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Simple Additive Weighting
method
ANT
Professor: Mohammad Hasan Maleki
Ph.D.
Collector: Azam Noori
Qom University
November 2018
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- 9
2 @ @
>
wey é
=
(omar
2
=
SAW
=>
@)
ME
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Introduction
SAW:
* Is one of the most important concepts in multiple
attribute decision-making.
* Is one of the easiest methods available in multiple
attribute decision-making.
* Its basis is decision matrix.
٠ Is also known as the simple weighted linear
combination method.
* Was introduced by C.L. HWANG & K. Yoon in 1981.
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Step 1: Decision Matrix Formation
Decision Matrix
Aj 5 Ci a
Ay 11 112
42 121 122
Am Tm1 Tm2
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SAW Method Steps
Step 2: Making decision matrix data dimensionless using
linear method
Ti;
> For Positive Indicators: ny = سس
ii
7 8 - 11:00 (ز:
> For Negative Indicators: nj -
rij
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SAW Method Steps
Normal Matrix
Aj 5 6“ C2 Qa
Ay 111 112 Nin
۸42 121 N22 Nan
Am Nm1 Nm2 Tmn
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Step 3: Determining the weight of each indicator
Ww: {
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8
SAW Method Steps
Step 4: Obtaining the utility of each option
72
D,=>) W ,*7,,
<م 1
Choosing the best 000۰ {
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Four types of building systems have been evaluated for
selecting
the optimal construction system.
These include:
The structure of the criteria includes:
Administrative criteria, Economic criteria and
Environmental criteria.
Assess the most optimal performance of building systems
using the SAW method.
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10
Decision Matrix
Environmental
Administrative Economic
criteria 8 criteria criteria
0.25 0.242 0.296
0.23 0.243 | 0.227
3D-panel 0.24 0.232 0.235
| PRCS 0.28 0.283 | 0.242
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11
Maximum Amount of Each Column
0.28 0.283 0.296
Making decision matrix data dimensionless
Administrativ Economic Environmental
e Criteria Criteria Criteria
0.25/0.28 = 0.242/0.283 = 0.296/0.296 = 1
0.89 0.85
0.23/0.28 = 0.243/0.283 = 0.227/0.296 =
0.82 0.86 0.77
0.24/0.28 = 0.232/0.283 = 0.235/0.296 =
0.86 0.82 0.79
0.28/0.28=1 £0.283/0.283 =1 0.242/0.296 =
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12
Normal Matrix
Administrativ Economic Environmental
e criteria criteria criteria
LSF 0.89 0.85 1
ICF 0.82 0.86 0.77
3D-panel 0.86 0.82 0.79
PRCS 1 1 0.82
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Determining Relative Weight of
Criterion:
Criteria Administrati Economic | Environment
ve criteria criteria (+) al criteria
(+) (+)
0.3319 0.3323 0.3358
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14
0.914
0.817
0.823
0.939
Obtaining the utility of each option:
0.89 5
0.82 0.86 0. 77 a
0.86 0.82 0.70 0.3358
1 1 2 1
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Choosing the best option:
1 PRCS 0.939
2 LSF 0.914
3 3D-panel 0.823
4 ICF 0.817
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16
References
Osxkarpour, Ol. (IQE9). OBOO. Outils Criteria Devisiwaxwahiay. (pp. GOC-COF).
Debra Peron Ouversip, Dekron Oaiversiy Publication.
Gpstew Oster Dutipte بان Woven, @. (IOS). Getevtiay the Optcod کر ,ره
Orvisiorwaking Cophusizicy oo Three Orthods ve POPGIG, GOO, ۰ سم
oP Girusturd acd Ovwsirusion Benieeerieny (ISO@). © (2). (0-8? امول
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