5 ELimination Et Choix Traduisant La REalité (ELECTRE)
33
And the standard matrix X should be obtained as in the form below:
X i j =
⎡
⎢
⎣
x 11 · · · x 1n
. . .
. . .
. . .
x m1 · · · x mn
⎤
⎥
⎦
(5.3)
Step 3 Calculating the Weighted Standard Decision Matrix (Y )
The significance of assessment factors (criteria) for the selection maker can also additionally vary. In set up to mirror those noteworthiness contrasts inside the ELECTRE
arrangement, the Y matrix need to be calculated. In set up to do this, the selection
maker need to first of all determine the burden of the evaluation additives (w i ), where:
n
i=1
w i = 1
( 5 . 4 )
Then, the Y matrix is made via way of means of multiplying the additives in every
column of the X community with the evaluating (w_i) esteem as seemed below:
Y i j =
⎡
⎢
⎣
w 1 x 11 w 2 x 12 · · · w n x 1n
. . .
. . .
. . .
. . .
w 1 x m1 w 2 x m2 · · · w n x mn
⎤
⎥
⎦
(5.5)
Step 4 Determination of Concordance Sets (C kl ) and Discordance Sets (D kl )
For the assurance of the concordance units of the options, the Y matrix should be
utilized and the choice focuses ought to be as compared with every different in
phrases of every assessment calculate. The concordance units can be characterized
through the relationship appeared inside the equation below:
C kl =
j, y k j ≥ y l j
(5.6)
This equation fundamentally relies upon on a contrast among the values of the
decision matrix row components. In a numerous decision issue with m options, the
wide variety of concordance units is (m.m–m). The wide variety of concordance
set components maximum extreme can be damage even with to the wide variety of
assessment components (n).
As an example, where k = 1 and l = 2, C 12 concordance set should be calculated
by the comparison of the 1 − th and 2 − nd rows and for the 5 criteria, C 12 should
consits a maximum of 5 elements. In this example, if the comparison results are as
follows:
33
And the standard matrix X should be obtained as in the form below:
X i j =
⎡
⎢
⎣
x 11 · · · x 1n
. . .
. . .
. . .
x m1 · · · x mn
⎤
⎥
⎦
(5.3)
Step 3 Calculating the Weighted Standard Decision Matrix (Y )
The significance of assessment factors (criteria) for the selection maker can also additionally vary. In set up to mirror those noteworthiness contrasts inside the ELECTRE
arrangement, the Y matrix need to be calculated. In set up to do this, the selection
maker need to first of all determine the burden of the evaluation additives (w i ), where:
n
i=1
w i = 1
( 5 . 4 )
Then, the Y matrix is made via way of means of multiplying the additives in every
column of the X community with the evaluating (w_i) esteem as seemed below:
Y i j =
⎡
⎢
⎣
w 1 x 11 w 2 x 12 · · · w n x 1n
. . .
. . .
. . .
. . .
w 1 x m1 w 2 x m2 · · · w n x mn
⎤
⎥
⎦
(5.5)
Step 4 Determination of Concordance Sets (C kl ) and Discordance Sets (D kl )
For the assurance of the concordance units of the options, the Y matrix should be
utilized and the choice focuses ought to be as compared with every different in
phrases of every assessment calculate. The concordance units can be characterized
through the relationship appeared inside the equation below:
C kl =
j, y k j ≥ y l j
(5.6)
This equation fundamentally relies upon on a contrast among the values of the
decision matrix row components. In a numerous decision issue with m options, the
wide variety of concordance units is (m.m–m). The wide variety of concordance
set components maximum extreme can be damage even with to the wide variety of
assessment components (n).
As an example, where k = 1 and l = 2, C 12 concordance set should be calculated
by the comparison of the 1 − th and 2 − nd rows and for the 5 criteria, C 12 should
consits a maximum of 5 elements. In this example, if the comparison results are as
follows: