FL P L t t t L f f f
( 123) ( , , ), ( , , )
=
( )
1123 2 1 2 3 FL P L t t f L f f t
( 12) ( , , ), ( , , )
=
( )
112 3 2 1 23
=
FL P L t f t L f t f
( 13) ( , , ), ( , , )
( )
11 23 2 12 3 FL P L f t t L t f f
( 23) ( , , ), ( , , )
=
( )
1 123 21 2 3
 
FL P L t f f L f t t
( 1) ( , , ), ( , , )
=
( )
11 2 3 2 123 FL P L f t f L t f t
( 2) ( , , ), ( , , )
=
( )
1 12 3 21 23 FL P L f f f L t t t
=
FL
( ( 0) ( , , ), ( , , )
P L f f t Ltt f 1 1 2 3 2123 3) ( , , ), ( , , )
( )
( )
1 1 23 212 3
=
We thus get the fuzzy truth-values as follows: 
FL P t t t FL P t t t t t t t t FL P t t t t t t t t FL P t t t t t t t t FL P t t t t t t t t t t t FL P t t t t t t t t t t t FL P
( 123) ( 12) (1 ) ( 13) (1 ) ( 23) (1 ) ( 1) (1 )(1 ) ( 2) (1 ) (1 ) ( 3)
=
= −= −
=− =−
=− = −
= − − =− − +
=− − =− − +
t 123 t 12 3 12 123 t 1 2 3 13 123 t 1 23 23 123
 
t 1 2 3 1 12 13 123 t 1 2 3 2 12 23 123 1 2 3 1 2 3 12 13 23 123
(1 )(1 )
( 0) (1 )(1 )(1 ) 1 t t t t t tt tt ttt FL P t t t t t t t t t t t t t t t
=− − =− − +
= − − − =− − − + + + − .

We, then, consider the same disjunction or union operator 1 21 2 (, ) , 1 F *d xy t t f f* =+ + − , if x and y are disjoint, and 1 2 t t + ≤1 allowing us to add the fuzzy truth values of each part of a shaded area. 

t 1 2 3 3 13 23 123

## Neutrophic Composition Law

 
Let's consider k ≥ 2 neutrophic variables, ( ) , , i ii i x TIF , for all i k ∈{ } 1, 2,..., . Let denote 

$$\begin{array}{l}{{T=\left(T_{1},...,T_{k}\right)}}\\ {{I=\left(I_{1},...,I_{k}\right)}}\\ {{F=\left(F_{1},...,F_{k}\right).}}\end{array}$$
 
$$o_{N}:\stackrel{-}{\left\{T,I,F\right\}}\rightarrow\left[0,1\right]$$

$\downarrow$    . 
 We now define a neutrosophic composition law N o in the following way: 

We now define a neutrosop  $$\begin{array}{c}\sigma_{N}:\{T\}\\ \mbox{If}\ z\in\{T,I,F\}\mbox{then}\ z_{\sigma_{N}}\bar{z}=\prod_{i=1}^{k}\bar{z}_{i}\.\end{array}$$  If $\bar{z},w\in\{T,I,F\}$ then 