去除量纲——极差法

如今有n个样本,30项指标,现要对指标值x i j ( j = 1 , 2 , . . . , n ; i = 1 , 2 , . . . , 30 ) x_{ij}(j = 1,2,...,n;i = 1,2,...,30)xij(j=1,2,...,n;i=1,2,...,30)做无量纲化处理,使

M i = m a x { x 1 i , x 2 i , x 3 i , . . . , x n i } M_i = max\left\{ x_{1i},x_{2i},x_{3i},...,x_{ni} \right\}Mi=max{x1i,x2i,x3i,...,xni}
m i = { x 1 i , x 2 i , x 3 i , . . . , x n i } m_i = \left\{ x_{1i},x_{2i},x_{3i},...,x_{ni} \right\}mi={x1i,x2i,x3i,...,xni}

去量钢化后的指标为:

x i j ∗ = x i j − m i M i − m i ∈ [ 0 , 1 ] x_{ij}^* =\frac{x_{ij}-m_i}{M_i - m_i} \in[0,1]xij=Mimixijmi[0,1]
x i j ∗ ( j = 1 , 2 , . . . , n ; i = 1 , 2 , . . . , 30 ) x_{ij}^*(j=1,2,...,n;i = 1,2,...,30)xij(j=1,2,...,ni=1,2,...,30)为去量纲化后的指标值


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