the generalized dice measures for multiple attribute decision making under simplified neutrosophic...
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8/20/2019 The generalized Dice measures for multiple attribute decision making under simplified neutrosophic environments
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The generalized Dice measures for multiple attribute decision making
under simplif ied neutrosophic environments
Abstract
Keywords:
1. Introduction
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2. The Dice measures of SNSs
Def inition 1 S X
X x xv xu xt xS S S S t S x X uS x X vS x X
x S t S x uS x vS x x X
x t S x uS x vS x S s x t x u x v x
t x u x v x t x u x v x
U
x
L
x x t t t
U
x
L
x x uuu
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n
j j j j j
n
j j j j j
n
j j j j j j j j
ww
wWSVNN
vut wvut w
vvuut t w
S S
S S S S D
n
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WINN
vvuut t w
vvuut t w
vvvvuuuut t t t w
S S
S S
S S D
4. The generalized Dice measures of SNSs
Def inition 4. S s s s n S s s s n s j t j u j v j
s j t j u j v j j n j S S
S S
n
j j j j j j j
j j j j j j
n
j j j
j j
SVNN
vut vut
vvuut t
n
ss
ss
nS S G
n
j j j j
n
j j j j
n
j j j j j j j
SVNN
vut vut
vvuut t
S S
S S S S G
n
j j j j
j j j j j jn
j j
j j
SVNN vut
vvuut t
ns
ss
nS S G
n
j j j j
j j j j j jn
j j
j j
SVNN vut
vvuut t
ns
ss
nS S G
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U
ij
L
ijij t t t U
ij
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ijij uuu
U
ij
L
ijij vvv i j n
n
jU
j
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INN
vut vut
vvvvuuuut t t t
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s
ss
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jU
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vvvvuuuut t t t
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ssn
S S G
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INN
vvuut t
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S S S S G
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INN
vvuut t
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S
S S S S G
sij i j n
W w w wn sij i j n w j
n
j jw
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S S S S
S S S S
S S S S
S S S
S i S S
S i S S
S S i S
7. Conclusion
References
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Applied Mat hematical Modelling 37
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Int ernational Journal o f Fuzzy Syst ems 16
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Mat hematical Modelling 38
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Syst ems 16
Neural Computing and Applications 25
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Neural Computing and Applications
Journal o f Int elligent
and Fuzzy Syst ems
Neural Computing and Applications
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