Geoscience Reference
In-Depth Information
that they do not maximise and minimise the memberships and so are convenient operators for
some situations:
(12.8)
µ
()
x
=
µ
() () ()
x
+
µ
x
−
µ
x
AB
∪
A
B
AB
∩
(12.9)
µ
()
x
∩
=
µ
() ()
x
⋅
µ
x
AB
A
B
Several researchers have argued that the application of fuzzy logic to geographical problems has
several advantages. Thus, Burrough (1989) shows that from observations of the amount of sand in
different soil horizons, it is possible to derive fuzzy set memberships of any horizon being sandy and
then of the membership of the soil being sandy in any layer or of being sandy throughout. Burrough
et al. (1992) argue that a fuzzy logic approach to soil evaluation for land use provides a more rigor-
ous approach with an outcome which better reflects the reality of the situation. Specifically, the crisp
set derived from the final fuzzy combination includes areas that meet any criteria of contiguity and
suitability but would be excluded by a Boolean analysis from the start.
The simplest example of the application of fuzzy logic in GC is Leung's (1987) suggestion that
the fuzzy
intersect
between two mapped geographical classes shows the degree to which any loca-
tion belongs to both classes, that is, the boundary class or, in ecology, the ecotone or, more correctly,
the ecocline (Kent et al., 2006). This suggestion was followed up by Arnot and Fisher (2007) who
undertook mapping of the ecocline at the Bolivian savanna-forest boundary. They showed various
ways the ecocline could be derived and visualised (Figure 12.8).
Fisher et al. (2006) present a more complex result of fuzzy logic applied to land cover change
mapping in the same area of Bolivia. They argue that although the logic of a change matrix is
based on the intersection of pairs of land cover types at different times, doing this with a standard
(a)
(b)
0.00
0.06
0.13
0.19
0.25
0.31
0.38
0.44
0.50
0.56
0.63
0.69
0.75
0.81
0.88
0.94
1.00
(c)
(d)
FIGURE 12.8
The derivation of a fuzzy ecotone: (a) the extent of wet savanna, (b) the extent of dry savanna,
(c) the fuzzy
intersect
of the two cover types and (d) the normalised
intersect
of the two covers. (From Arnot,
C. and Fisher, P., Mapping the ecotone with fuzzy sets, in:
Geographic Uncertainty in Environmental Security
,
Morris, A. and Kokhan, S., eds., Springer, Dordrecht, the Netherlands, 2007, pp. 19-32.)
