An Introduction to Ordered Weighted Averaging (OWA)
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An Introduction toOrdered Weighted Averaging (OWA) By: Mohsen Taleb
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- 1. An Introduction toOrdered Weighted Averaging (OWA)
- 2. OWA
ANP TOPSIS ELECTRE I-III AHP ...
/
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- 3.
F
:
[1]
: i X
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- 4.
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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
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- 6. ORness
Orness OWA AND () OR ()
DM .
[2]
ORness .
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- 7. ORness -
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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.
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* 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
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(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
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- 21.
:
* n
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- 22.
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- 23.
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- 24. OWA TOPSIS
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