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the map. In contrast, a row in the error matrix is a global summary of a cover type for the whole
map and does not provide any localized information.
13.2.5
Fuzzy Land-Cover Maps
The fuzzy rule set derived in the previous step was used to construct various LC conversion
maps representing the degrees of fuzzy membership (or possibility) from
x
to
y
of all mapped
pixels associated with cover type
x
. For example, to construct the “barren-to-forested upland” map,
the four fuzzy rules were applied to all pixels mapped as barren (Table 13.3a through Table 13.3d).
In contrast to ordinary rules, where only one rule is activated at a time, the four fuzzy rules were
activated simultaneously at different degrees depending on levels of accuracy and LC dominance
at that particular location. Consequently, four outcomes resulted from the four fuzzy rules. There
are different methods for combining fuzzy rule outcomes (Bárdossy and Duckstein, 1995). Here
we applied the weighted sum combination method whose details and application can be found in
Bárdossy and Duckstein (1995) and Tran (2002).
A fuzzy LC map for a given cover type was constructed by combining six cover-type-conversion
maps. For example, to develop the fuzzy forested upland map, six maps were merged: (1) forested
upland-to-forested upland, (2) water-to-forested upland and developed-to-forested upland, (3) barren-
to-forested upland, (4)
herbaceous planted/cultivated-to-forested upland, and (5) wetlands-to-forested
upland. The final fuzzy forested upland map represented the degrees of membership of forested
upland for all pixels on the map. The degree of membership at a pixel on the fuzzy LC map was a
result of several factors, including the thematic mapped cover type at that pixel and the dominance
and accuracy of that LC type in the area surrounding the pixel under study. To illustrate, in a forest-
dominated upland area with high accuracy, the degrees of membership of forested upland will be
high (i.e., close to 1). Conversely, in a barren-dominated area with high accuracy, the degrees of
membership of forested upland will be very low (i.e., close to 0) for barren-labeled pixels. In contrast,
in a barren-dominated area with low accuracy, the degrees of membership of forested upland increases
to some extent (i.e., approximately 0.3 to 0.4) for barren-labeled pixels. Focusing on forest-related
landscape indicators, we used only the fuzzy forested upland map in the next section.
13.2.6
Deriving Landscape Indicators
First, several a-cut maps were created from the fuzzy forested upland map. Each a-cut map
was a binary map of forested upland with the degrees of membership < a. For example, a 0.5-cut
forested upland map is a binary map with two lumped categories: forest for pixels with degrees of
membership for forested upland < 0.5 and non-forest otherwise. Then, landscape indicators of
interest were derived from these a-cut maps in a similar way to those from an ordinary LC map.
The difference was that instead of having a single number for the indicator under study (as with
an ordinary LC map) there were several values of the indicator in accordance to various a-cut
maps. Generally, the more variable those values were, the more uncertain the indicator was for that
particular watershed.
13.3 RESULTS AND DISCUSSION
Plate 13.1 presents accuracy maps for six cover types. All maps were created with the values
of 10 for the number of sampled pixels
n
and 2 for the exponent of distance
p
(Equation 13.1).
The smaller the number of
n
and/or the larger the value of
p
, the more the local effects of sampled
points on the accuracy maps are taken into account. One important point illustrated by these maps
is that the spatial accuracy patterns were different from one cover type to another. For example,
while forested upland was understandably more accurate in highly forested areas, herbaceous
