Fuzzify Layer
Represents a Fuzzyfy relation block in the neural network model.
This block is used to implement fuzzy logic inside the neural network.
[1]:
# uncomment the command below to install the nnodely package
#!pip install nnodely
from nnodely import *
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>-- nnodely_v1.5.0 --<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Basic Usage
Create a fuzzy layer with 5 membership functions in a range [1,5] of the input variable
(if not specified, by default it uses the ‘triangular’ function)
[2]:
x = Input('x')
fuz = Fuzzify(5,[1,5])
out = Output('out',fuz(x.last()))
example = Modely(visualizer=MPLNotebookVisualizer())
example.addModel('model',out)
example.neuralizeModel()
example.visualizer.showFunctions(list(example._model_def['Functions'].keys()))
================================ nnodely Model =================================
{'Constants': {},
'Functions': {'FFuzzify2': {'centers': [1.0, 2.0, 3.0, 4.0, 5.0],
'dim_out': {'dim': 5},
'functions': 'Triangular',
'names': 'Triangular'}},
'Info': {'SampleTime': 1,
'nnodely_version': '1.5.0',
'ns': [1, 0],
'ntot': 1,
'num_parameters': 0},
'Inputs': {'x': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]}},
'Models': 'model',
'Outputs': {'out': 'Fuzzify2'},
'Parameters': {},
'Relations': {'Fuzzify2': ['Fuzzify', ['SamplePart1'], 'FFuzzify2'],
'SamplePart1': ['SamplePart', ['x'], -1, [-1, 0]]}}
================================================================================
Rectangular function
Create 6 membership functions by dividing the range from 1, 6 with rectangular functions centers are in [1,2,3,4,5,6] functions are 1 wide except the first and last.
the result vector should be: [[-inf, 1.5] [1.5,2.5] [2.5,3.5] [3.5,4.5] [4.5,5.5] [5.5.inf]]
[3]:
x = Input('x')
fuz = Fuzzify(6,[1,6], functions = 'Rectangular')
out = Output('out',fuz(x.last()))
example = Modely(visualizer=MPLNotebookVisualizer())
example.addModel('model',out)
example.neuralizeModel()
example.visualizer.showFunctions(list(example._model_def['Functions'].keys()))
[check_names] The name 'x' is already in defined as NeuObj but it is overwritten.
[check_names] The name 'out' is already in defined as NeuObj but it is overwritten.
================================ nnodely Model =================================
{'Constants': {},
'Functions': {'FFuzzify5': {'centers': [1.0, 2.0, 3.0, 4.0, 5.0, 6.0],
'dim_out': {'dim': 6},
'functions': 'Rectangular',
'names': 'Rectangular'}},
'Info': {'SampleTime': 1,
'nnodely_version': '1.5.0',
'ns': [1, 0],
'ntot': 1,
'num_parameters': 0},
'Inputs': {'x': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]}},
'Models': 'model',
'Outputs': {'out': 'Fuzzify5'},
'Parameters': {},
'Relations': {'Fuzzify5': ['Fuzzify', ['SamplePart4'], 'FFuzzify5'],
'SamplePart4': ['SamplePart', ['x'], -1, [-1, 0]]}}
================================================================================
Custom functions
Create 10 membership functions by dividing the range from -5, 5 with a custom function (tanh). The centers are in [-5,-4,-3,-2,-1,0,1,2,3,4,5]
[4]:
def fun(x):
import torch
return torch.tanh(x)
x = Input('x')
fuz = Fuzzify(output_dimension=11, range=[-5,5], functions=fun)
out = Output('out',fuz(x.last()))
example = Modely(visualizer=MPLNotebookVisualizer())
example.addModel('model',out)
example.neuralizeModel()
example.visualizer.showFunctions(list(example._model_def['Functions'].keys()))
[check_names] The name 'x' is already in defined as NeuObj but it is overwritten.
[check_names] The name 'out' is already in defined as NeuObj but it is overwritten.
