Page 14 - Contributed Paper Session (CPS) - Volume 2

CPS1407 D.Dilshanie Deepawansa et al.
new method called “Synthesis Method” developed earlier (see Deepawamsa
et al. 2018). The method combines the fuzzy set theory introduced by Cerioli
and Zani (1990) and further developed by Cheli and Lemmi (1995), Betti et al
(2005a, 2005b), Chakravarty (2006), Betti & Verma (2008), Betti et al.
(1999,2002,2004), Belhadj (2012), and Verma, et al. (2017), and the counting
method introduced by Alkire and Santos (2010) followed by Alkire et al. (2015).
The Counting method is an axiomatic approach which has been empirically
implemented worldwide to calculate the Multidimensional Poverty Index (MPI)
and provides a more flexible framework to produce MPI measures. In contrast,
the Synthesis method (Deepavansa et al. 2018) identifies the poor using the
Fuzzy Membership Function and aggregates the Fuzzy Deprivation Score
using the methods introduced by Alkire et al. (2015). The Fuzzy Deprivation
Score extends the methods developed by Foster, Greer and Thorbeck (1984)
to compute the indices denoting deprivation in social factors that in turn
condition poverty.
The Fuzzy Membership Function is estimated as follows. If is the set of
elements such that ∈ , then the fuzzy sub set can be denoted as,
= {, ()}. (1)

In this equation () is the membership function, (m.f) is a mapping from
→ [0,1]. The value of is the degree of membership in the incident of in
. When = 1 then completely belongs to . But if = 0 then does
not belong to . However, if the elements q is 0 < () < 1 then partially
belongs to . So the degree of q’s membership in the fuzzy set increases when
its propensity () is closer to 1.
Let the term n of the set of individuals (n; i=1 ……. n) be a sub set . Then
the Fuzzy Set Approach describes the poor as follows:
i= 1,2……………. n. (2)

The value of the membership function is defined by the following
equation.;
() = 1 if 0 ≤ <
. −
() = < < (3)

. − .
() = 0 if ≥ ,

th
th
Where is the value of i individual in j indicator where (i=1,2……n) and
(j=1,2……k) in the poor set . Then the Membership Function for each
individual is given by equation (4) which averages the membership scores of
all indicators to provide a fundamental product of the fuzzy set of poor of the
i individual.
th

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