the 
stic 
ach 
ally 
and 
as 
ind 
est 
| is 
ind 
et 
Les 
tifs 
ant 
jon 
ted 
Daoud Brikci, Hichem 
  
However, the different studies done until now showed that this approach was not reliable (A. Schárlig, 1985) but it is 
still used since the partial aggregation (outranking) approach cumbersome due to the inter-comparison of all the 
alternatives (actions) which represents, in the case of an image (pixels), about 100 million of operations (F. Joerin, 
1995). 
Our study is based on the integration of ELECTRE (ÉLimination Et Choix Traduisant la RÉalité) methods into a raster 
GIS aiming to resolve spatial decision problems. This helps to build a model of the decision maker preferences to 
process it while choosing one of the several alternatives. 
2 METHODOLOGY 
When modelling a real world decision problem using multiple criteria decision aid, several problematic (or problem 
formulations) can be considered. [Roy, 1985] distinguishes three basic problematic: choice (01), sorting (01) and ranking 
(D). 
Given a set A of alternatives (or actions), the choice (or selection) problematic consists in a choice of a subset A'—4A, as 
small as possible, composed of alternatives being judged as the most satisfying. 
he sorting problematic consist in formulating the decision problem in terms of classification so as to assign each 
alternative a to the appropriate category should rely on the intrinsic value of a (and not on the comparison of a to other 
alternatives from A). 
The ranking problematic consists in establishing a preference pre-order (either partial or complete) in the set of 
alternatives A. 
The outranking methods deal with only one of the reference problematic. Therefore ELECTRE methods are also 
concerned by this rule: 
  
  
  
  
  
  
  
  
  
  
  
  
    
e ELECTRE I: 0 problematic, 
e FLECTRE IX: 0, | Spatial decision problem | 
e ELECTRE HI: 0, wv wv wv 
e ELECTRE IV: L), Set of categories Set of 
e ELECTRE TRE: 0, and profiles alternatives 
e ELECTRE Is: D. 
preference Weight- 
ELECTRE Tri is a multiple criteria sorting method, i.e., a method |indifferenc ELECTRE importance 
that assigns alternatives to predefined categories. The assignment of e TRI Coefficients 
an alternative a results from the comparison of a with the profiles and veto (AHP 
defining the limits of the categories. This method requires the technique) 
elicitation of parameters ( weights, discrimination thresholds, Assignment 
category limits,...) in order to construct a preference model of the to predefined categories 
decision maker. New set of 
alternatives 
The main objective of our approach is to reduce the number of the problematic? (best category) 
  
    
  
  
alternatives using ELECTRE Tri (sort). In fact, when the 
problematic used is different from sorting (choice or ranking), the 
other ELECTRE should be applied involving the best category 
yielded by ELECTRE Tri (see fig.1). 
  
ye 
  
  
UY p p 
electre |; electre || electre i! electre electre 
! Il II IV Is | 
  
The level III of Goraducci [1993] was adopted to build our 
prototype. The user is now provided by a programme and its data 
base which contains both spatial data and multicriteria methods 
base. The multicriteria algorithm is performed either in GIS | Robustness analysis b Recommendation | 
language or in an external routine to be called using the same 
language. This algorithm will be used as a function such as the Figure 1. ELECTRE approach scheme. 
spatial analysis modules. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 307