\chapter{Foundations}
\label{ch:Foundations}

\todo[author=Robert, inline]{Zu den Definitionen in der Foundation Section noch etwas Text schreiben.}

\section{Recommender System}
\label{sec:Foundations:RecommenderSystem}

A recommender system is a system that gives individualized recommendations to users to guide them through a large space of objects \cite[~ p. 331]{burkeHybridRecommenderSystems2002}.

There are several approaches to recommender systems presented in \cite{felfernigGroupRecommenderSystems2018}, these are: collaborative filtering, content-based filtering, critiquing-based filtering, constraint-based, hybrid recommendation.

\subsection{Collaborative Filtering}
In collaborative filtering a users rating for unknown items is predicted by finding similar users who have rated it. Their rating is used as prediction
\cite[~ pp. 7, 8]{felfernigDecisionTasksBasic2018}.

Collaborative Filtering can not only be done using users, it can also be item-based. Hereby the similarity between items is used for a recommendation and not similar users \cite{ricciRecommenderSystemsHandbook2015}. In the context of configuration the similarity to other historic configurations can be used which makes it an item based approach. 


\subsection{Content-Based Filtering}
Items and users are assigned to categories. Based on consumption and rating of items a user will have implicit ratings for categories. Predictions are now made based on a categories of the new item \cite[~ pp. 10, 11]{felfernigDecisionTasksBasic2018}.

\subsection{Critiquing-Based Recommendation}
Items are recommended and a user can then critique on attributes of the recommendation. Based on that a similar item which does not have those critiques can be recommended. User preferences are implicitly collected this way \cite{knijnenburgEachHisOwn2011}.

\subsection{Constraint-Based Recommendation}
Hereby filter rules are defined which filter out items that don't fulfil specified rules. A user models their requirements with these rules and thereby gets a list of recommended items \cite[~ p. 12]{felfernigDecisionTasksBasic2018}

\subsection{Hybrid Recommendation}
A hybrid recommender combines different recommendation approaches to use the strengths of each individual one and to reduce effects of weaknesses \cite{burkeHybridRecommenderSystems2002}.

\todo[inline]{add more detailed description of recommendation systems - do they need historicle data  which conditions for usage are needed, strengths and weaknesses}

\section{Group Recommender System}

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 this model recommendation strategies as described in \ref{sec:Foundations:RecommenderSystem} can be used to generate recommendations \cite{jamesonRecommendationGroups2007}.

\section{Product Configuration}
\label{sec:Foundations:ProductConfiguration}

Product configuration is a process consisting of a series of decision tasks whereby a product is constructed of components which interact with each other. During a configuration process no new components are created. Their interplay and specification is defined beforehand \cite[~ pp. 42, 43]{sabinProductConfigurationFrameworksa1998}.

Formally a configuration problem can be specified as a \emph{constraint satisfaction problem (CSP)} \cite{tsangFoundationsConstraintSatisfaction1993} as 
\[
    CSP(V,D,C)
\]
where \( V = \{v_1,\dots, v_n\} \) is a set of variables, \( D = dom : V \mapsto X \) is a relation of variables and their corresponding domain definitions \( X \), and \( C = C_{PREF} \cup C_{KB} \) is a set of constraints with customer preferences \( C_{PREF} \) and configuration knowledge base \( C_{KB} \) \cite{felferningGroupBasedConfiguration2016, felfernigOpenConfiguration2014}.


\section{Group-Based Product Configuration}
\label{sec:Foundations:GroupBasedProductConfiguration}

If instead of a single person configuring a product we would like to have a group of people which can be useful in multi-stakeholder decisions, it needs mechanisms for describing the preferences of multiple people. Therefore we extend the definition of product configuration from (\ref{sec:Foundations:ProductConfiguration}) to 
\[ 
    C_{PREF} = \bigcup 
PREF_i \]
with preferences of user \( i \) as \( PREF_i \) \cite{ felferningGroupBasedConfiguration2016}.

\section{Group-Based Configuration-Solution}
\label{sec:Foundations:GroupBasedConfigurationSolution}

\ref{sec:Foundations:ProductConfiguration} and \ref{sec:Foundations:GroupBasedProductConfiguration} expand to a solution of a group-based configuration with the addition of variable assignments
\[
    C_{CONF} = \bigcup_{v_i \in V} \{ v_i = x_i \}, \ x_i \in dom(v_i)
\]
and where \( C_{CONF} \cup C_{PREF} \cup C_{KB} \) is consistent \cite{ felferningGroupBasedConfiguration2016}.

\section{Group Bias}
\label{sec:Foundations:GroupBias}

Groups have biases same as individuals. Some of these stem from individual biases that are transferred to a group and others only occur in group settings. This section covers some of those effects. These effects are described by \citeauthor{felfernigBiasesGroupDecisions2018} \cite{felfernigBiasesGroupDecisions2018}.

\subsection{GroupThink}

The bias called GroupThink occurs, when group members prefer to avoid conflicts instead of being mainly interested in getting the best decision outcome. Alternative options are in these circumstances not analysed close enough \cite{janis1982groupthink}.
An avoidance strategy for this effect is for leaders to delay stating there opinion until all alternatives have been viewed in detail \citeauthor{felfernigBiasesGroupDecisions2018}. Recommender systems can aid group decision quality through encouraged information exchange as discussed by \citeauthor{atasItemRecommendationUsing2017} in \cite{atasItemRecommendationUsing2017}.


\subsection{Anchoring}

The first information provided is relied upon to heavily. In a group setting this can be triggered by the group member to first express their opinion. Often this is triggered if group members see preferences of others too early, therefore recommender systems should not show the rating of other users \cite{cosley2003seeing}.

\subsection{Serial Position Effects}

The serial positioning effects is the effect that users have a higher retention rate of items in a list that are presented first or last and these items are more closely examined \cite{felfernigPersuasiveRecommendationSerial2007,murphyPrimacyRecencyEffects2006}. Additionally to remembering and examining items at the start and the end of a list also the order of items can change the option the user chooses in the end \cite{felfernigBiasesGroupDecisions2018}.


