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change definition of domain mappin function

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hannes.kuchelmeister
2020-02-17 13:36:58 +01:00
parent 406b8c2319
commit 7015de5420
1 changed files with 14 additions and 18 deletions
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25_Outline/outline.tex
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@@ -164,7 +164,7 @@ Set of variables:
Set of their domains of values:
\begin{equation}
D = \{D_1, \dotsc, D_m\}, \qquad where \ D_i = \{d_1, \dotsc, d_o\}
\mathfrak{D} : V \to D; x \mapsto \mathfrak{D}(x) \qquad where \ D = \{d_1, \dotsc, d_o\}
\end{equation}
Set of users:
@@ -175,7 +175,7 @@ Set of users:
Users utility for a domain value of a variable:
\begin{equation}
\begin{split}
u_i(d_j), \qquad \text{where}\ & d_j \in D_j,\\
u_i(d_j), \qquad \text{where}\ & d_j \in \mathfrak{D}(j),\\
& 1 <= j <= m, \\
& 1 <= i <= n
\end{split}
@@ -184,18 +184,18 @@ Users utility for a domain value of a variable:
User preferences:
\begin{gather}
P = \{ P_1, \dotsc, P_n\},\ \text{where} \\
P_i = \{(d,\ u_i(d)) \ | \ \forall d \in D_i,\ i=1,\dotsc,m \} \notag
P_i = \{(d,\ u_i(d)) \ | \ \forall d \in \mathfrak{D}(i),\ i=1,\dotsc,m \} \notag
\end{gather}
Configuration state:
\begin{equation}
S = \{ (v_i,\ d) \ |\ v_i \in V \ \land \ d \in D_i,\ i=1,\dotsc,m \}
S = \{ (v_i,\ d) \ |\ v_i \in V \ \land \ d \in \mathfrak{D}(i),\ i=1,\dotsc,m \}
\end{equation}
Finished configuration state:
\begin{equation}
\begin{split}
S_F \subset S,\ where \ & \forall v_i \in V (\exists (v_i, d) \in S_F : d \in D_i) \\
S_F \subset S,\ where \ & \forall v_i \in V (\exists (v_i, d) \in S_F : d \in \mathfrak{D}(i)) \\
& \land is\_valid(S_F)
\end{split}
\end{equation}
@@ -232,24 +232,20 @@ An example group configuration scoring function is $score_{group}$ with
V = \{ & Heimisch, Klimaresilient, Verwertbar, Ernteaufwand, \\
& Menge, Preis, Walderfahrung \},
\end{split} \notag \\
\begin{split}
D = \{ & D_{Heimisch}, D_{Klimaresilient}, D_{Verwertbar}, \\
& D_{Ernteaufwand}, D_{Menge}, D_{Preis}, D_{Walderfahrung}\},
\end{split} \notag \\
D_{Heimisch} = \{ & Gering, Mittel, Hoch\}, \notag \\
D_{Klimaresilient} = \{ & Gering, Mittel, Hoch\}, \notag \\
D_{Verwertbar} = \{ & Gering, Mittel, Hoch\}, \notag \\
D_{Ernteaufwand} = \{ & Motormanuel, Harvester, Vollautomatisch\}, \notag \\
D_{Menge} = \{ & Keine, Gering, Hoch\}, \notag \\
D_{Preis} = \{ & Gering, Mittel, Hoch\}, \notag\\
D_{Walderfahrung} = \{ & Gering, Mittel, Intensiv\},\notag \\
\mathfrak{D}(Heimisch) = \{ & Gering, Mittel, Hoch\}, \notag \\
\mathfrak{D}(Klimaresilient) = \{ & Gering, Mittel, Hoch\}, \notag \\
\mathfrak{D}(Verwertbar) = \{ & Gering, Mittel, Hoch\}, \notag \\
\mathfrak{D}(Ernteaufwand) = \{ & Motormanuel, Harvester, Vollautomatisch\}, \notag \\
\mathfrak{D}(Menge) = \{ & Keine, Gering, Hoch\}, \notag \\
\mathfrak{D}(Preis) = \{ & Gering, Mittel, Hoch\}, \notag\\
\mathfrak{D}(Walderfahrung) = \{ & Gering, Mittel, Intensiv\},\notag \\
U = \{ & 1,2\} \notag\\
P = \{ & P_1, P_2\} \notag\\
\begin{split}
P_1 = \{ & (Motormanuel, 0.5), (Harvester, -0.3) \} \\
& \cup \{ (d,0)\ |\ d \in D_i,\ D_i \in D,\ i \notin \{ Motormanuel, Harvester\} \ \} \
& \cup \{ (d,0)\ |\ d \in \mathfrak{D}(i),\ i \in V,\ i \notin \{ Motormanuel, Harvester\} \ \} \
\end{split} \notag \\
P_2 = \{ & (d,0)\ |\ d \in D_i,\ D_i \in D \} \notag \\
P_2 = \{ & (d,0)\ |\ d \in \mathfrak{D}(i),\ i \in V \} \notag \\
S = \{ & (Heimisch, Gering), (Menge, Gering) \} \notag \\
\begin{split}
S_F = \{ & (Heimisch, Gering), (Klimaresilient, Gering), (Verwertbar, Gering), \\