def get_rule(data_item):
#get degrees (firing strengths) of each rule
ants = {} #antecedents of each rule in form ['function', 'var'] : ('ling', degree) where degree is firing strengths
for inKey in inputMFs: #for each input key
if not fuzzyDataFlag:
[inXs, inYs] = fuzzyOps.rangeToMF(data_item[q][inKey], inDataMFs) #build input MF
else:
[inXs, inYs] = data_item[q][inKey]
max_fs = ('none', 0.0) #keep track of MF with maximum firing strength
for ling in inputMFs[inKey]: #for each MF in the input
#with Timer() as t:
fs_x,fs_y = fuzz.fuzzy_and(inputMFs[inKey][ling][0],inputMFs[inKey][ling][1], inXs, inYs)
#print '----------> AND time:', t.msecs, 'ms for input:', inKey, 'at length', len(fs_y)
fs = max(fs_y) #get firing strength of data point and given antecedent MF
if fs > max_fs[1]: max_fs = (ling,fs)
if max_fs[0] <> 'none':
ants[inKey + (max_fs[0],)] = max_fs[1] #append rule with highest firing strength to antecedent
if len(ants) > 0:
rule_deg = reduce(operator.mul, [ants[k] for k in ants]) #use to calc "degree" or strength of each rule
else:
rule_deg = 0.0
# repeat for outputs
conts = {} #consequents of each rule in form output : ('ling', degree)
for outKey in outputMFs: #for each output key
if not fuzzyDataFlag:
[outXs, outYs] = fuzzyOps.rangeToMF(data_item[2], outDataMFs) #build outputMF
else:
[outXs, outYs] = data_item[2]
max_fs = ('none', 0.0) #keep track of MF with maximum firing strength
for ling in outputMFs[outKey]: #for each MF in the input
#with Timer() as t:
fs_x, fs_y = fuzz.fuzzy_and(outputMFs[outKey][ling][0], outputMFs[outKey][ling][1], outXs, outYs)
#print '----------> AND output time:', t.msecs, 'ms'
fs = max(fs_y) #get firing strength of data point and given antecedent MF
if fs > max_fs[1]: max_fs = (ling,fs)
conts[(outKey,) + (max_fs[0],)] = max_fs[1] #append rule with highest firing strength to antecedent
if len(conts) > 0:
rule_deg = rule_deg * reduce(operator.mul, [conts[k] for k in conts]) #use to calc "degree" or strength of each rule
else: rule_deg = 0.0
return [ants, conts, rule_deg]
def firing_strength(self, input_name, input_, input_sys):
if not isinstance(input_, list): #if a singleton and not a list
fs = self.fuzzy_single_AND(
input_,
[input_sys.MFs[input_name][0], input_sys.MFs[input_name][1]])
return fs
x_min, y_min = fuzz.fuzzy_and(
input_sys.MFs[input_name][0], input_sys.MFs[input_name][1],
input_[0],
input_[1]) #use AND operator to get minimum of two functions
return max(y_min)
def firing_strength(self, input_name, input_, input_sys):
"""
get firing stregth of an input/output
input_name - linguistic input name
input_ - list corresponding to input [x,y] or singleton
input_sys - object corresponding to system input MFs
"""
if not isinstance(input_, list): #if a singleton and not a list
fs = self.fuzzy_single_AND(input_, [input_sys.MFs[input_name][0],input_sys.MFs[input_name][1]])
return fs
x_min,y_min = fuzz.fuzzy_and(input_sys.MFs[input_name][0],input_sys.MFs[input_name][1],input_[0],input_[1]) #use AND operator to get minimum of two functions
return max(y_min)
def firing_strength(self, input_name, input_, input_sys):
"""
get firing stregth of an input/output
input_name - linguistic input name
input_ - list corresponding to input [x,y] or singleton
input_sys - object corresponding to system input MFs
"""
if not isinstance(input_, list): #if a singleton and not a list
fs = self.fuzzy_single_AND(
input_,
[input_sys.MFs[input_name][0], input_sys.MFs[input_name][1]])
return fs
x_min, y_min = fuzz.fuzzy_and(
input_sys.MFs[input_name][0], input_sys.MFs[input_name][1], input_[0],
input_[1]) #use AND operator to get minimum of two functions
return max(y_min)
def firing_strength(self, input_name, input_, input_sys):
"""
Get firing stregth of an input
------INPUTS------
input_name : string
linguistic input name
input_ : list or float
corresponding to input [x,y] or singleton
input_sys - input object
object corresponding to system input MFs
------OUTPUTS------
firing_strength : float
firing strength of input and MF
"""
if not isinstance(input_, list): #if a singleton and not a list
fs = self.fuzzy_single_AND(input_, [input_sys.MFs[input_name][0],input_sys.MFs[input_name][1]])
return fs
x_min,y_min = fuzz.fuzzy_and(np.array(input_sys.MFs[input_name][0]),
np.array(input_sys.MFs[input_name][1]),
np.array(input_[0]),np.array(input_[1])) #use AND operator to get minimum of two functions
return max(y_min)
X = np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)
