Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 31)

Publication LOGIX-UM004A-EN-P - March 2007
FuzzyDesigner Component Library 31
Trapezoidal Membership Function with Parameters (vertices): (a,b,c,d)
If a = b then A(a) = 1. If c = d then A(c) = 1.
Trapezoidal membership functions can be used in input and output
linguistic variable components.
S-shape Membership Function (cubic spline) with Parameters: (a,b,c,d)
If a = b then A(a) = 1. If c = d then A(c) = 1.
S-shape membership functions can be used in input and output
linguistic variable components.
Inverse Trapezoidal Membership Function with Parameters (vertices): (a,b,c,d)
If a = b then A(a) = 1. If c = d then A(c) = 1.
Inverse trapezoidal membership functions can be used in an input
linguistic variable component.
0
( ) /( ) [ , )
( ) 1 [ , ]
( ) /( ) ( , ]
0
if x a
x a b a if x a b
A x if x b c
x d c d if x c d
if x d
< ⎧
⎪ −
− ∈
⎪⎪
= ∈ ⎨
⎪ −
− ∈
⎪
> ⎪⎩
a b c d
0
1
A(x)
x a b c d
0
1
A(x)
x a b c d
0
1
A(x)
x
2
3
2
3
0
2 3
( ) [ , )
( ) 2
( ) 1 [ , ]
2 3
( ) ( , ]
( ) 2
0
if x a
b a
x a x if x a b
a b
A x if x b c
c d
x d x if x c d
d c
if x d
< ⎧
⎪
− ⎛ ⎞
⎪ − − ∈ ⎜ ⎟
⎪ − ⎝ ⎠
⎪
= ∈ ⎨
⎪
− ⎛ ⎞
⎪ − − ∈
⎜ ⎟
− ⎪ ⎝ ⎠
⎪
> ⎩ a b c d
0
1
A(x)
x
a b c d
0
1
A(x)
x
a b c d
0
1
A(x)
x
1
( ) /( ) ( , ]
( ) 0 ( , )
( ) /( ) [ , )
1
if x a
x b a b if x a b
A x if x b c
x c d c if x c d
if x d
≤ ⎧
⎪ −
− ∈
⎪⎪
= ∈ ⎨
⎪ −
− ∈
⎪
≥ ⎪⎩
a b c d
0
1
A(x)
x
a b c d
0
1
A(x)
x
a b c d
0
1
A(x)
x