- Non Stationary Fuzzy Sets
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Petrônio Cândido
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@ -8,6 +8,8 @@ IEEE Transactions on Fuzzy Systems, v. 16, n. 4, p. 1072-1086, 2008.
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import numpy as np
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from pyFTS import *
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from pyFTS.common import FuzzySet, Membership
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from pyFTS.partitioners import partitioner
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from pyFTS.nonstationary import perturbation
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class MembershipFunction(object):
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@ -32,23 +34,31 @@ class MembershipFunction(object):
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self.parameters = parameters
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self.location = kwargs.get("location", None)
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self.location_params = kwargs.get("location_params", None)
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self.location_roots = kwargs.get("location_roots", 0)
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self.width = kwargs.get("width", None)
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self.width_params = kwargs.get("width_params", None)
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self.width_roots = kwargs.get("width_roots", 0)
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self.noise = kwargs.get("noise", None)
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self.noise_params = kwargs.get("noise_params", None)
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self.cache = {}
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self.perturbated_parameters = {}
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if self.location is not None and not isinstance(self.location, (list,set)):
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self.location = [self.location]
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self.location_params = [self.location_params]
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self.location_roots = [self.location_roots]
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if self.width is not None and not isinstance(self.width, (list, set)):
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self.width = [self.width]
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self.width_params = [self.width_params]
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self.width_roots = [self.width_roots]
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def perform_location(self, t, param):
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if self.location is None:
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return param
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if not isinstance(self.location, (list,set)):
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self.location = [self.location]
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self.location_params = [self.location_params]
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l = len(self.location)
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inc = sum([self.location[k](t, self.location_params[k]) for k in np.arange(0,l)] )
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inc = sum([self.location[k](t + self.location_roots[k], self.location_params[k]) for k in np.arange(0,l)] )
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if self.mf == Membership.gaussmf:
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#changes only the mean parameter
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@ -66,13 +76,9 @@ class MembershipFunction(object):
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if self.width is None:
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return param
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if not isinstance(self.width, (list, set)):
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self.width = [self.width]
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self.width_params = [self.width_params]
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l = len(self.width)
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inc = sum([self.width[k](t, self.width_params[k]) for k in np.arange(0, l)])
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inc = sum([self.width[k](t + self.width_roots[k], self.width_params[k]) for k in np.arange(0, l)])
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if self.mf == Membership.gaussmf:
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#changes only the variance parameter
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@ -81,7 +87,8 @@ class MembershipFunction(object):
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#changes only the smooth parameter
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return [param[0] + inc, param[1]]
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elif self.mf == Membership.trimf:
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return [param[0] - inc, param[1], param[2] + inc]
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tmp = inc/2
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return [param[0] - tmp, param[1], param[2] + tmp]
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elif self.mf == Membership.trapmf:
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l = (param[3]-param[0])
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rab = (param[1] - param[0]) / l
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@ -97,19 +104,83 @@ class MembershipFunction(object):
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:return: membership value of x at this fuzzy set
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"""
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if t not in self.cache:
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param = self.parameters
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param = self.perform_location(t, param)
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param = self.perform_width(t, param)
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self.cache[t] = param
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self.perturbate_parameters(t)
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tmp = self.mf(x, self.cache[t])
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tmp = self.mf(x, self.perturbated_parameters[t])
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if self.noise is not None:
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tmp += self.noise(t, self.noise_params)
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return tmp
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def perturbate_parameters(self, t):
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if t not in self.perturbated_parameters:
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param = self.parameters
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param = self.perform_location(t, param)
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param = self.perform_width(t, param)
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self.perturbated_parameters[t] = param
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def __str__(self):
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tmp = ""
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if self.location is not None:
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tmp += "Loc. Pert.: "
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for ct, f in enumerate(self.location):
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tmp += str(f.__name__) + "(" + str(self.location_params[ct]) + ") "
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if self.width is not None:
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tmp += "Wid. Pert.: "
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for ct, f in enumerate(self.width):
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tmp += str(f.__name__) + "(" + str(self.width_params[ct]) + ") "
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return str(self.mf.__name__) + "(" + str(self.parameters) + ") " + tmp
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def get_midpoint(self, t):
