 Then consider a binary *T conorm* − (disjunction or union), denoted by (, ) F *d xy* : 
( ) [ ][ ] [ ][ ] 2
: 0,1 0,1 0,1 0,1 F d × →×
 ( )( ) 1 21 2 , ,1 F *d xy t t f f* =+ +−
if x and y are disjoint and 1 2 t t + ≤1. 

 This fuzzy disjunction operator of disjoint variables allows us to add the fuzzy truthvalues of disjoint parts of a shaded area in the below table. When the truth-value increases, the false value decreases. More general, ( 1 2 , ,..., ) kF k *d xx x* , as a k-ary disjunction (or union), for k ≥ 2 , is defined as: 
 : 0,1 0,1 0,1 0,1 ( ) [ ][ ] [ ][ ] k kF d × →×
( )( ) 12 1 2 1 2 , ,..., ... , ... 1 kFk k k *d xx x t t t f f f k* = + + + + + + −+
if all i x are disjoint two by two and 1 2 ... 1 k *tt t* + ++≤ . 

 As a particular case let's take as a binary fuzzy conjunction: 
 ( )( ) 12 1 2 1 2 , , F *c x y tt f f f f* = +−
and as unary fuzzy negation: 
 *n x t f ft* F ( ) 1 ,1 , =− − = ( ) 1 1 11 ( ), 
where 1 1 *FL x t f* () (, ) = , with 1 1 t f + =1, and 1 1 0 , 1 ≤ t f ≤ ; 2 2 *FL y t f* () (, ) = , with 2 2 t f + =1, and 2 2 0 , 1 ≤ t f ≤ . 

whence: 
 ( ) 1 2 1 2 12 *FL P tt f f f f* ( 12) , = +−
( ) 1 2 1 2 12 *FL P t f f t f t* ( 1) , = +−
( ) 12 1 2 1 2 *FL P ft t f t f* ( 2) , = +−
( ) 1 2 1 2 12 *FL P f f t t t t* ( 0) , = +−
 The Venn Diagram for n = 2 and considering only the truth values, becomes: 

![0_image_0.png](0_image_0.png)

