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s
η l Sup
ij
r ( k )
ij
r ( k )
ij
r ( l )
T
( ˜
) =
˜
, ˜
(1.101)
l
=
1
l
=
k
ξ ( k )
ij
r ( k )
ij
and calculate the weights
(
k
=
1
,
2
,...,
s
)
associated with the IVIFVs
˜
(
k
=
1
,
2
,...,
s
)
:
η k 1
r ( k )
ij
+
T
( ˜
)
ξ ( k )
ij
k = 1 η k 1
,
=
k
=
1
,
2
,...,
s
(1.102)
r ( k )
ij
+
T
( ˜
)
s , and k = 1 ξ ( k )
ξ ( k )
ij
where
≥
0
,
k
=
1
,
2
,...,
=
1.
ij
Step 3 Utilize the IVIFPWA operator ( 1.71 ):
r ( 1 )
ij
r ( 2 )
ij
r ( s )
ij
r ij =
˜
( ˜
, ˜
,..., ˜
)
IVIFPWA
1
ij
s
s
k = 1 (
k = 1 (
) ξ ( k )
) ξ ( k )
− μ − ( k )
ij
− μ + ( k )
ij
=
−
1
,
1
−
1
,
ij
s
ij
s
k = 1 (
k = 1 (
) ξ ( k )
) ξ ( k )
v − ( k )
ij
v + ( k )
ij
,
,
ij
s
ij
s
s
s
k = 1 (
k = 1 (
k = 1 (
k = 1 (
) ξ ( k )
) ξ ( k )
) ξ ( k )
) ξ ( k )
− μ + ( k )
ij
v + ( k )
ij
− μ − ( k )
ij
v − ( k )
ij
1
−
,
1
−
ij
ij
ij
⎛
⎝
⎡
⎣
⎤
⎦ ,
r (
k
)
r (
k
)
η k (
1
+
T
( ˜
))
η k (
1
+
T
( ˜
))
s
ij
s
ij
s
k
s
k
r (
k
)
r (
k
)
− μ − ( k )
ij
− μ + ( k )
ij
1 η k (
1
+
T
( ˜
))
1 η k (
1
+
T
( ˜
))
=
−
1 (
)
,
−
1 (
)
1
1
1
1
=
ij
=
ij
k
=
k
=
⎡
⎣
⎤
⎦ ,
r (
k
)
r (
k
)
η k (
1
+
T
( ˜
))
η k (
1
+
T
( ˜
))
ij
ij
s
s
k = 1 (
j = 1 (
k
i
r (
k
)
r (
k
)
v − ( k )
ij
v + ( k )
ij
1 η k (
1
+
T
( ˜
))
1 η i (
1
+
T
( ˜
))
)
,
)
=
ij
=
ij
⎡
⎣
r (
k
)
r (
k
)
η k (
1
+
T
( ˜
))
η k (
1
+
T
( ˜
))
s
ij
s
ij
k = 1 (
k = 1 (
s
i
s
k
r (
k
)
r (
k
)
− μ + ( k )
ij
v + ( k )
ij
1 η i (
1
+
T
( ˜
))
1 η k (
1
+
T
( ˜
))
1
)
−
)
,
=
ij
=
ij
⎤
⎦
⎞
⎠
r (
k
)
r (
k
)
η k (
1
+
T
( ˜
))
η k (
1
+
T
( ˜
))
ij
ij
s
s
k = 1 (
k = 1 (
s
k =
s
k =
r (
k
)
r (
k
)
− μ − ( k )
ij
v − ( k )
ij
1 η k (
1
+
T
( ˜
))
1 η k (
1
+
T
( ˜
))
(1.103)
1
)
−
)
ij
ij
or the IVIFPWG operator ( 1.78 ):
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