def GeneralizedSugenoLambda(F1, F2, x, mu, l=None, verbose=False):
"""Generalized Sugeno Lambda integral
:param x: values
:param mu: fuzzy measure
:param l: value of lambda, if None (Default) it's get calculated
:param verbose: If true prints data to the console
:rtype: Generalized Sugeno lambda-Integral with lambda computed based on :math:`\\mu`
:math:`SFI(x)_{\\mu} = F2_{i=1}^{n}F1(f(x_{\\sigma_i}),g(A_j))`.
"""
x = np.array(x)
mu = np.array(mu)
sortedindex = np.argsort(x)
xsorted = np.take(x, sortedindex)
musorted = np.take(mu, sortedindex)
if l is None:
l = bisectionLien(FLambda, mu)
nmu = generateGMeasure(musorted, l)
gsugeno = F2([F1(a, b) for a, b in zip(xsorted, nmu)])
if verbose:
print("X:", x, "X sorted:", xsorted)
print("mu", mu, "Mu sorted:", musorted)
print("Lambda:", l)
print("Generated measures:", nmu)
print("Sugeno:", gsugeno)
return gsugeno
def test_GenerateMuLambda1(self):
# C.G. Magadun an M.S. Bapat
# http://www.researchmathsci.org/IJFMAart/IJFMA-v15n2-1.pdf
mu = [0.4, 0.5, 0.5, 0.7, 0.8, 0.8]
l = -0.9981565
expected = [1.0, 0.9987725, 0.9957093, 0.9895943, 0.9611798, 0.8]
out = list(utils.generateGMeasure(mu, l))
for e, o in zip(expected, out):
self.assertAlmostEqual(o, e, places=3)
def test_GenerateMuLambda3(self):
# C.G. Magadun an M.S. Bapat
# http://www.researchmathsci.org/IJFMAart/IJFMA-v15n2-1.pdf
# FChoquet fails with this data. An error in the paper?
mu = [0.7, 0.5, 0.5, 0.8, 0.8, 0.4]
l = -0.9981565
expected = [1.0, 0.9957168, 0.9896093, 0.9774167, 0.8805899, 0.4]
out = list(utils.generateGMeasure(mu, l))
for e, o in zip(expected, out):
self.assertAlmostEqual(o, e, places=3)
def test_GenerateMuLambda2(self):
# C.G. Magadun an M.S. Bapat
# http://www.researchmathsci.org/IJFMAart/IJFMA-v15n2-1.pdf
mu = [0.8, 0.8, 0.5, 0.7, 0.5, 0.4]
l = -0.9981565
expected = [
1.0, 0.992679806032971, 0.9563469279183847, 0.911014400788915,
0.7003687, 0.4
]
out = list(utils.generateGMeasure(mu, l))
for e, o in zip(expected, out):
self.assertAlmostEqual(o, e, places=3)
def ChoquetLambda(x, mu, l=None, verbose=False):
"""Choquet Lambda integral
:param x: values
:param mu: fuzzy measure
:param l: value of lambda, if None (Default) it's get calculated
:param verbose: If true prints data to the console
:rtype: Choquet lambda-Integral with lambda computed based on :math:`\\mu`
:math:`CFI(x)_{\\mu} = \\displaystyle\\sum_{i=1}^{n}(f(x_{\\sigma_i})-f(x_{\\sigma_{(i-1)}}))* g(A_j)`.
"""
x = np.array(x)
mu = np.array(mu)
# sortedindex = np.argsort(x)
# xsorted = np.take(x, sortedindex)
# musorted = np.take(mu, sortedindex)
sortedindex = list(zip(x, mu))
sortedindex.sort() # key=lambda x: x[0]
xsorted, musorted = zip(*sortedindex)
xsorted, musorted = np.array(xsorted), np.array(musorted)
if l is None:
l = bisectionLien(FLambda, mu)
nmu = generateGMeasure(musorted, l)
# choquet = sum(np.diff(np.append([0], xsorted)) * nmu) # Twice as slow
choquet = np.dot((np.append(xsorted[0], xsorted[1:] - xsorted[0:-1])), nmu)
if verbose:
print("X:", x, "X sorted:", xsorted)
print("mu", mu, "Mu sorted:", musorted)
print("Lambda:", l)
print("Generated measures:", nmu)
print("Choquet:", choquet)
return choquet
def GeneralizedChoquetLambda(F1, F2, x, mu, l=None, verbose=False):
"""Choquet Lambda integral
:param x: values
:param mu: fuzzy measure
:param F1: Function1
:param F2: Function2
:param l: value of lambda, if None (Default) it's get calculated
:param verbose: If true prints data to the console
:rtype: Generalized Choquet lambda-Integral with lambda computed based on :math:`\\mu`
:math:`CFI(x)_{\\mu} = F2_{i=1}^{n}F1(f(x_{\\sigma_i})-f(x_{\\sigma_{(i-1)}})),g(A_j))`.
"""
x = np.array(x)
mu = np.array(mu)
sortedindex = np.argsort(x)
xsorted = np.take(x, sortedindex)
musorted = np.take(mu, sortedindex)
if l is None:
l = bisectionLien(FLambda, mu)
nmu = generateGMeasure(musorted, l)
gchoquet = F2(F1(np.diff(np.append([0], xsorted)), nmu))
# For numpy >= 1.16
# gchoquet = F2(F1(np.diff(xsorted,prepend=[0]),nmu))
if verbose:
print("X:", x, "X sorted:", xsorted)
print("mu", mu, "Mu sorted:", musorted)
print("Lambda:", l)
print("Generated measures:", nmu)
print("Choquet:", gchoquet)
return gchoquet