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self.perturbate_parameters(t)
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if self.mf == Membership.gaussmf:
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return self.perturbated_parameters[t][0]
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elif self.mf == Membership.sigmf:
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return self.perturbated_parameters[t][1]
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elif self.mf == Membership.trimf:
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return self.perturbated_parameters[t][1]
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elif self.mf == Membership.trapmf:
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param = self.perturbated_parameters[t]
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return (param[2] - param[1]) / 2
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else:
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return self.perturbated_parameters[t]
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def get_lower(self, t):
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self.perturbate_parameters(t)
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param = self.perturbated_parameters[t]
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if self.mf == Membership.gaussmf:
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return param[0] - 3*param[1]
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elif self.mf == Membership.sigmf:
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return param[0] - param[1]
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elif self.mf == Membership.trimf:
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return param[0]
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elif self.mf == Membership.trapmf:
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return param[0]
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else:
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return param
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def get_upper(self, t):
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self.perturbate_parameters(t)
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param = self.perturbated_parameters[t]
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if self.mf == Membership.gaussmf:
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return param[0] + 3*param[1]
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elif self.mf == Membership.sigmf:
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return param[0] + param[1]
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elif self.mf == Membership.trimf:
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return param[2]
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elif self.mf == Membership.trapmf:
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return param[3]
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else:
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return param
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class FuzzySet(FuzzySet.FuzzySet):
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"""
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@ -127,4 +198,105 @@ class FuzzySet(FuzzySet.FuzzySet):
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def membership(self, x, t):
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return self.mf.membership(x,t)
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def __str__(self):
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return self.name + ": " + str(self.mf)
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class PolynomialNonStationaryPartitioner(partitioner.Partitioner):
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"""
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Non Stationary Universe of Discourse Partitioner
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"""
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def __init__(self, data, part, **kwargs):
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""""""
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super(PolynomialNonStationaryPartitioner, self).__init__(name=part.name, data=data, npart=part.partitions,
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func=part.membership_function, names=part.setnames,
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prefix=part.prefix, transformation=part.transformation,
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indexer=part.indexer)
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self.sets = []
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loc_params, wid_params = self.get_polynomial_perturbations(data, **kwargs)
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for ct, set in enumerate(part.sets):
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loc_roots = np.roots(loc_params[ct])[0]
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wid_roots = np.roots(wid_params[ct])[0]
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mf = MembershipFunction(name=set.name, mf=set.mf, parameters=set.parameters,
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location=perturbation.polynomial,
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location_params=loc_params[ct],
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location_roots=loc_roots, #**kwargs)
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width=perturbation.polynomial,
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width_params=wid_params[ct],
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width_roots=wid_roots, **kwargs)
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tmp = FuzzySet(set.name, mf, **kwargs)
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self.sets.append(tmp)
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def poly_width(self, par1, par2, rng, deg):
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a = np.polyval(par1, rng)
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b = np.polyval(par2, rng)
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diff = [b[k] - a[k] for k in rng]
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tmp = np.polyfit(rng, diff, deg=deg)
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return tmp
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def get_polynomial_perturbations(self, data, **kwargs):
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w = kwargs.get("window_size", int(len(data) / 5))
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deg = kwargs.get("degree", 2)
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xmax = [0]
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tmax = [0]
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xmin = [0]
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tmin = [0]
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lengs = [0]
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tlengs = [0]
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l = len(data)
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for i in np.arange(0, l, w):
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sample = data[i:i + w]
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tx = max(sample)
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xmax.append(tx)
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tmax.append(np.ravel(np.argwhere(data == tx)).tolist()[0])
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tn = min(sample)
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xmin.append(tn)
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tmin.append(np.ravel(np.argwhere(data == tn)).tolist()[0])
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lengs.append((tx - tn)/self.partitions)
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tlengs.append(i)
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cmax = np.polyfit(tmax, xmax, deg=deg)
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#cmax = cmax.tolist()
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cmin = np.polyfit(tmin, xmin, deg=deg)
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#cmin = cmin.tolist()
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cmed = []
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for d in np.arange(0, deg + 1):
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cmed.append(np.linspace(cmin[d], cmax[d], self.partitions)[1:self.partitions - 1])