================================ nnodely Model =================================
{'Constants': {},
'Functions': {'FFuzzify8': {'centers': [-5.0,
-4.0,
-3.0,
-2.0,
-1.0,
0.0,
1.0,
2.0,
3.0,
4.0,
5.0],
'dim_out': {'dim': 11},
'functions': 'def fun(x):\n'
' import torch\n'
' return torch.tanh(x)\n',
'names': 'fun'}},
'Info': {'SampleTime': 1,
'nnodely_version': '1.5.0',
'ns': [1, 0],
'ntot': 1,
'num_parameters': 0},
'Inputs': {'x': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]}},
'Models': 'model',
'Outputs': {'out': 'Fuzzify8'},
'Parameters': {},
'Relations': {'Fuzzify8': ['Fuzzify', ['SamplePart7'], 'FFuzzify8'],
'SamplePart7': ['SamplePart', ['x'], -1, [-1, 0]]}}
================================================================================
Multiple custom functions
Create 2 custom periodic functions that are positioned at -1 and 5
[5]:
def fun1(x):
import torch
return torch.sin(x)
def fun2(x):
import torch
return torch.cos(x)
x = Input('x')
fuz = Fuzzify(2,range=[-1,5],functions=[fun1,fun2])
out = Output('out',fuz(x.last()))
example = Modely(visualizer=MPLNotebookVisualizer())
example.addModel('model',out)
example.neuralizeModel()
example.visualizer.showFunctions(list(example._model_def['Functions'].keys()))
[check_names] The name 'x' is already in defined as NeuObj but it is overwritten.
[check_names] The name 'out' is already in defined as NeuObj but it is overwritten.
================================ nnodely Model =================================
{'Constants': {},
'Functions': {'FFuzzify11': {'centers': [-1.0, 5.0],
'dim_out': {'dim': 2},
'functions': ['def fun1(x):\n'
' import torch\n'
' return torch.sin(x)\n',
'def fun2(x):\n'
' import torch\n'
' return torch.cos(x)\n'],
'names': ['fun1', 'fun2']}},
'Info': {'SampleTime': 1,
'nnodely_version': '1.5.0',
'ns': [1, 0],
'ntot': 1,
'num_parameters': 0},
'Inputs': {'x': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]}},
'Models': 'model',
'Outputs': {'out': 'Fuzzify11'},
'Parameters': {},
'Relations': {'Fuzzify11': ['Fuzzify', ['SamplePart10'], 'FFuzzify11'],
'SamplePart10': ['SamplePart', ['x'], -1, [-1, 0]]}}
================================================================================
Repeated custom functions
Create 4 custom membership functions that are positioned at [-1,0,3,5]
[6]:
import torch
def fun1(x):
return torch.sin(x)
def fun2(x):
return torch.cos(x)
x = Input('x')
F = Input('F')
fuz = Fuzzify(centers=[-1,0,3,5],functions=[fun1,fun2,fun1,fun2])
out = Output('out',fuz(x.last())+fuz(F.last()))
example = Modely(visualizer=MPLNotebookVisualizer())
example.addModel('model',out)
example.neuralizeModel()
example.visualizer.showFunctions(list(example._model_def['Functions'].keys()))
[check_names] The name 'x' is already in defined as NeuObj but it is overwritten.
[check_names] The name 'out' is already in defined as NeuObj but it is overwritten.
================================ nnodely Model =================================
{'Constants': {},
'Functions': {'FFuzzify15': {'centers': [-1, 0, 3, 5],
'dim_out': {'dim': 4},
'functions': ['def fun1(x):\n'
' return torch.sin(x)\n',
'def fun2(x):\n'
' return torch.cos(x)\n',
'def fun1(x):\n'
' return torch.sin(x)\n',
'def fun2(x):\n'
' return torch.cos(x)\n'],
'names': ['fun1', 'fun2', 'fun1', 'fun2']}},
'Info': {'SampleTime': 1,
'nnodely_version': '1.5.0',
'ns': [1, 0],
'ntot': 1,
'num_parameters': 0},
'Inputs': {'F': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]},
'x': {'dim': 1, 'ns': [1, 0], 'ntot': 1, 'sw': [-1, 0]}},
'Models': 'model',
'Outputs': {'out': 'Add18'},
'Parameters': {},
'Relations': {'Add18': ['Add', ['Fuzzify14', 'Fuzzify17']],
'Fuzzify14': ['Fuzzify', ['SamplePart13'], 'FFuzzify15'],
'Fuzzify17': ['Fuzzify', ['SamplePart16'], 'FFuzzify15'],
'SamplePart13': ['SamplePart', ['x'], -1, [-1, 0]],
'SamplePart16': ['SamplePart', ['F'], -1, [-1, 0]]}}
================================================================================
