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Sup r ( k )
ij
ij
r ( l )
r ( k )
ij
r ( l )
ij
,
=
1
−
d
(
,
),
k
,
l
=
1
,
2
,...,
s
(1.51)
which satisfy the support conditions (1)-(3) in Sect. 1.2.3 . Here, without loss of
generality, we calculate d
r ( k )
ij
r ( l )
ij
(
,
)
with the normalized Hamming distance ( 1.28 ):
μ ( k )
ij
ij +
ij +
π ( k )
ij
ij
1
2
r ( k )
ij
r ( l )
ij
− μ ( l )
v ( k )
ij
v ( l )
− π ( l )
d
(
,
) =
−
,
k
,
l
=
1
,
2
,...,
s
(1.52)
Step 2 Utilize the weights
η k (
k
=
1
,
2
,...,
s
)
of the experts e k (
k
=
1
,
2
,...,
s
)
r ( k )
ij
of the IFV r ( k )
ij
by the other IFVs r ( l )
ij
to calculate the weighted support T
(
)
( l
=
1
,
2
,...,
s , and l
=
k
)
:
s
η l Sup r ( k )
ij
r ( k )
ij
r ( l )
T
(
) =
,
(1.53)
ij
1
l = k
l
=
ξ ( k )
ij
associated with the IFVs r ( k )
ij
and calculate the weights
(
k
=
1
,
2
,...,
s
)
(
k
=
1
,
2
,...,
s
)
:
η k 1
r ( k )
ij
+
T
(
)
ξ ( k )
ij
k = 1 η k 1
,
=
k
=
1
,
2
,...,
s
(1.54)
r ( k )
ij
+
T
(
)
s , and k = 1 ξ ( k )
ξ ( k )
ij
where
≥
0
,
k
=
1
,
2
,...,
=
1.
ij
Step 3 Utilize the IFPWA operator ( 1.26 ):
r ( 1 )
ij
r ( 2 )
ij
r ( s )
ij
r ij =
IFPWA
(
,
,...,
)
⎛
⎝
η k ( 1 + T ( r ( k )
ij
η k ( 1 + T ( r ( k )
ij
))
))
s
s
k
k
r ( k )
ij
r ( k )
ij
− μ ( k )
ij
v ( k )
ij
1 η k (
1
+
T
(
))
1 η k (
1
+
T
(
))
=
1
−
1 (
1
)
,
1 (
)
,
=
=
k
=
j
=
⎞
r ( k )
ij
r ( k )
ij
η k (
1
+
T
(
))
η k (
1
+
T
(
))
s
s
s
s
k = 1 η k ( 1 + T ( r (
k
)
k = 1 η k ( 1 + T ( r (
k
)
⎠
− μ ( k )
ij
v ( k )
ij
))
))
1 (
1
)
−
1 (
)
(1.55)
ij
ij
k
=
k
=
or the IFPWG operator ( 1.38 ):
 
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