|; 223%
riterion
e intra-
validate
nce and
Two types of inter-criteria preference parameters intervene in
the construction of S:
e the set of weight-importance coefficients (kj, k2, …, Ka) is
used in the concordance test when computing the relative
importance of the coalitions of criteria being in favour of
the assertion aSb,,
e the set of veto thresholds (vi(by), v2(by), ..., v.(b,)) is used
in the discordance test. v,(b, represents the smallest
difference g,(b,)-g((a) incompatible with the assertion
aSb,..
The parameters used in this study are illustrated in the
following table :
Table 2: an example of initial parameters.
Criteria k; q; Di V;
Habitation 006 100 $500 1000
road 0.06 100 500 1000
well 0.12 100 500 1000
hydrography 0.12 100 500 1000
Slope 0.23: 20:5 1 10
Soil 0.41 1 2 5
ELECTRE Tri builds an index o(a,by e[ 0, 1] (o(b,,a), resp.)
that represents the degree of credibility of the assertion aSb,
(b»Sa, resp.), VaeA, VheB. The assertion aSb, (bsSa, resp.) is
considered to be valid if o(a,b,)2A (o(b,a) 2A,resp.), À being a
"cutting level" such that A ef 0.5, 1].
Two assignment procedures are then available:
e Pessimistic procedure (see fig.4):
a- compare a successively to b;, for i-p, p-1, ..., 0,
b- b, being the first profile such that aSb,,
assign a to category C,.;.
e Optimistic procedure (see fig.5):
a- compare a successively to b,, for i=1, 2, ..., p,
b- b, being the first profile such that b, ¢ a,
assign a to category Cj.
Figure 4: pessimistic results.
Figure 5: optimistic results.
Bl Category 1
ESB Category 2
[3 Category 3
3.3 Results
Decision problem may be resolved in several ways according to
the way of thinking of the decision maker:
-Restrictive hypothesis are introduced in such a way that the
problem should be resolved using a classical method.
-A multicriteria method based on models using both restrictive
mathematical hypothesis and information acquired by the
decision maker.
When using the unique criterion approach, the problematic
became at the same time choice, ranking and sorting.
The drawbacks of the weighted sum "classical method" are:
e sensitivity to scale transformation; In fact, if the proximity
to roads criteria is expressed in km, then the result will be
wrong (pixel score is divided by 1000).
e criteria compensation: a pixel may have very bad scores on
almost all the criteria but it may be compensated by a good
evaluation on a highly weighted criterion.
On the other hand the scale transformation and criteria
compensation do not take part of ELECTRE approach. The
major difficulty is, however, to give a right interpretation of the
result. This would point out the conflict and multicriteria
features of the decision problem.
Furthermore, the robustness analysis is very useful for choice
of the initial values of the parameters. When the parameters
are changed regarding their initial values, the results do not
change and this represents a robust recommendation.
4. CONCLUSION
The objective of the study was not to compare these two
methods since they are based on different mathematical bases.
It was noted that the use of IDRISI modules facilitated the
interpretation of the results. But this would never say that
ELECTRE methods are not suitable for such a study, since
these methods lead to an intermediate result between dominant
relationship (very poor to be useful) and multi attribute utility
function (very rich to be reliable).
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 89
