Daoud Brikci, Hichem 
  
Preferences restricted to the significance axis of each criterion are defined through pseudo-criteria. The indifference and 
preference thresholds (q;(b,) and p;(b;)) constitute the intra-criterion preferential information. 
At the comprehensive level of preferences, in order to validate the assertion aSh, (or b,Sa), the conditions of 
concordance and non-discordance should be verified. 
Two types of inter-criteria preference parameters intervene in the construction of S: 
e the set of weight-importance coefficients (k;, k», ..., k,,) 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 (v;(by), v2(by), ..., vim(by) is used in the discordance test. v;(b;) represents the smallest 
difference g;(5,)-g;(a) incompatible with the assertion aSb;.. 
The parameters used in this study are illustrated in the following table : 
  
  
  
  
  
  
  
  
  
Criteria k; q; D; V; 
Habitation | 0.06 | 100 | 500 | 1000 
road 0.06 | 100 | 500 | 1000 
well 0.12 | 100 | 500 | 1000 
hydrography | 0.12 | 100 | 500 | 1000 
Slope 0.23 | 0.5 1 10 
Soil 0.41 1 2 S 
  
  
  
  
  
Table 2: an example of initial parameters. 
ELECTRE Tri builds an index [1(a,b;) ef 0, 1] (D (by, a), resp.) that represents the degree of credibility of the assertion 
aSb, (bySa, resp.), VaeA, VheB. The assertion aSb, (b,Sa, resp.) is considered to be valid if O(a b,)>0 
(U (by, a) 2LI,resp.), L1 being a "cutting level" such that (1 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, à a, 
assign a to category C,. 
  
ELECTRE TRI Approach 
( Pessimistic Result ) 
ELECTRE TRI Approach 
( Optimistic Result ) 
      
     
   
    
  
  
EA Category 1 
Category 2 
EJ Category 3 
    
    
EB Category 1 
FA Category 2 
E79 Category 3 
  
  
  
  
  
  
  
  
  
  
  
  
Figure 4: Pessimistic results Figure 5. Optimistic results. 
  
310 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.