sed on minimal 
y in pessimistic 
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and for larger 
ximum attribute 
egated seismic 
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Five distinct 
In other words, 
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tical units are 
sse OWL 
ensis QW 20.75 
ei O(W)-0.5 
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vibes QI W]zO 
  
e for five 
sm degree has a 
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atistical units. 
the Minimal 
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of the model 
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alue of minimal 
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ptimism degree 
it to which the 
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ic vulnerability 
e vulnerability 
introduced in 
he vulnerability 
1e variation of 
ility degree of a 
  
  
  
   
  
   
   
   
   
  
  
   
  
  
   
   
   
  
   
    
  
    
   
statistical unit, the more robust the vulnerability degree is 
calculated under the uncertainty of optimism degree. Figure 3 
demonstrates aggregated seismic vulnerability degrees and their 
calculated sensitivity for the five selected statistical units. The 
results indicate that the sensitivity degree has a direct 
relationship with vulnerability degree. In other words, the 
vulnerability degree of vulnerable and very vulnerable statistical 
units is more sensitive to optimism degree in comparison to 
lower seismic vulnerable statistical units. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
# Vulnerability {i Sensitivity 
1 
9 0.9 
$ 0.8 
= 0.7 
$ os 
= 0.5 
5 0.4 
= 13 
0.2 
0.1 
0 
| 1 2 3 4 
irisensitivity © 0.05 0.16 0.13 0.11 0.08 
ulnerability 0.34 0.76 0.61 0.57 0.44 
Urban statistical unit 
  
  
  
Figure 3. Sensitivity and vulnerability measures for five 
randomly selected statistical units 
Figure 4 demonstrates the sensitivity degree for all statistical 
units in TMA. A number of statistical units in southern part of 
Tehran and most of the units in northern part of the city are very 
sensitive to optimism degree. It means that uncertainty involved 
in optimism degree results in high uncertainty in seismic 
vulnerability of these statistical units. 
SUE STATE 
"d 
5 
ré 
SEISCE 
       
  
WGS - 1984 UTM Zone 39 N 
FSRTON 
Legend 
É Sensitivity Degree 
  
8 SIDE SUITE BADE STALE SUITE % 
Figure 4. Sensitivity measure for statistical units of Tehran 
Metropolitan Area 
A number of statistical units in northern part of Tehran are 
vulnerable and very vulnerable due to the very short distance to 
North Tehran Fault. Non-standard construction causes a 
number of statistical units to be very vulnerable. Due to direct 
relationship between vulnerability degree and sensitivity of 
vulnerability degree, the statistical units which are vulnerable 
are very sensitive as well. 
4. DISCUSSION 
In ill-structured multi-criteria decision making problems such as 
seismic vulnerability assessment and loss estimation, in order to 
compare the efficiency of models, additional measures are 
required. One of the most significant measures that facilitate the 
comparison of different models is sensitivity measure. 
Calculating the sensitivity of vulnerability degrees of statistical 
units beside their vulnerability degrees enables experts to 
compare the stability and robustness of models. In minimal 
variability OWA model of seismic vulnerability assessment, the 
maximum of sensitivity measure is 0.27 which is 25% of its 
vulnerability degree. In other words, the variation of optimism 
degree will make a fluctuation between 0.9% and 25% in 
aggregated vulnerability degree. It means that the model 
considerably depend on optimism degree. However, in a 
number of safer areas, the model has an acceptable robust 
behaviour. In other words, in the minimal variability OWA, a 
more stable decision is made for the alternatives which have a 
lower aggregated value (safer statistical unit). As a conclusion, 
the minimal variability OWA model of seismic vulnerability 
assessment has a robust behaviour under uncertainty of 
optimism degree if the statistical units are not vulnerable or very 
vulnerable. 
5. CONCLUSION 
This paper proposed a model to analyse the sensitivity of 
seismic vulnerability degrees obtained by using minimal 
variability OWA operator. This additional measure facilitates 
seismic loss estimation under uncertainty. Sensitivity measure 
of seismic vulnerability model demonstrates which statistical 
unit have a more stable seismic vulnerability degree. The 
research indicates that sensitivity of seismic vulnerability 
degrees has a direct relationship with seismic vulnerability 
degrees. Consequently, the seismic vulnerability degree 
obtained from minimal variability OWA is more robust for safer 
statistical units, while for vulnerable and very vulnerable 
statistical units a higher level of uncertainty is involved in 
aggregated vulnerability degree. The results also demonstrate 
that the minimal variability OWA model for seismic 
vulnerability assessment have more precise values in central 
areas of TMA especially in areas that are not vulnerable to 
earthquake. However, the minimal variability OWA model is 
noticeably sensitive to optimism degree in northern areas and a 
number of southern parts which are more vulnerable to 
earthquake. Although this paper proposed a model to analyse 
the internal sensitivity of minimal variability OWA model to 
some extents, further researches may be focused on external 
accuracy of the model which could be calculated either by 
comparison of results with real earthquake damages (if happens 
in future) or by comparison to results obtained using other 
models of seismic vulnerability assessment. 
REFERENCES 
Samadi Alinia, H. S., and Delavar, M., 2011. Tehran’s seismic 
vulnerability classification using granular computing 
approach. Applied Geomatics, 3(4), 229-240. 
Baker, J. W., and Cornell, C. A., 2008. Uncertainty propagation 
in probabilistic seismic loss estimation. Structural 
Safety, 30(3), pp. 236-252.