import numpy as np
from pyFTS import *
from pyFTS.common import Membership
[docs]class FuzzySet(object):
"""
Fuzzy Set
"""
def __init__(self, name, mf, parameters, centroid, alpha=1.0, **kwargs):
"""
Create a Fuzzy Set
"""
self.name = name
"""The fuzzy set name"""
self.mf = mf
"""The membership function"""
self.parameters = parameters
"""The parameters of the membership function"""
self.centroid = centroid
"""The fuzzy set center of mass (or midpoint)"""
self.alpha = alpha
"""The alpha cut value"""
self.type = kwargs.get('type', 'common')
"""The fuzzy set type (common, composite, nonstationary, etc)"""
self.variable = kwargs.get('variable', None)
"""In multivariate time series, indicate for which variable this fuzzy set belogs"""
self.Z = None
"""Partition function in respect to the membership function"""
if parameters is not None:
if self.mf == Membership.gaussmf:
self.lower = parameters[0] - parameters[1] * 3
self.upper = parameters[0] + parameters[1] * 3
elif self.mf == Membership.sigmf:
k = (parameters[1] / (2 * parameters[0]))
self.lower = parameters[1] - k
self.upper = parameters[1] + k
else:
self.lower = min(parameters)
self.upper = max(parameters)
self.metadata = {}
[docs] def membership(self, x):
"""
Calculate the membership value of a given input
:param x: input value
:return: membership value of x at this fuzzy set
"""
return self.mf(self.transform(x), self.parameters) * self.alpha
[docs] def partition_function(self, uod=None, nbins=100):
"""
Calculate the partition function over the membership function.
:param uod:
:param nbins:
:return:
"""
if self.Z is None and uod is not None:
self.Z = 0.0
for k in np.linspace(uod[0], uod[1], nbins):
self.Z += self.membership(k)
return self.Z
def __str__(self):
return self.name + ": " + str(self.mf.__name__) + "(" + str(self.parameters) + ")"
def __binary_search(x, fuzzy_sets, ordered_sets):
"""
Search for elegible fuzzy sets to fuzzyfy x
:param x: input value to be fuzzyfied
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:param ordered_sets: a list with the fuzzy sets names ordered by their centroids.
:return: A list with the best fuzzy sets that may contain x
"""
max_len = len(fuzzy_sets) - 1
first = 0
last = max_len
while first <= last:
midpoint = (first + last) // 2
fs = ordered_sets[midpoint]
fs1 = ordered_sets[midpoint - 1] if midpoint > 0 else ordered_sets[0]
fs2 = ordered_sets[midpoint + 1] if midpoint < max_len else ordered_sets[max_len]
if fuzzy_sets[fs1].centroid <= fuzzy_sets[fs].transform(x) <= fuzzy_sets[fs2].centroid:
return (midpoint - 1, midpoint, midpoint + 1)
elif midpoint <= 1:
return [0]
elif midpoint >= max_len:
return [max_len]
else:
if fuzzy_sets[fs].transform(x) < fuzzy_sets[fs].centroid:
last = midpoint - 1
else:
first = midpoint + 1
[docs]def fuzzyfy(data, partitioner, **kwargs):
"""
A general method for fuzzyfication.
:param data: input value to be fuzzyfied
:param partitioner: a trained pyFTS.partitioners.Partitioner object
:param kwargs: dict, optional arguments
:keyword alpha_cut: the minimal membership value to be considered on fuzzyfication (only for mode='sets')
:keyword method: the fuzzyfication method (fuzzy: all fuzzy memberships, maximum: only the maximum membership)
:keyword mode: the fuzzyfication mode (sets: return the fuzzy sets names, vector: return a vector with the membership
values for all fuzzy sets, both: return a list with tuples (fuzzy set, membership value) )
:returns a list with the fuzzyfied values, depending on the mode
"""
alpha_cut = kwargs.get('alpha_cut', 0.)
mode = kwargs.get('mode', 'sets')
method = kwargs.get('method', 'fuzzy')
if isinstance(data, (list, np.ndarray)):
if mode == 'vector':
return fuzzyfy_instances(data, partitioner.sets, partitioner.ordered_sets)
elif mode == 'both':
mvs = fuzzyfy_instances(data, partitioner.sets, partitioner.ordered_sets)
fs = []
for mv in mvs:
fsets = [(partitioner.ordered_sets[ix], mv[ix])
for ix in np.arange(len(mv))
if mv[ix] >= alpha_cut]
fs.append(fsets)
return fs
else:
return fuzzyfy_series(data, partitioner.sets, method, alpha_cut, partitioner.ordered_sets)
else:
if mode == 'vector':
return fuzzyfy_instance(data, partitioner.sets, partitioner.ordered_sets)
elif mode == 'both':
mv = fuzzyfy_instance(data, partitioner.sets, partitioner.ordered_sets)
fsets = [(partitioner.ordered_sets[ix], mv[ix])
for ix in np.arange(len(mv))
if mv[ix] >= alpha_cut]
return fsets
else:
return get_fuzzysets(data, partitioner.sets, partitioner.ordered_sets, alpha_cut)
[docs]def set_ordered(fuzzy_sets):
"""
Order a fuzzy set list by their centroids
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:return: a list with the fuzzy sets names ordered by their centroids.
