Fuzzy Arithmetic - Fuzzy Logic: An Introductory Course for Engineering Students - page 146

μ m , with 1

μ m x , if x = 0

1

or μ n ÷ μ m = μ n ( x ) =

0 ,

and

μ m

0 , if x =

1

μ m m =

1.
Let's compute the example μ 3 ÷ μ 3 , with μ 3 as in Sect. 6.2.2 . It will be:

∈ 4 ,

3

⊧
⊨

1 1

4 −

y ,

if y

3

∈ 3 ,

2

1
μ

1 1

( y ) =

y −

2 , if y

⊩

, .

0 otherwise

1
μ

Hence, for μ 3 ÷ μ 3 = μ 3

3 , it will be

(μ 3 ÷ μ 3 )( 1 ) = 1, and

1
y

= ʱ + 2
4

4 t − 2

• L , ʱ = 4 − = x − 2 ⃒ t = x · y

− ʱ ⃒ ʱ =

t + 1

1 4 − ʱ

ʱ +

4 − 2 t

• R , ʱ = 4 − x =

y −

2 ⃒ t = x · y = ⃒ ʱ =

1 .

2 t +

That is

⊧
⊨

⊫
⊬

4 t − 2 1

t + 1 ,

if t ∈[

2 ,

1 ]

4 − 2 t

(μ 3 ÷ μ 3 )( ) = = μ 1 ( )

t

1 ,

if t ∈[ 1 , 2 ] t

⊩

t +

⊭

0 , otherwise

Graphically,

Remark 6.2.3 Obviously, like in the product's case, the result is not a linear-
triangular fuzzy number, and the basic interval [ a , b ] is not symmetrical respect

n

to the point

m .

6.2.3 Note

] R , and As it is easy to see, if μ, ˃ ∈[ 0 , 1 ∗∈{+ , − , · , :} , it follows the relation

ʱ

between the corresponding -cuts: