Norm
Bases: TNorm
TNorm to compute the drastic product of any two values.
Equation
\(a \otimes b = \begin{cases} \min(a,b) & \mbox{if } \max(a,b)=1 \cr 0 & \mbox{otherwise} \end{cases}\)
related
Functions¶
Compute the drastic product of two membership function values.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
a
|
Scalar
|
membership function value |
required |
b
|
Scalar
|
membership function value. |
required |
Returns:
| Type | Description |
|---|---|
Scalar
|
\(a \otimes b = \begin{cases} \min(a,b) & \mbox{if } \max(a,b)=1 \cr 0 & \mbox{otherwise} \end{cases}\) |
Bases: SNorm
SNorm to compute the drastic sum of any two values.
Equation
\(a \oplus b=\begin{cases} \max(a,b) & \mbox{if } \min(a,b)=0 \cr 1 & \mbox{otherwise} \end{cases}\)
related
Functions¶
Compute the drastic sum of two membership function values.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
a
|
Scalar
|
membership function value |
required |
b
|
Scalar
|
membership function value |
required |
Returns:
| Type | Description |
|---|---|
Scalar
|
\(a \oplus b=\begin{cases} \max(a,b) & \mbox{if } \min(a,b)=0 \cr 1 & \mbox{otherwise} \end{cases}\) |
Bases: SNorm
SNorm to compute the nilpotent maximum of any two values.
Equation
\(a \oplus b=\begin{cases} \max(a,b) & \mbox{if } a+b<0 \cr 1 & \mbox{otherwise} \end{cases}\)
related
Functions¶
Compute the nilpotent maximum of two membership function values.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
a
|
Scalar
|
membership function value |
required |
b
|
Scalar
|
membership function value |
required |
Returns:
| Type | Description |
|---|---|
Scalar
|
\(a \oplus b=\begin{cases} \max(a,b) & \mbox{if } a+b<0 \cr 1 & \mbox{otherwise} \end{cases}\) |
Bases: TNorm
TNorm to compute the nilpotent minimum of any two values.
Equation
\(a \otimes b=\begin{cases} \min(a,b) & \mbox{if }a+b>1 \cr 0 & \mbox{otherwise} \end{cases}\)
related
Functions¶
Compute the nilpotent minimum of two membership function values.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
a
|
Scalar
|
membership function value |
required |
b
|
Scalar
|
membership function value |
required |
Returns:
| Type | Description |
|---|---|
Scalar
|
\(a \otimes b=\begin{cases} \min(a,b) & \mbox{if }a+b>1 \cr 0 & \mbox{otherwise} \end{cases}\) |
Bases: ABC
Abstract class for norms.
related
Functions¶
__repr__() -> str
Return the code to construct the norm in Python.
Returns:
| Type | Description |
|---|---|
str
|
code to construct the norm in Python. |
TNorm or SNorm based on a term function on any two values.
Equation
\(a \oplus b = a \otimes b = f(a,b)\)
This Norm is not registered in the SNormFactory or TNormFactory.
related
Attributes¶
Functions¶
__init__(function: Function) -> None
Constructor.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
function
|
Function
|
function \(f(a,b)\). |
required |
TNorm or SNorm based on a \(\lambda\) function on any two values.
Equation
\(a \oplus b = a \otimes b = \lambda(a,b)\)
This Norm is not registered in the SNormFactory or TNormFactory.
related
Bases: Norm
Base class for S-Norms, used as fuzzy logic operator for disjunction and aggregation in rule blocks.
related
Bases: Norm
Base class for T-Norms, used as fuzzy logic operator for conjunction and implication in rule blocks.