"""Fuzzy logic membership functions.
Extracted from scikit-fuzzy library to prevent conda breaking:
https://github.com/scikit-fuzzy/scikit-fuzzy
"""
import numpy as np
def gaussmf(x, mean: float, sigma: float):
"""Gaussian fuzzy membership function.
Args:
x: Independent variable (1d array or iterable).
mean: Gaussian parameter for center (mean) value.
sigma: Gaussian parameter for standard deviation.
Returns:
Gaussian membership function for x.
"""
return np.exp(-((x - mean) ** 2) / (2 * sigma**2))
def zmf(x, a: float, b: float):
"""Z-function fuzzy membership generator.
Named for its Z-like shape.
Args:
x: Independent variable (1d array).
a: Ceiling, where the function begins falling from 1.
b: Foot, where the function reattains zero.
Returns:
Z-function membership values.
"""
assert a <= b, "a <= b is required."
y = np.ones(len(x))
idx = np.logical_and(a <= x, x < (a + b) / 2)
y[idx] = 1 - 2 * ((x[idx] - a) / (b - a)) ** 2
idx = np.logical_and((a + b) / 2 <= x, x <= b)
y[idx] = 2 * ((x[idx] - b) / (b - a)) ** 2
idx = x >= b
y[idx] = 0
return y
def smf(x, a: float, b: float):
"""S-function fuzzy membership generator.
Named for its S-like shape.
Args:
x: Independent variable (1d array).
a: Foot, where the function begins to climb from zero.
b: Ceiling, where the function levels off at 1.
Returns:
S-function membership values.
"""
assert a <= b, "a <= b is required."
y = np.ones(len(x))
idx = x <= a
y[idx] = 0
idx = np.logical_and(a <= x, x <= (a + b) / 2)
y[idx] = 2 * ((x[idx] - a) / (b - a)) ** 2
idx = np.logical_and((a + b) / 2 <= x, x <= b)
y[idx] = 1 - 2 * ((x[idx] - b) / (b - a)) ** 2
return y
def interp_membership(x, xmf, xx, zero_outside_x: bool = True):
"""Find the degree of membership u(xx) for a given value of x = xx.
For use in Fuzzy Logic, where an interpolated discrete membership function
u(x) for discrete values of x on the universe of x is given. This function
computes the membership value u(xx) using linear interpolation.
Args:
x: Independent discrete variable vector (1d array).
xmf: Fuzzy membership function for x. Same length as x.
xx: Value(s) on universe x where the interpolated membership is desired.
zero_outside_x: If True, extrapolated values will be zero. If False,
the first or last value in x will be returned. Defaults to True.
Returns:
Membership function value at xx, u(xx).
"""
if not zero_outside_x:
kwargs = (None, None)
else:
kwargs = (0, 0)
return np.interp(xx, x, xmf, left=kwargs[0], right=kwargs[1])
def defuzz(x, mfx, mode: str):
"""Defuzzification of a membership function.
Args:
x: Independent variable (1d array, length N).
mfx: Fuzzy membership function (1d array, length N).
mode: Defuzzification method ('mom': mean of maximum,
'som': min of maximum, 'lom': max of maximum).
Returns:
Defuzzified result.
Raises:
ValueError: When membership function data is inconsistent or mode invalid.
"""
mode = mode.lower()
x = x.ravel()
mfx = mfx.ravel()
n = len(x)
if n != len(mfx):
raise ValueError("inconsistent membership function")
elif "mom" in mode:
return np.mean(x[mfx == mfx.max()])
elif "som" in mode:
return np.min(x[mfx == mfx.max()])
elif "lom" in mode:
return np.max(x[mfx == mfx.max()])
else:
raise ValueError(f"The mode: {mode} was incorrect.")
