumulate on the seafloor, entering the food chain [86]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of most common PCPs. Equation (1) is used when the value (V) of the variable is inversely proportional to the evaluation variable, while Equation (2) is used when there is a directly proportional relationship between (V) and the evaluation variable. For the values obtained by applying Equation (1), one must be subtracted from the calculated value so that the results obtained in both equations are normalized. The rating range of the criteria or variables ranges from 0 to 1, with one being the highest rating [88]. When the criterion is closer to 1, this means that it better approaches the stated objective of sustainability. In the present investigation, the diffuse Saaty method was applied individually in each treatment technique. By evaluating the criteria (A) of maintenance cost, construction cost, efficiency and development stage, qualitative variables were assigned a quantitative value (weighting) on a scale of 1 to 9 to calculate the initial value (V\({}_{\text{o}}\)) of the weighting assigned to each variable, and Equation (1) or Equation (2) is applied depending on the proportionality of each variable.