T-Preorders and T-Indistinguishabilities - Fuzzy Logic: An Introductory Course for Engineering Students - page 134

It is also

⊛
⊝

⊞
⊠

13 / 41 / 21 / 4

113 / 41 / 2

J ˃ W ]=

[

1 / 4

1111

21 13 /

since, f.e.,

min 1 min 1

3
4 +

1
2

1
4 +

3
4

J ˃ W ( 4, J ˃ W (

1 , 2 ) = , 1 − = 3 / 3 , 1 ) = , 1 − = 1 / 2 ,

min 1 min 1 0

3
4

1
4 +

J ˃ W ( 1, J ˃ W ( , ) = , − + = , ) = , − = /

4 1 1 0 3 4 1 3 4, etc.

Hence,

⊛ ⊞

13 / 41 / 21 / 4

⊝ ⊠

3 / 413 / 41 / 2

J ˃ W ] , [ J ˃ W ] ) = [ E W ]= min ( [

1 / 23 / 413 / 4

1 / 41 / 23 / 41

is a W-indistinguishability on X , with the directed graph

4

1/4 3/4

1/2

1 3

1/2

3/4

3/4

2