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add group recommender explanation foundations

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30_Thesis/sections/10_foundations.tex
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@@ -182,10 +182,11 @@ A hybrid recommender combines different recommendation approaches to use the str
A group recommender system is a recommender system aimed at making recommendations for a group instead of a single user. To make recommendations group members preferences have to be aggregated. This can be done by either aggregating single user recommendations or by merging preferences of each user into a group preference model. Based on the resulting preference model recommendation strategies as described in \autoref{sec:Foundations:RecommenderSystem} can be used to generate recommendations \cite{jamesonRecommendationGroups2007}.
\todo[inline]{example of a group recommender}
\todo[inline]{go more into detail about preference aggregation}
The strategy of aggregating predictions can be further divided into two strategies. \citeauthor{felfernigAlgorithmsGroupRecommendation2018} \cite{felfernigAlgorithmsGroupRecommendation2018} describes merging recommendations and "ranking of candidate items". Merging recommendations can be used when multiple possible solutions should be presented. The recommender picks $n$ recommendation from each user's individual recommendations and merges them into a list. The second approach is that each user's individual recommender ranks all items. The group member specific rankings can are aggregated to get a group ranking of items. Instead of ranking it is also possible to simply predict a users rating for an item.
Merging preferences has to be done using an aggregation strategy. This section presents three strategies: multiplication, average and least misery. The multiplication strategy multiplies preferences of users and thereby combines them into a group preference. Similarly the average strategy takes the average of a rating and the least misery strategy takes the lowest rating among group members. To illustrate the example in \autoref{tab:Foundations:RecommenderSystem:MoviePreferences} is used. A group is formed out of Lucy, Eric and Diane. The resulting ratings for each strategy are shown in \autoref{tab:Foundations:RecommenderSystem:AggregationStrategy}.
The aggregation of preferences uses a merging strategy to combine the individual preferences into group preferences. This allows a group to change its preferences during the course of the decision without changing individual preferences.
Both the approach of merging preferences and the approach of using individual users rankings require some kind of aggregation strategy. This section presents three strategies: multiplication, average and least misery. The multiplication strategy multiplies preferences of users and thereby combines them into a group preference. Similarly the average strategy takes the average of a rating and the least misery strategy takes the lowest rating among group members. To illustrate the example in \autoref{tab:Foundations:RecommenderSystem:MoviePreferences} is used. A group is formed out of Lucy, Eric and Diane. The resulting ratings for each strategy are shown in \autoref{tab:Foundations:RecommenderSystem:AggregationStrategy}.
\begin{table}
\centering