Page 35 - Contributed Paper Session (CPS) - Volume 4

CPS2109 Khalid S. et al.
Step 1:Weighting Scheme
Determining the weight of dimension is the main concern of the
multidimensional poverty measurement. The choice of an appropriate weight
is one of the fundamental steps in the calculation of poverty composite indices
of. As part of this work, we use the method proposed by Cerioli and Zani, which
evolves around the following relationship:
n
∑ n n
w = ln [ i=1 i ] (1) avec ∑ x n > 0
j
∑ n x n ij i
ij i
i=1
i=1
x_ij represents the score of the i-th individual in relation to the j-th dimension,
and n_i is the weight of an individual or group of individuals. This means that
the weighting of each dimension is weighted by the logarithm of the inverse
of the frequency of non-full or partial fulfillment of this dimension (the
dimension of deprivation score).
Step 2: Standardization of measurement variables: Determination of the
the score function.
This function is defined as follows:
1 si φ = φ min
ij j
φ max − φ ij
φ = j si φ min ≤ φ ≤ φ max (2)
ij
ij
j
j
φ max − φ min
j
j
max
{ 0 si φ = φ j
ij
with Φ_ij the score of the i-th individual in relation to the variable j-th; φ_j ^
min ^ φ_j and max are the minimum and maximum values. Each score is
associated with a value between 0 and 1, representing this variable in a given
individual or household, the degree of deprivation.
For each dimension with more than one variable, a weighted score is
calculated as follows:

= ∑ (3)

=
With n_k number of variable dimension j, r_p is the relative weight assigned
to the variable p with r ≥ 0 and ∑ n k r = 1, and φ is the membership
ip
p
p
p=1
function of household i for the variable p.
The r_p weight is obtained from equation (1) by replacing j with p.
Step 3: Calculate the composite deprivation index (CDI)
After calculating the weight assigned to each attribute (variable) or
dimension, the last step is the determination of composite indices (fuzzy)
deprivation. To do this, we must first calculate the deprivation composite index
of each individual or household a_i through the following relationship:

∑ m x w j
j=1
ij
μ (a ) = , 0 ≤ μ (a ) ≤ 1 (5)
i
B
B
i
∑ m w
j=1 j
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