原文链接：决策表
Definition 1. A decision system is a 5-tuple
S
=
(
U
,
C
,
D
,
V
,
I
)
S = (\mathbf{U}, \mathbf{C}, \mathbf{D}, \mathbf{V}, I)
S=(U,C,D,V,I), where
- U = { x 1 , x 2 , … , x n } \mathbf{U} = \{x_1, x_2, \dots, x_n\} U={x1,x2,…,xn} is the set of instances.
- C = { a 1 , a 2 , … , a n } \mathbf{C} = \{a_1, a_2, \dots, a_n\} C={a1,a2,…,an} is the set of conditions attributes.
- D = { d 1 , d 2 , … , d n } \mathbf{D} = \{d_1, d_2, \dots, d_n\} D={d1,d2,…,dn} is the set of decisional attributes.
- V = ⋃ a ∈ C ∪ D V a \mathbf{V} = \bigcup_{a \in \mathbf{C} \cup \mathbf{D}} \mathbf{V}_a V=⋃a∈C∪DVa
- V a \mathbf{V}_a Va is the domain of a ∈ C ∪ D a \in \mathbf{C} \cup \mathbf{D} a∈C∪D,
- I : U × ( C ∪ D ) → V I: \mathbf{U} \times (\mathbf{C} \cup \mathbf{D}) \to \mathbf{V} I:U×(C∪D)→V is the information function.
- 写出下表中的
U
,
C
,
D
,
V
\mathbf{U}, \mathbf{C}, \mathbf{D}, \mathbf{V}
U,C,D,V. 注: 最后两个属性为决策属性.
U = { x 1 , x 2 , … , x 7 } \mathbf{U} = \{x_1, x_2, \dots, x_7\} U={x1,x2,…,x7}.
C = { Yes , No , High , Normal , Low } \mathbf{C} = \{\textrm{Yes}, \textrm{No}, \textrm{High}, \textrm{Normal}, \textrm{Low}\} C={Yes,No,High,Normal,Low}
D = { Normal , Abnormal , Yes , No } \mathbf{D} = \{ \textrm{Normal}, \textrm{Abnormal}, \textrm{Yes}, \textrm{No}\} D={Normal,Abnormal,Yes,No}
V = { Yes , No , High , Normal , Low , Abnormal } \mathbf{V} = \{\textrm{Yes}, \textrm{No}, \textrm{High}, \textrm{Normal}, \textrm{Low}, \textrm{Abnormal}\} V={Yes,No,High,Normal,Low,Abnormal}
- 定义一个标签分布系统, 即各标签的值不是 0/1, 而是 [0,1] 区间的实数, 且同一对象的标签和为 1.
Definition: A label distribution system is a tuple S = ( X , Y ) S = (\mathbf{X}, \mathbf{Y}) S=(X,Y) where X = [ x i j ] n × m ∈ R n × m \mathbf{X} = [x_{ij}]_{n \times m} \in \mathbb{R}^{n \times m} X=[xij]n×m∈Rn×m is the data matrix, Y = [ y i k ] n × l ∈ [ 0 , 1 ] n × l \mathbf{Y} = [y_{ik}]_{n \times l} \in [0, 1]^{n \times l} Y=[yik]n×l∈[0,1]n×l is the label matrix and ∑ k = 1 l y i k = 1 \sum_{k=1}^l y_{ik} = 1 ∑k=1lyik=1, n n n is the number of instances, m m m is the number of features, and l l l is the number of labels.