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@@ -251,15 +251,13 @@ By including the current configuration state, the scoring function can take into
\section{Illustration}
\label{sec:Concept:Illustration}
\todo[]{Leser sind faul, bitte schreibe die Berechnung bzw wenigstens die Ergebnisse für $score$, $penalty$, $score_\text{group}$ zu jedem Vergleich dazu}
This section gives an example to illustrate how the recommendation works. The example in \autoref{fig:Concept:ForestExample} is used for that but the preferences are extended. \autoref{tab:Concept:UseCaseConfigurations} shows the current configuration state which consists of the characteristic moderate for the feature \textit{indigenous} and \textit{resilient} respectively. $S_{F1}$ to $S_{F4}$ show the stored configurations for this example. The features that will be focused on are \textit{indigenous}, \textit{resilient} and \textit{effort}. In the presented example $S_{F1}$ performs best. The exact reason for that will be presented here. $S_{F1}$ is compared to $S_{F2}$ to show the effect of divergence from the configuration state. A comparison between $S_{F1}$ and $S_{F3}$ is done to show the difference between preferences and the effect on the score and last, $S_{F4}$ is done to show the effect of switching to better preferences but diverging from the current state. The configurations all differ to $S_{F1}$ in only one characteristic that is chosen differently. As aggregation strategy the \emph{average} metric is used (see \autoref{sec:Foundations:GroupRecommenderSystem}). The parameter $\alpha$ (see \autoref{subsubsec:Concept:SolutionGeneration:ScoringFunction:Penalty}) is set to 1. A lower $\alpha$ reduces the penalty given to configurations that deviate from the configuration state $S$ and a higher $\alpha$ increase the reluctance to change.
This section gives an example to illustrate how the recommendation works. The example in \autoref{fig:Concept:ForestExample} is used for that but the preferences are extended. \autoref{tab:Concept:UseCaseConfigurations} shows the current configuration state which consists of the characteristic moderate for the feature \textit{indigenous} and \textit{resilient} respectively. $S_{F1}$ to $S_{F4}$ show the stored configurations for this example. The features that will be focused on are \textit{indigenous}, \textit{resilient} and \textit{effort}. In the presented example $S_{F1}$ performs best. The exact reason for that will be presented here. $S_{F1}$ is compared to $S_{F2}$ to show the effect of divergence from the configuration state. A comparison between $S_{F1}$ and $S_{F3}$ is done to show the difference between preferences and the effect on the score and last, $S_{F4}$ is done to show the effect of switching to better preferences but diverging from the current state. The configurations all differ to $S_{F1}$ in only one characteristic that is chosen differently. As aggregation strategy the \emph{average} metric is used \todo[]{referenz zur erklärung}. The parameter $\alpha$ (see \autoref{subsubsec:Concept:SolutionGeneration:ScoringFunction:Penalty}) is set to 1. A lower $\alpha$ reduces the penalty given to configurations that deviate from the configuration state $S$ and a higher $\alpha$ increase the reluctance to change.
The difference between $S_{F1}$ and $S_{F2}$ is that instead of containing \emph{moderate} for the feature \emph{resilient} $S_{F2}$ contains \emph{high}. The scores for these two characteristics are the same, with a value of $0.55$,as both users have rated them at $0.5$ but as $S_{F2}$ deviates from the configuration state there will be a penalty. There are two characteristics in the configuration state $S$ therefore the the penalty is $(\frac{1}{2})^\alpha = (\frac{1}{2})^1 = 0.5$. This means the score of $S_{F2}$ is half that of $S_{F1}$. Resulting in a final score of $0.275$ compared to $0.55$.
The difference between $S_{F1}$ and $S_{F2}$ is that instead of containing \emph{moderate} for the feature \emph{resilient} $S_{F2}$ contains \emph{high}. The scores for these two characteristics is the same as both users have rated them at $0.5$ but as $S_{F2}$ deviates from the configuration state there will be a penalty. There are two characteristics in the configuration state $S$ therefore the the penalty is $(\frac{1}{2})^\alpha = (\frac{1}{2})^1 = 0.5$. This means the score of $S_{F2}$ is half that of $S_{F1}$.
The only difference between $S_{F1}$ and $S_{F3}$ is that $S_{F3}$ changes the selection for the feature \emph{effort}. The characteristic \emph{manual} is chosen in $S_{F1}$ and the characteristic \emph{harvester} for $S_{F3}$. The individual score for user one increases as he prefers \emph{harvester} with $0.8$ over \emph{manual} with $0.6$. However, user two has an individual score reduction as her score changes from $0.8$ for \emph{manual} to $0.3$ for \emph{harvester}. The larger decrease in the score of user two causes a decrease in the overall score when comparing $S_{F1}$ to $S_{F3}$ with a score of $0.55$ to $0.53$. The scores for both users are closer together for $S_{F1}$ however this doesn't necessarily have to be the case because if the preference of user two for harvester were to change to $0.6$ both configurations would have the same score. A different user preference aggregation strategy can change that.
The only difference between $S_{F1}$ and $S_{F3}$ is that $S_{F3}$ changes the selection for the feature \emph{effort}. The characteristic \emph{manual} is chosen in $S_{F1}$ and the characteristic \emph{harvester} for $S_{F3}$. The individual score for user one increases as he prefers \emph{harvester} with $0.8$ over \emph{manual} with $0.6$. However, user two has an individual score reduction as her score changes from $0.8$ for \emph{manual} to $0.3$ for \emph{harvester}. The larger decrease in the score of user two causes a decrease in the overall score when comparing $S_{F1}$ to $S_{F3}$. The scores for both users are closer together for $S_{F1}$ however this doesn't necessarily have to be the case because if the preference of user two for harvester were to change to $0.6$ both configurations would have the same score. A different user preference aggregation strategy can change that.
Last, $S_{F1}$ and $S_{F4}$ differentiate in terms of characteristic choice for the feature \emph{indigenous}. The switch from \emph{moderate} to \emph{high} when changing from $S_{F1}$ to $S_{F4}$ causes an increase in the individual scoring function of user two. This is caused because her preference for \emph{moderate} is $0.6$ and for \emph{high} is $0.9$. Yet, the change that causes the preference scoring function to give a higher score entails a penalty as the characteristic \emph{high} is not part of the configuration state. This penalty causes the overall score to drop far below that of $S_{F1}$.
Last, $S_{F1}$ and $S_{F4}$ differentiate in terms of characteristic choice for the feature \emph{indigenous}. The switch from \emph{moderate} to \emph{high} when changing from $S_{F1}$ to $S_{F4}$ causes an increase in the individual scoring function of user two. This is caused because her preference for \emph{moderate} is $0.6$ and for \emph{high} is $0.9$. This results in a score of $0.57$ for $S_{F4}$. Yet, the change that causes the preference scoring function to give a higher score entails a penalty as the characteristic \emph{high} is not part of the configuration state. This penalty causes the overall score to drop to $0.29$ compared to the score of $S_{F1}$ with $0.55$.
\begin{table}
\tiny