"""
if len(fuzzy_sets) > 0:
tmp1 = [fuzzy_sets[k] for k in fuzzy_sets.keys()]
return [k.name for k in sorted(tmp1, key=lambda x: x.centroid)]
[docs]def fuzzyfy_instance(inst, fuzzy_sets, ordered_sets=None):
"""
Calculate the membership values for a data point given fuzzy sets
:param inst: data point
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:param ordered_sets: a list with the fuzzy sets names ordered by their centroids.
:return: array of membership values
"""
if ordered_sets is None:
ordered_sets = set_ordered(fuzzy_sets)
mv = np.zeros(len(fuzzy_sets))
for ix in __binary_search(inst, fuzzy_sets, ordered_sets):
mv[ix] = fuzzy_sets[ordered_sets[ix]].membership(inst)
return mv
[docs]def fuzzyfy_instances(data, fuzzy_sets, ordered_sets=None):
"""
Calculate the membership values for a data point given fuzzy sets
:param inst: data point
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:param ordered_sets: a list with the fuzzy sets names ordered by their centroids.
:return: array of membership values
"""
ret = []
if ordered_sets is None:
ordered_sets = set_ordered(fuzzy_sets)
for inst in data:
mv = fuzzyfy_instance(inst, fuzzy_sets, ordered_sets)
ret.append(mv)
return ret
[docs]def get_fuzzysets(inst, fuzzy_sets, ordered_sets=None, alpha_cut=0.0):
"""
Return the fuzzy sets which membership value for a inst is greater than the alpha_cut
:param inst: data point
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:param ordered_sets: a list with the fuzzy sets names ordered by their centroids.
:param alpha_cut: Minimal membership to be considered on fuzzyfication process
:return: array of membership values
"""
if ordered_sets is None:
ordered_sets = set_ordered(fuzzy_sets)
try:
fs = [ordered_sets[ix]
for ix in __binary_search(inst, fuzzy_sets, ordered_sets)
if fuzzy_sets[ordered_sets[ix]].membership(inst) > alpha_cut]
return fs
except Exception as ex:
raise ex
[docs]def get_maximum_membership_fuzzyset(inst, fuzzy_sets, ordered_sets=None):
"""
Fuzzify a data point, returning the fuzzy set with maximum membership value
:param inst: data point
:param fuzzy_sets: a dictionary where the key is the fuzzy set name and the value is the fuzzy set object.
:param ordered_sets: a list with the fuzzy sets names ordered by their centroids.
:return: fuzzy set with maximum membership
"""
if ordered_sets is None:
ordered_sets = set_ordered(fuzzy_sets)
mv = np.array([fuzzy_sets[key].membership(inst) for key in ordered_sets])
key = ordered_sets[np.argwhere(mv == max(mv))[0, 0]]
return fuzzy_sets[key]
[docs]def get_maximum_membership_fuzzyset_index(inst, fuzzy_sets):
"""
Fuzzify a data point, returning the fuzzy set with maximum membership value
:param inst: data point
:param fuzzy_sets: dict of fuzzy sets
:return: fuzzy set with maximum membership
"""
mv = fuzzyfy_instance(inst, fuzzy_sets)
return np.argwhere(mv == max(mv))[0, 0]
[docs]def fuzzyfy_series_old(data, fuzzy_sets, method='maximum'):
fts = []
for item in data:
fts.append(get_maximum_membership_fuzzyset(item, fuzzy_sets).name)
return fts
[docs]def fuzzyfy_series(data, fuzzy_sets, method='maximum', alpha_cut=0.0, ordered_sets=None):
fts = []
if ordered_sets is None:
ordered_sets = set_ordered(fuzzy_sets)
for t, i in enumerate(data):
mv = fuzzyfy_instance(i, fuzzy_sets, ordered_sets)
if len(mv) == 0:
sets = check_bounds(i, fuzzy_sets.items(), ordered_sets)
else:
if method == 'fuzzy':
ix = np.ravel(np.argwhere(mv > alpha_cut))
sets = [fuzzy_sets[ordered_sets[i]].name for i in ix]
elif method == 'maximum':
mx = max(mv)
ix = np.ravel(np.argwhere(mv == mx))
sets = fuzzy_sets[ordered_sets[ix[0]]].name
fts.append(sets)
return fts
[docs]def grant_bounds(data, fuzzy_sets, ordered_sets):
if data < fuzzy_sets[ordered_sets[0]].lower:
return fuzzy_sets[ordered_sets[0]].lower
elif data > fuzzy_sets[ordered_sets[-1]].upper:
return fuzzy_sets[ordered_sets[-1]].upper
else:
return data
[docs]def check_bounds(data, fuzzy_sets, ordered_sets):
if data < fuzzy_sets[ordered_sets[0]].lower:
return fuzzy_sets[ordered_sets[0]]
elif data > fuzzy_sets[ordered_sets[-1]].upper:
return fuzzy_sets[ordered_sets[-1]]
[docs]def check_bounds_index(data, fuzzy_sets, ordered_sets):
if data < fuzzy_sets[ordered_sets[0]].get_lower():
return 0
elif data > fuzzy_sets[ordered_sets[-1]].get_upper():
return len(fuzzy_sets) - 1
