## 4 Research Methodology
### Analysis and Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Time** & **Cost** & **Quality** \\ \hline
**Time** & 1.00 & 1.04 & 3.32 \\
**Cost** & 0.96 & 1.00 & 3.81 \\
**Quality** & 0.30 & 0.26 & 1.00 \\
**Sum of Columns** & 2.26 & 2.30 & 8.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Aggregated matrix. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Time** & **Cost** & **Quality** & **Priority Vector** \\ \hline
**Time** & =1.00/2.26 = 0.44 & =1.04/2.30 = 0.45 & 0.43 & =(0.44 + 0.45 + 0.43)/3 = 0.43 \\
**Cost** & =0.96/2.26 = 0.42 & 0.43 & 0.44 & 0.44 \\
**Quality** & =0.30/2.26 = 0.13 & 0.11 & 0.12 & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Normalized decision matrix and priority vector. sum matrix values by values of the priority vector (Table 9). The average of Eigen values (\(\lambda_{\text{max}}\)) was calculated as given in Table 9.  
CI was found as 0.00179. To find CR, CI was divided by RI (n: 3-0.58). As a result of the analysis, CR was found as 0.00309, which is lower than 0.1. In the second step, it was requested that responders evaluate defined FM KPIs against defined criteria. In the evaluation, the 1-5 Likert scale (1-not important, 2-slightly important, 3-moderately important, 4-important, and 5-very important) was used. Collected data and weights coming from AHP analysis were inputted into PROMETHEE&GAIA software. The usual preference function was also chosen in the PROMETHEE calculations. As a result of the analysis, the PROMETHEE flows (PROMETHEE II) and the GAIA planes were obtained. Net flow values--PROMETHEE II (Phi values) were used to determine ranks and importance of healthcare FM KPIs. Besides this, Decision Lab allows one to represent the decision problem in the GAIA plane, in which actions are represented with points and criteria are represented by vectors. PROMETHEE II Phi values for \"Environmental Aspect in Healthcare Facilities\" are given in Table 10. According to PROMETHEE II results (complete ranking), \"Prediction of Resource/Energy load profile (E4)\", \"Energy/Resource efficiency (E13)\", and \"Resource/Energy consumption with respect to working days and non-working days (E1)\" are the most important FM KPIs in environmental analysis, respectively. Negative flows show how negative KPIs are dominated by the positive KPIs. PROMETHEE II analysis results for \"User Aspect in Healthcare Facilities\" are given in Table 11. According to analysis results, \"Prediction of indoor air parameters and indoor quality (U2)\", \"Indoor air quality (U1)\", and \"Identification of space occupancy (U14)\" were thought to be the most important healthcare FM KPIs for user aspect by responders, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Phi Values** & **Indicator** & **Phi Values** \\ \hline E4 & 0.7576 & E9 & 0.0101 \\ E13 & 0.6010 & E10 & \(-\)0.3569 \\ E1 & 0.5320 & E11 & \(-\)0.4731 \\ E3 & 0.4966 & E6 & \(-\)0.7012 \\ E8 & 0.3788 & E12 & \(-\)0.7542 \\ E2 & 0.3670 & E5 & \(-\)0.8897 \\ E7 & 0.0320 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: PROMETHEE II results for environmental aspect in healthcare facilities. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Weighted Sum Matrix** & **Eigen Values** \\ \hline
**Time** & =(1 \(\times\) 0.43 + 1.04 \(\times\) 0.44 + 3.32 \(\times\) 0.12) = 1.30 & =1.30/0.43 = 3.0045 \\
**Cost** & 1.33 & 3.0048 \\
**Quality** & 0.37 & 3.0013 \\ \hline \hline  & \(\mathbf{\lambda_{\text{max}}}\) & =(3.0045 + 3.0048 + 3.0013)/3 = 3.0035 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Weighted sum matrix and Eigen values. PROMETHEE II results for \"Emergency and Safety Management in Healthcare Facilities\" are given in Table 12. According to analysis results, \"Number of accidents per year (S2)\", \"Number of lost work days per year (S4)\", and \"Number of health and safety complaints per year (S3)\" are the most important FM KPIs for emergency and safety management, respectively.