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loc_params = [cmin.tolist()]
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for i in np.arange(0, self.partitions - 2):
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tmp = [cmed[k][i] for k in np.arange(0, deg + 1)]
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loc_params.append(tmp)
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loc_params.append(cmax.tolist())
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rng = np.arange(0, l)
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clen = []
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for i in np.arange(1, self.partitions-1):
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tmp = self.poly_width(loc_params[i - 1], loc_params[i + 1], rng, deg)
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clen.append(tmp)
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tmp = self.poly_width(loc_params[0], loc_params[1], rng, deg)
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clen.insert(0, tmp)
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tmp = self.poly_width(loc_params[self.partitions-2], loc_params[self.partitions-1], rng, deg)
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clen.append(tmp)
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tmp = (loc_params, clen)
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return tmp
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def build(self, data):
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pass
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@ -8,15 +8,11 @@ from pyFTS.common import FuzzySet, Membership
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def linear(x, parameters):
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return parameters[0]*x + parameters[1]
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return np.polyval(parameters, x)
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def polynomial(x, parameters):
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n = len(parameters)
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tmp = 0.0
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for k in np.arange(0,n):
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tmp += parameters[k] * x**k
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return tmp
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return np.polyval(parameters, x)
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def exponential(x, parameters):
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@ -24,4 +20,4 @@ def exponential(x, parameters):
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def periodic(x, parameters):
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return np.sin(x * parameters[0] + parameters[1])
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return parameters[0] * np.sin(x * parameters[1])
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@ -6,19 +6,22 @@ import matplotlib.pyplot as plt
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from pyFTS.common import Membership, Util
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def plot_sets(uod, sets, num=10, tam=[5, 5], colors=None, save=False, file=None):
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def plot_sets(uod, sets, start=0, end=10, tam=[5, 5], colors=None, save=False, file=None):
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ticks = []
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fig, axes = plt.subplots(nrows=1, ncols=1, figsize=tam)
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for t in np.arange(0,num,1):
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for t in np.arange(start,end,1):
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for ct, set in enumerate(sets):
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x = [2*t + set.membership(v, t) for v in uod]
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if colors is not None: c = colors[ct]
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axes.plot(x, uod, c=c)
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set.membership(0, t)
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param = set.mf.perturbated_parameters[t]
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if set.mf.mf == Membership.trimf:
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axes.plot([t, t+1, t], param)
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ticks.extend(["t+"+str(t),""])
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axes.set_ylabel("Universe of Discourse")
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axes.set_xlabel("Time")
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plt.xticks([k for k in np.arange(0,2*num,1)], ticks, rotation='vertical')
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plt.xticks([k for k in np.arange(0,2*end,1)], ticks, rotation='vertical')
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plt.tight_layout()
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@ -1,20 +1,38 @@
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import numpy as np
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from pyFTS.common import Membership
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from pyFTS.nonstationary import common,pertubation,util
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import importlib
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from pyFTS.nonstationary import common,perturbation,util
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from pyFTS.partitioners import Grid
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importlib.reload(util)
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uod = np.arange(0,20,0.1)
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def generate_heteroskedastic_linear(mu_ini, sigma_ini, mu_inc, sigma_inc, it=10, num=35):
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mu = mu_ini
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sigma = sigma_ini
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ret = []
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for k in np.arange(0,it):
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ret.extend(np.random.normal(mu, sigma, num))
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mu += mu_inc
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sigma += sigma_inc
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return ret
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kwargs = {'location': pertubation.linear, 'location_params': [1,0],
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'width': pertubation.linear, 'width_params': [1,0]}
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mf1 = common.MembershipFunction('A1',Membership.trimf,[0,1,2], **kwargs)
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mf2 = common.MembershipFunction('A2',Membership.trimf,[1,2,3], **kwargs)
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mf3 = common.MembershipFunction('A3',Membership.trimf,[2,3,4], **kwargs)
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mf4 = common.MembershipFunction('A4',Membership.trimf,[3,4,5], **kwargs)
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lmv1 = generate_heteroskedastic_linear(1,0.1,1,0.3)
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sets = [mf1, mf2, mf3, mf4]
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util.plot_sets(uod, sets)
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ns = 5 #number of fuzzy sets
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ts = 200
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train = lmv1[:ts]
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w = 25
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deg = 4
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tmp_fs = Grid.GridPartitioner(train[:35], 10)
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fs = common.PolynomialNonStationaryPartitioner(train, tmp_fs, window_size=35, degree=1)
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uod = np.arange(0, 2, step=0.02)
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util.plot_sets(uod, fs.sets,tam=[15, 5], start=0, end=10)
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for set in fs.sets:
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print(set)
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