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39 lines
1.9 KiB
TeX
39 lines
1.9 KiB
TeX
\chapter{Foundations}
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\label{ch:Foundations}
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\section{Recommender System}
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\label{Foundations:RecommenderSystem}
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\section{Product Configuration}
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\label{Foundations:ProductConfiguration}
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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[~ p. 42-43]{sabinProductConfigurationFrameworksa1998}.
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Formally a configuration problem can be specified as a \emph{constraint satisfaction problem (CSP)} \cite{tsangFoundationsConstraintSatisfaction1993} as
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\[
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CSP(V,D,C)
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\]
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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{felfernigOpenConfiguration2014, felferningGroupBasedConfiguration2016}.
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\section{Group-Based Product Configuration}
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\label{Foundations:GroupBasedProductConfiguration}
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To define group-based product configuration we extend the definition (\ref{Foundations:ProductConfiguration}) to
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\[
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C_{PREF} = \bigcup
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PREF_i \]
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with preferences of user \( i \) as \( PREF_i \) \cite{ felferningGroupBasedConfiguration2016}.
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\section{Group-Based Configuration-Solution}
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\label{Foundations:GroupBasedConfigurationSolution}
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\ref{Foundations:ProductConfiguration} and \ref{Foundations:GroupBasedProductConfiguration} expand to a solution of a group-based configuration with the addition of variable assignments
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\[
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C_{CONF} = \bigcup_{v_i \in V} \{ v_i = x_i \}, \ x_i \in dom(v_i)
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\]
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and where \( C_{CONF} \cup C_{PREF} \cup C_{KB} \) is consistent \cite{ felferningGroupBasedConfiguration2016}.
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