The distance
to wildlife reserve factor, for instance, starts to rise
above 0.0 immediately at the park boundary, but
approaches 1.0 at a distance of 5 kilometres. Further
distance does not lead to an increase in the factor
score since the distance is far enough.
6 DETERMINATION OF WEIGHTS
Given the consideration of factors as fuzzy sets
and the nature of the aggregation process, the
criterion weights of weighted linear combination
clearly represent trade-off weights – that is,
expressions of the manner in which they will trade
with other factors when aggregated in multi-criteria
evaluation. Rao et al (1991) have suggested that a
logical process for the development of such weights
is the procedure of pairwise comparisons
developed by Saaty (1977). In this process each
factor is rated for its importance relative to every
other factor using a 9-point reciprocal scale (i.e. if
7 represents substantially more important, 1/7
would indicate substantially less important). This
leads to a n x n matrix of ratings (where n is the
number of factors being considered). Saaty (1977)
has shown that the principal eigenvector of this
matrix represents a best fit set of weights. Figure 5,
for example, illustrates this rating scale along with
a completed comparison matrix and the best fit
weights produced. Eastman et al (1993) have
implemented this procedure in a raster GIS with a
modification that also allows the degree of
consistency to be evaluated as well as the location
of inconsistencies to allow for an orderly reevaluation.
The process is thus an iterative one that
converges on a consistent set of consensus weights.
A problem still exists, however, in how these
weights should be applied in the context of the
ordered weighted average discussed above. It seems
clear that these weights will have full effect with the
weighted linear combination operator (where full
trade-off exists), and that they should have no effect
when no trade-off is in effect (i.e. with the minimum
and maximum operators).
The distanceto wildlife reserve factor, for instance, starts to riseabove 0.0 immediately at the park boundary, butapproaches 1.0 at a distance of 5 kilometres. Furtherdistance does not lead to an increase in the factorscore since the distance is far enough.6 DETERMINATION OF WEIGHTSGiven the consideration of factors as fuzzy setsand the nature of the aggregation process, thecriterion weights of weighted linear combinationclearly represent trade-off weights – that is,expressions of the manner in which they will tradewith other factors when aggregated in multi-criteriaevaluation. Rao et al (1991) have suggested that alogical process for the development of such weightsis the procedure of pairwise comparisonsdeveloped by Saaty (1977). In this process eachfactor is rated for its importance relative to everyother factor using a 9-point reciprocal scale (i.e. if7 represents substantially more important, 1/7would indicate substantially less important). Thisleads to a n x n matrix of ratings (where n is thenumber of factors being considered). Saaty (1977)has shown that the principal eigenvector of thismatrix represents a best fit set of weights. Figure 5,for example, illustrates this rating scale along witha completed comparison matrix and the best fitweights produced. Eastman et al (1993) haveimplemented this procedure in a raster GIS with amodification that also allows the degree ofconsistency to be evaluated as well as the locationof inconsistencies to allow for an orderly reevaluation.The process is thus an iterative one thatconverges on a consistent set of consensus weights.A problem still exists, however, in how theseweights should be applied in the context of theordered weighted average discussed above. It seemsclear that these weights will have full effect with theweighted linear combination operator (where fulltrade-off exists), and that they should have no effectwhen no trade-off is in effect (i.e. with the minimumand maximum operators).
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