![](bg9.png)
ure 1) would be:
M
e
=
n
m
(x)
g
, m
(y)
g
o
m
(x)
g
= median
^
i=1,...,3
p
(i,x)
g
= (58, 75, 75, 94)
m
(y)
g
= median
^
i=1,...,3
p
(i,y)
g
= (31,49, 49,68).
And the min-max center (see Figure 2) would be:
Z
e
=
n
z
(x)
f
, z
(y)
f
o
z
(x)
f
=
1
2
∑
i∈
{
1,3
}
p
([i],x)
^
= (49.667, 64.333, 66, 80.333)
z
(y)
f
=
1
2
∑
i∈
{
1,3
}
p
([i],y)
^
= (42.667, 57.333, 58.333, 72.667) .
As we can see from the figures, the option of using
fuzzy numbers to model the demand points is much
more closer to what in reality geographers and plan-
ners face. The results obtained will give them flexi-
bility in the final location of the center, according to
constraints not easily modeled otherwise.
6 CONCLUSIONS
In this paper we have shown that the results found for
the solution of the median center and the min-max
center can be extended to fuzzy environments, where
both the demand points and the center are modeled
with fuzzy numbers. The use of fuzzy numbers is due
to the need to reflect the uncertainty about available
information on demand. Not only the data might be
vague or subjective, but it could also involve disagree-
ments or lack of confidence in the methodology used
in its collection. Therefore, it is necessary to have a
solution that, while simply obtained, incorporates this
uncertainty.
Fuzzy solutions can also give flexibility to plan-
ners on the final location of the center, according to
constraints that are not easily modeled. The selected
center will have a membership value that reflects its
“appropriateness” according to the data.
Future work deriving from this methodology will
follow solving the fuzzy 1-median problem as well
as the barycenter, when the solution is modeled with
fuzzy numbers. We would like to use the results found
for multicriteria analysis, creating a fuzzy Pareto front
by intersecting the solutions found for different values
of p.
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ON THE EXTENSION OF THE MEDIAN CENTER AND THE MIN-MAX CENTER TO FUZZY DEMAND POINTS
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