ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
63
U=iu i
|V,.)
(7)
V = ^i
IV. I
(8)
where «. represents contaminant i, and v . is for age group
1 J
j-
A fuzzy subset of UxV, which is a binary fuzzy relation from U
to V, can be characterized through the following membership
function:
R :(J xV —> [0,1] (9)
Thus, we have fuzzy relation matrix:
R = {r | i = l,2,3,4; j = 1,2,3,4,5) (10)
V
Fig. 2 relationship between contaminant intake and
cancer possibility
r ij <«y}
r ij = (Xij ~ fly ) /(by - fly ){<3y <X<b i j) (11)
r tJ = l{x > by }
Thus we got the matrix format for equation (10).
Since individual contaminant will have different overall impacts
on human health, we can construct a weighting set on U as:
where x-- is the membership function of different contaminant
V
intake to cancer risk for contaminant I versus different age
group j, which is a function of contaminant concentration and
age group.
The membership function of fuzzy set A to input factor x,
denoted as JU A (x){0 < fJ. A (x) < 1} , will be defined as a
linear function (Figure 2). It requires two parameters (a- and
by , which denoted as the lower and upper bounds of
allowable exposure dose). The relevant standards for setting
fly and by are considered and acquired from the orientation
materials and established standards from USEPA and
published statewide and local government standards. For
example, USEPA t and California local environmental
department respectively take 0.005mg/L and 0.001 mg/L as
federal and local guidelines for Benzene concentration in the
groundwater to assess the potential health carcinogenicity.
And Maximum Contaminant Level Goals (MCLG) for benzene
has been set at zero because USEPA believes this level of
protection would not cause any of the health effects.
For age group 5, referring to above-mentioned guidelines, the
most conservative standard 0.0mg/L and most popular
standard 0.005mg/L are used to estimate and by . Taking
those two values as concentration inputs into the contaminant
intake calculation equation, the according ingestion dose-
based standards will be derived. Following the similar
concentration standard acquirement methodology, the
respective concentration standards and ingestion dose- based
standards for the rest of three contaminants can be obtained.
Instead of having a detailed distribution for explaining the
uncertainties, we have the membership grade of x tj • (Intake
Dose) to cancer risk calculate as following:
4
W={W1 ,W2,W3,W4) and =1
1
(W1=0.71, W2=0.11, W3=0.09, W4=0.09)
(12)
Therefore, the comprehensive possibility of cancer risk posed
by different age group could be calculated through the
synthesizing process of a weighting set W and fuzzy relation
matrix R:
W ° R <-> ß woR
(13)
here we define ° as a max-* composition, so the membership
grade
MwoR =X < 14 )
and the result
B=(0.80183,0.8009,0.80048,0.724288,0.723402)
Which could be explained as the possibility that Age1, Age2,
Age3, Age4, Age5 could have when exposed to the sample
contaminant concentration. Therefore, besides knowing only
the membership function value of cancer risk for each
contaminant for different age group, and integrated possibility
of causing cancer risk by concerned contaminants for different
group is also presented as well.
2.3 Extended Health Risk Assessment Approach by
Using Fuzzy Set Theory
The limitation of conventional overall risk assessment
calculation method, which was spreadly accepted, occurs in
the procedure of final overall risk evaluation. Regardless of the
physical and chemical characteristic differences or
interrelationships for both carcinogens and non-carcinogens,
the overall cancer risk or non-cancer risk measurement for
exposure to multiple carcinogens and non-carcinogens is
normally the risk summarization of individual contaminant to
provide the final measurement of risk.
We introduced the concept of constructing risk analysis by
fuzzy set theory in the above measurement of the individual
health risk assessment. However, it’s by the number term of
