ABSTRACT
The ELECTRE I model was first developed by Roy (1968) to find the kernel solution in a situation where true criteria and restricted outranking relations are given. That is, ELECTRE I cannot derive the ranking of alternatives but the kernel set. In ELECTRE I, two indices called the concordance index and the discordance index are used to measure the relations between objects. For the concordance index, C(a, b) measures how much a is at least as good as b. On the other hand, the discordance index, D(a, b) measures the degree to which b is strictly preferred to a. The concordance index and the discordance index in ELECTRE I can be defined by
C a b w
w
m ,
(6.1)
and
D a b w g b g a
,
max
max
( ) = ( ) − ( )( ) ( ) −
∈ ( ) , (6.2)
where C(a, b) and D(a, b) ∈ [0,1], gj(k) denote the preferred scores of the jth attribute for the kth alternative, Q(a, b) denotes the set of criteria for which a is equal or preferred to b, R(a, b) is the set of criteria for which b is strictly preferred to a, and A denotes the set of all alternatives.
