## 2 Materials and Methods
### Definition of New Integrated LCA+C2C Categories  
The new integrated LCA+C2C categories were classified into three analysis groups to facilitate the interpretation and use of the results:  
1. **Group I or cause-effect categories:** A set of categories that provide information regarding the impacts generated by the system individually, associated with: 1. Inputs: Set \(J\) of consumed and used resources to which land (L), materials (M), energy (E), water (W), human (H) and information (I) belong. This group provides impact data related to the causes. This set is defined as: \(\text{J}_{\text{k}}=\{\text{1,2,3,4,5,6}\}=\{\text{L,M,E,W,H,I}\}=\{\text{Land, Materials, Energy, Water, Human, Information}\}\); 2. Outputs: Set \(\text{J}_{jk}\) of midpoint impacts caused by products, by-products or substances generated in a life cycle process. These impacts are caused on resources defined in set \(J\) (land, materials, energy, water, human and information) and are quantified through endpoint impact categories (K). 2. **Group II or quality categories (Q\({}_{\text{K}}\)):** A set of four LCA+C2C endpoint indicators of integrated environmental and social assessment, which provide information on the level of \"care\" to the _protected areas (K)_. Four endpoint categories are defined, divided into society and ecosystem: 1. Human health (Q\({}_{\text{HH}}\)); 2. Security and well-being (Q\({}_{\text{SH}}\)); 3. Biotic system (flora and fauna) (Q\({}_{\text{BS}}\)); 4. Abiotic system (hydrosphere, hydrosphere and lithosphere) (Q\({}_{\text{AS}}\)). Evaluation based on these indicators makes it possible to directly control impacts through the causes that originate them, i.e., by modifying inputs (or resources), it is possible to reduce the effects or otherwise increase the quality of the results. These categories have a distribution of both environmental and social indicators. The results are compiled in the Quality Effects Inventory (QEI). With expressions (1) to (5), the result of each Q\({}_{\text{K}}\) category is calculated. Table 2 contains the necessary information for the calculation. \[\text{Q}_{\text{K}}=\sum_{\text{j}\in\text{J}_{\text{k}}}\text{R}_{\text{jk}} \tag{1}\]  
\[\text{R}_{\text{jk}}=\sum_{\text{i}\in\text{J}_{\text{jk}}}\alpha_{\text{ijk} }\cdot\text{N}_{\text{i}}=\sum_{\text{i}\in\text{J}_{\text{jk}}}\text{w}_{ \text{ijk}} \tag{2}\]  
\[\text{N}_{\text{K}}=\sum_{\text{i}\in\text{K}}\text{N}_{\text{i}}=\sum_{\text {i}\in\text{K}}\frac{\text{C}_{\text{i}}}{\text{n}_{\text{i}}} \tag{3}\]  
\[\text{W}_{\text{R}}=1-\frac{\text{R}_{\text{JK}}}{\text{N}_{\text{K}}} \tag{4}\]  
\[\text{W}_{\text{K}}=1-\frac{\text{Q}_{\text{K}}}{\text{N}_{\text{K}}} \tag{5}\]  
For the grouping and calculation of results, the following data sets are defined:  
* Set \(\text{J}_{k}\) or _inputs_ (resources) as: \(\text{J}_{\text{k}}=\{\text{1,2,3,4,5,6}\}=\{\text{L,M,E,W,H,I}\}=\{\text{ Land, Materials, Energy, Water, Human, Information}\}\);
* Set \(\text{I}_{\text{jk}}\) or outputs (midpoint) as: \(\text{I}_{\text{jk}}=\{\text{C}_{\text{i}}\}_{\text{i=1}}^{n}\ \forall\text{i}\in\text{J}_{\text{k}}\);
* Set K of \"damages\" in protected areas (LCA+C2C endpoint) as: K =[1,2,3,4]= [HH, SH, BS, AS]= [Human Health, Human Safety, Biotitic System, Abiotic System]. The following are necessary as **starting data**: 1. is the impact category;* \(\rm C_{i}\) is the characterized impact of the impact category I;
* \(\rm N_{i}\) is the normalized results of impact category i--it permits results on the same scale and shows the contribution to the overall environmental problem;
* \(\rm n_{i}\) is the normalization reference--the normalization factor for the category i in the reference system (for example, CML, Recipe H or ILCD). Finally, the **results obtained** from the LCA+C2C endpoint weighting are defined as:
* \(\rm Q_{K}\) is the LCA+C2C endpoint impact for each K (HH, SH, BS and AS) category. It measures the level of interference of each resource in the LCA+C2C endpoint categories, i.e., the loss of value by the cause-effect relationship.