ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
the occurrence possibility, which is difficult to communicate 
with the non-expert. In this part, a methodology for evaluating 
risk assessment by linguistic value and fuzzy relation analysis 
is utilized subsequently. As described previously, the use of 
fuzzy sets will allow an analyst to communicate degree of 
health risk of individual elements to people in a readily 
understood language term. Once these individual risk elements 
are communicated, fuzzy set theory would then permit an 
evaluation of the risk of human health to contaminated waste in 
linguistic variable. 
Thus, we have fuzzy relation matrix: 
R = {r ij | i = l,2,3,4; j = 1,2,3,4,5} (18) 
where r- is the membership function of contaminant i versus 
different cancer risk level j, which is a function of contaminant 
concentration and risk level criteria. 
The groundwater monitoring data for four Volatile Organic 
Petroleum Contaminants (VOPC) can be presented as C¡,. 
The membership grade between c and the polluted level 
grade j can be calculated, according to v the criterion for 
pollutant i at polluted level j. 
Table 3. Criteria of Risk Levels Under Different Concentrations 
for each contaminant (pg/L) 
Clean Slightly Contaminated Significantly Extremely 
Contaminated Contaminated Contaminated 
Benzene 0 1.32 ~ 2.55 3.77 5 
EthylBenzene 13.2 174.9 186.6 347.7 700 
Toluene 40 230 530 780 1000 
Xylenes 8.8 116.6 224.4 332.2 10QQ00 
(1) when C, 6 [V,. 
_lgc,-igv,,_y (19) 
/lgv # -lgv 1J4 
(2) when C, s K,,,v„ >+1 ] 
Based on the previously established criteria, consideration of 
public health, federal and statewide regulatory limits for 
groundwater, and well-accepted drinking water quality 
standards, making use of the survey results from experts in the 
environmental field, sets of linguistic value-supported and more 
detailed risk level criteria according to the allowed ingestion 
dose were established. Here, our study is mainly focused on 
the age group 5. 
Fig. 3 Membership grade of polluted level of Benzene 
The overall fuzzy risk assessment can be preliminarily 
processed by defining the sets for petroleum contaminants U 
and criteria of risk levels V respectively, this definition 
procedure is actually as same as what we previously did. 
JgV,-lgC,/ (20| 
" /Igvr'g''« 
3) when Cj < Vy or C ( > v ( - - +1 
4 = 0, Vi,* (21) 
Thus a parameter of fuzzy related matrix can be obtained as 
follows: 
R ± =\r*\i = WAJ = V>~5\ 
Similarly, a weighting set for petroleum contaminants and the 
max-* composition methodology of set W and R defined 
previously are utilized 
For this case, B= (0.23654, 0.05364, 0, 0, 0.71) 
V={u¡ |V, } (15) 
And MaxB = 0.71 (Extremely Contaminated) 
V = {v 7 J } (16) 
where ui represents contaminant i, and Vj represents risk level. 
Putting in the linguistic terms, sets U and V can be specified 
as: 
U={ Benzene, EthylBenzene, Toluene, Xylenes} 
V={Clean, Practically-not risky, slightly-risky, risky, highly-risky} 
A fuzzy subset of UxV, which is a binary fuzzy relation from set 
U to V, can be characterized through the following membership 
function: 
R .UxV [0,1] (17) 
Therefore, we can determine the risk level for the sampling 
well is extremely contaminated, high demands exist for the 
future remediation. 
3. GIS SUPPORTED RISK ASSESSMENT 
Integrating GIS with environmental risk models can provide a 
more meaningful interpretation of the problem within a 
georeferenced environment. A few studies have focused on 
using GIS for environmental risk assessment. Chen et al. 
(1998) provided linking GIS with a groundwater model and 
decision support system for the purpose of a petroleum 
contaminated site assessment. Miller et al. (1996) conducted a 
project using GIS to calculate human health risks at a large 
military facility. For example, spatial and temporal attributes of 
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