# Personalizing Environmental Awareness through Smartphones Using AHP and PROMETHE II
## 3 Defining MCDM Based on User Model
### AHP for Calculating Weights of Criteria  
AHP seeks to analyze a qualitative problem through a quantitative method. According to [47], after having developed the goal hierarchy, in order to apply AHP, the pair-wise comparison matrix of criteria has to be set up. In applying AHP, first, the set of evaluators has to be formed, acting as decision-makers in the application of AHP for the calculation of the weights of criteria. In fact, selecting an expert correctly would provide valid and reliable results. As a result, domain experts and software engineers have been chosen to participate in the experiment to improve the reliability of the results. Regarding domain experts, they were environmentalists and ecologists. Specifically, the six human experts that participated in the first phase as well as two software engineers and two experts in user modeling were asked to conduct the pairwise comparisons of criteria.  
The steps that need to be implemented are:  
(1) Setting up a pair-wise comparison matrix of criteria: In this step, a comparison among the criteria of the same level is conducted. For this reason, a comparison matrix is created, and each decision-maker was asked to fill in the comparison matrix by adding the frequency that reveals that pairwise comparison of the criterion in the row with the criterion in the column. They are invited to use the values of the nine-point scale for the pairwise comparison as presented in Table 1.  
Thereby, six different matrixes were collected. The values in the cells of the final matrix are computed as an average of the corresponding values of the cells of the six matrixes. Table 2 presents the final pair-wise comparison matrix of criteria.  
(2) Calculating weights of criteria: After performing pair-wise comparisons, estimations are made resulting in the final set of weights of the criteria. For simplicity, the 'Priority Estimation Tool' (PriEst) [48] has been used, which is an open-source decision-making software that implements AHP, to perform calculations for the theory (Figure 1).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Importance** & **Definition** & **Explanation** \\ \hline
1 & Equivalent Importance & Both criteria are equally important. \\
2 & Low & \\
3 & Average Importance & A small advantage of one criterion \\
4 & Extra Average & over another. \\
5 & High Importance & Strong advantage of one criterion \\
6 & Extra High & over another. \\
7 & Very High Importance & Very strong advantage of one criterion over another. \\
8 & Very, Very High & \\
9 & Highest Importance & A criterion is certainly more favored \\  & & than another criterion. \\ \hline \hline \end{tabular}
\end{table}
Table 1: The nine-point scale for pairwise comparison.  
This process resulted in the following weights for the ten criteria evaluated:  
* C1: Compatibility of current location\(\rightarrow\)\(w_{c1}=0.172\)
* C2: Compatibility with the environment of residence\(\rightarrow\)\(w_{c2}=0.084\)
* C3: Compatibility with user's habits\(\rightarrow\)\(w_{c3}=0.183\)
* C4: Compatibility with user's interests\(\rightarrow\)\(w_{c4}=0.234\)
* C5: Compatibility with user's needs\(\rightarrow\)\(w_{c5}=0.161\)
* C6: Compatibility with age\(\rightarrow\)\(w_{c6}=0.105\)
* C7: Compatibility with season\(\rightarrow\)\(w_{c7}=0.061\)