Download ELECTRE TRI 2.0a METHODOLOGICAL GUIDE AND

2.2.4 Consistency in the definition of the categories
The ordered p+1 categories C1, C2, ..., Cp+1 are defined in ELECTRE TRI by p profiles b1, b2, ...,
bp, bh being the upper limit of category Ch and the lower limit of category Ch+1, h=1, 2, ...,p. For
the categories to be consistently defined, the profiles should respect the two following
conditions:
Condition 1 : ∀j∈F, ∀h=1..p-1, gj(bh+1) ≥ gj(bh)
This condition simply states that the categories should be ordered. As ELECTRE TRI considers
ordered categories, it is not possible to use the method if this condition is not fulfilled.
Condition 2 : ∀j∈F, ∀h=1..p-1, gj(bh+1) - pj(bh+1) ≥ gj(bh) + pj(bh)
In order to define ”distinguishableç categories, it is reasonable to impose that no alternative can
be indifferent to more than one profile, i.e., ∀a∈A, ∀h=1..p-1, aIbh ⇒ [not aIbh+1 and not aIbh-1]
(a situation in which aIbh and aIbh+1 would implicitly mean that the category delimited by the
profiles bh and bh+1 is ”insufficiently wideç). Condition 2 is a sufficient condition for the
preceeding property to hold. In other words, it is possible to run ELECTRE TRI with profiles that
do not fulfill condition 2 but in such cases some alternatives can be indifferent to two
consecutive profiles.
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