with T
x , x ,
n max
max
1
I n
2
max
x , x , max
1
2
F n
max
max
x1 , x2 as the degree of truth,
n indeterminacy and falsity membership function of Neutrosophic set max ;
n max max x3 , x4 , T
with T
n max
max
n max
x , x , I x , x , F x , x max
x3 , x4 ,
I n
max
3
4
max
n max
max
3
n max
4
max
3
4
(5.29)
x3 , x4 , F max x3 , x4 as the degree of truth, n max
n indeterminacy and falsity membership function of Neutrosophic set max ; and
n max max x3 , x4 , T
with T
n max
n max
x , x , max
3
4
x , x , I x , x , F x , x max
3
n max
4
max
x , x ,
I n
max
max
3
4
3
F n
max
4
n max
max
x , x max
3
4
3
4
(5.30)
as the degree of truth,
n indeterminacy and falsity membership function of Neutrosophic set max
5.1.3
Optimization of WBD in Neutrosophic Environment
To solve the WBD (P5.2) step 1 of sect.1.29 is used and we will get optimum solutions of two sub problem as X 1 and X 2 . After that according to step 2 we find upper and lower bound of
membership function of objective function as UCT X ,UCI X ,UCF X and
LTC X , LIC X , LFC X where
,
U CT X max C X 1 , C X 2
(5.31)
,
LTC X min C X 1 , C X 2
(5.32)
Therefore
U
T T UCF X UCT X , LFC X LTC X C X where 0 C X U C X LC X
LIC X LTC X ,U CI X LTC X C X where 0 C X
for Model-I,II-BL,BN F T I UWT UWT UWT
U
T F LTWT LWT LTWT WT where 0 WT UWT I LWT LTWT WT where 0 WT
T WT
LTWT
Page 162
T C X
LTC X
(5.33) (5.34)