First, despite a casual expectation that the two
procedures should yield similar results, they very often
do not. For example, the results of the decision
portrayed in the lower right of Figures 1 and 2 are in
agreement only by 53 per cent. The reason clearly has
to do with the logic of the aggregation operation. For
example, Boolean intersection results in a very hard
AND – a region will be excluded from the result if any
single criterion fails to exceed its threshold. Conversely,
the Boolean union operator implements a very liberal
mode of aggregation – a region will be included in the
result even if only a single criterion meets its threshold.
Weighted linear combination is quite unlike these
options. Here a low score on one criterion can be
compensated by a high score on another – a feature
known as trade-off or substitutability.While human
experience is replete with examples of both trade-off
and non-substitutability in decision making, the tools
for flexibly incorporating this concept are poorly
developed in GIS. Furthermore, a theoretical
framework that can link the aggregation operators of
Boolean overlay and weighted linear combination has,
until recently (Eastman and Jiang 1996), been lacking.
The second problem with MCE has to do with
the standardisation of factors in weighted linear
combination.
First, despite a casual expectation that the twoprocedures should yield similar results, they very oftendo not. For example, the results of the decisionportrayed in the lower right of Figures 1 and 2 are inagreement only by 53 per cent. The reason clearly hasto do with the logic of the aggregation operation. Forexample, Boolean intersection results in a very hardAND – a region will be excluded from the result if anysingle criterion fails to exceed its threshold. Conversely,the Boolean union operator implements a very liberalmode of aggregation – a region will be included in theresult even if only a single criterion meets its threshold.Weighted linear combination is quite unlike theseoptions. Here a low score on one criterion can becompensated by a high score on another – a featureknown as trade-off or substitutability.While humanexperience is replete with examples of both trade-offand non-substitutability in decision making, the toolsfor flexibly incorporating this concept are poorlydeveloped in GIS. Furthermore, a theoreticalframework that can link the aggregation operators ofBoolean overlay and weighted linear combination has,until recently (Eastman and Jiang 1996), been lacking.The second problem with MCE has to do withthe standardisation of factors in weighted linearcombination.
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