1. An Introduction toOrdered Weighted Averaging (OWA)

2. OWA
ANP TOPSIS ELECTRE I-III AHP ...
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2

3.
F

:
[1]
: i X
3

4.
4
0.8 0.95 0.2 0.38
X=(, , , )
X
w=(1,0.3,0.5,0)
0.95x1 + 0.8x0.3 + 0.38x0.5 + 0.2x0 = ?

5. OWA
OWA
ORness
Trade off
5

6. ORness
Orness OWA AND () OR ()
DM .
[2]
ORness .
6

7. ORness -
7
OR
AND

8. ORness -
OWA :
ORness(w) > 0.5
ORness(w) = 0.5
ORness(w) < 0.5
ANDness = 1 - ORness
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9. Trade off

:
[3]
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10. OWA
OWA . Yager 3 OWA :
Max
Min
Average
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11. OWA
.
2 :

(Linguistic Quantifiers)
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12. (a,b)
(0.3 , 0.8)
(0 , 0.5)
(0.5, 1)
* Q
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13.
13
* 7

14. OWA
Yager :
[6]
[7]
* (a,b)
* i n .
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15. OWA
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16.
5 . 0.5 ( ) ( ) :
F(0.8, 0.95, 0.2, 0.38, 0.1)
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17. (0.3,0.8)
:
:
F(0.8,0.95, 0.2,0.38,0.1) = .95x0 + .8x.2 + .38x4 + .2x.4 + .1x0 = 0.392
17
(a,b) = (0.3, 0.8)

18. (0,0.5)
:
:
F(0.8,0.95,0.2,0.38,0.1) = .95x.4 + .8x.4 + .38x.2 + .2x0 + .1x0 = 0.776
0.776 > 0.5

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19. Case Study

20. 20

21.
:
* n
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22.
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23.
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24. OWA TOPSIS
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25. 25