## 4 Results
Ultimately, if one expects a clear recommendation, the most straightforward approach can be used, which unfortunately overlooks the uncertainty in the rankings resulting from different utility functions, i.e., determining the average ranks. The results differ slightly from those obtained with the arbitrarily chosen function (BT(0.7, 0.4)), but the differences are not significant (see Table 7). \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Town**} & \multicolumn{2}{c}{**Rank**} & \multirow{2}{*}{**Rank Difference**} \\ \cline{2-3} \cline{5-4}  & **for BT(0.7, 0.4)** & & **avg. Simulated** & \\ \hline Zürich & 1 & 1 & 0 \\ \hline Groningen & 2 & 2 & 0 \\ \hline Aalborg & 3 & 3 & 0 \\ \hline Luxembourg & 4 & 5 & 1 \\ \hline Wien & 5 & 4 & 1 \\ \hline München & 6 & 6 & 0 \\ \hline Genève & 7 & 7 & 0 \\ \hline Cardiff & 8 & 8 & 0 \\ \hline Graz & 9 & 9 & 0 \\ \hline Rennes & 10 & 10 & 0 \\ \hline Helsinki & 11 & 13 & 2 \\ \hline Oslo & 12 & 12 & 0 \\ \hline Kobenhavn & 13 & 11 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparing BTOPSIS ranks for initial utility function BT(0.7, 0.4) and average simulated. Figure 5: Hasse diagram showing the occurrence of FSD relations between cities based on their simulated ranking positions. _Appl. Sci._**2024**, _14_, 11051 \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Town**} & \multicolumn{2}{c}{**Rank**} & \multirow{2}{*}{**Rank Difference**} \\ \cline{2-3} \cline{5-5}  & **for BT(0.7, 0.4)** & **avg. Simulated** & \\ \hline Bialystok & 14 & 15 & 1 \\ \hline Hamburg & 15 & 14 & 1 \\ \hline Dublin & 16 & 16 & 0 \\ \hline Ljubljana & 17 & 17 & 0 \\ \hline Belfast & 18 & 18 & 0 \\ \hline Tyneside conurbation & 19 & 19 & 0 \\ \hline Malmó & 20 & 20 & 0 \\ \hline Amsterdam & 21 & 21 & 0 \\ \hline Antwerpen & 22 & 23 & 1 \\ \hline Reykjavik & 23 & 22 & 1 \\ \hline Dortmund & 24 & 24 & 0 \\ \hline Strasbourg & 25 & 27 & 2 \\ \hline Leipzig & 26 & 26 & 0 \\ \hline Rostock & 27 & 25 & 2 \\ \hline Rotterdam & 28 & 28 & 0 \\ \hline Stockholm & 29 & 29 & 0 \\ \hline Oulu & 30 & 30 & 0 \\ \hline Gdärsk & 31 & 31 & 0 \\ \hline Bordeaux & 32 & 32 & 0 \\ \hline Oviedo & 33 & 35 & 2 \\ \hline Tallinn & 34 & 34 & 0 \\ \hline Glasgow & 35 & 33 & 2 \\ \hline Praha & 36 & 36 & 0 \\ \hline Manchester & 37 & 37 & 0 \\ \hline Essen & 38 & 38 & 0 \\ \hline Berlin & 39 & 39 & 0 \\ \hline London & 40 & 40 & 0 \\ \hline Antalya & 41 & 41 & 0 \\ \hline Vilnius & 42 & 42 & 0 \\ \hline Lille & 43 & 44 & 1 \\ \hline Cluj-Napoca & 44 & 43 & 1 \\ \hline Ostrava & 45 & 45 & 0 \\ \hline Piatra Neamt & 46 & 46 & 0 \\ \hline Braga & 47 & 48 & 1 \\ \hline Bologna & 48 & 47 & 1 \\ \hline Bruxelles & 49 & 50 & 1 \\ \hline Burgas & 50 & 49 & 1 \\ \hline Liege & 51 & 54 & 3 \\ \hline Riga & 52 & 51 & 1 \\ \hline Malaga & 53 & 52 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._In summary, a simple comparative analysis of the results and simulation studies has shown that BTOPSIS provides a relatively stable ranking with respect to various monotonic utility functions that may be assigned to the 5-level evaluation scales from surveys. Our adaptation of BTOPSIS, which uses simulation-based FSD analysis, additionally demonstrates the possibility of accounting for uncertainty arising from changes in ranking positions in individual replications and reconciling common ranking positions for cities if differences cannot be resolved through the concept of stochastic dominance. The choice of the final solution (i.e., results based on an arbitrarily assumed scale, averaging simulation results, or accounting for uncertainty through FSD) depends on the decision-making context in which the decision-maker finds themselves, their needs, and--under conditions of cognitive limitations--their ability to interpret uncertain data.