Notes on TOPSIS Method The given numbers xij and their matrix
x11 x 21 X = xm1
x1n x2 n xmn
x12 x22 xm 2
(2)
must be balanced, since the numbers xij present values of different criteria with different measuring units. One must also take into account the given weights w j of the criteria x j . First, the measuring numbers xij of the criteria x j are replaced with the normalized or relative numbers
rij =
xij
(3)
m
x
2 ij
i =1
belonging to the open interval 0,1 . Then, according to the share w j x j of the criteria x j , the normalized numbers rij are replaced with the weighted normalized numbers
aij = w j rij = w j
xij
(4)
m
x
2 ij
i =1
belonging to 0,1 . The further data processing uses the weighted normalized decision matrix
a1n a11 a12 a a2 n 21 a22 . (5) A = amn am1 am 2 If all weights w j are mutually equal, in which case w j = 1 / n , the numbers rij can be applied in the matrix
A as the numbers aij . Working Table. The weighted normalized decision matrix one table.
A and all the data that will be calculated, we try to write in
Table 2. Working table for TOPSIS method
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