# Create two fuzzy sets by defining any membership function
# (trapmf(), gbellmf(), gaussmf(), etc).
abc1 = [0, 25, 50]
abc2 = [25, 50, 75]
young = fuzz.membership.trimf(X, abc1)
middle_aged = fuzz.membership.trimf(X, abc2)
# Compute the different operations using inbuilt functions.
one = np.ones(75)
zero = np.zeros((75,))
# 1. Union = max(µA(x), µB(x))
union = fuzz.fuzzy_or(X, young, X, middle_aged)[1]
# 2. Intersection = min(µA(x), µB(x))
intersection = fuzz.fuzzy_and(X, young, X, middle_aged)[1]
# 3. Complement (A) = (1- min(µA(x))
complement_a = fuzz.fuzzy_not(young)
# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
difference = fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
alg_sum = young + middle_aged - (young * middle_aged)
# 6. Algebraic Product = (µA(x) * µB(x))
alg_product = young * middle_aged
# 7. Bounded Sum = min[1,(µA(x), µB(x))]
bdd_sum = fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
# 8. Bounded difference = min[0,(µA(x), µB(x))]
bdd_difference = fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]
# max-min composition
# max-product composition
stop = 10 + delta step = 0.5 x = np.arange(start, stop + delta, step) # Triangular membership function x1 = np.arange(0, 5 + delta, step) trimf = fuzz.trimf(x1, [0, 2.5, 5]) # Trapezoidal membership function x2 = np.arange(4, 10 + delta, step) trapmf = fuzz.trapmf(x2, [4, 6, 8, 10]) # fuzzy logic tri_not = fuzz.fuzzy_not(trimf) trap_not = fuzz.fuzzy_not(trapmf) x3, tri_trap_and = fuzz.fuzzy_and(x1, trimf, x2, trapmf) x3, tri_trap_or = fuzz.fuzzy_or(x1, trimf, x2, trapmf) # Defuzzify centroid_x = fuzz.defuzz(x3, tri_trap_or, "centroid") centroid_y = fuzz.interp_membership(x3, tri_trap_or, centroid_x) bisector_x = fuzz.defuzz(x3, tri_trap_or, "bisector") bisector_y = fuzz.interp_membership(x3, tri_trap_or, bisector_x) mom_x = fuzz.defuzz(x3, tri_trap_or, "mom") mom_y = fuzz.interp_membership(x3, tri_trap_or, mom_x) som_x = fuzz.defuzz(x3, tri_trap_or, "som") som_y = fuzz.interp_membership(x3, tri_trap_or, som_x) lom_x = fuzz.defuzz(x3, tri_trap_or, "lom") lom_y = fuzz.interp_membership(x3, tri_trap_or, lom_x) # Whole config
plt.plot(x, medio, 'b', linewidth=1.5, label='Medio')
plt.title('Funcion union Maxima')
plt.ylabel('Membresia')
plt.xlabel('Velocidad km/h')
plt.legend(loc='center right', bbox_to_anchor=(
1.25, 0.5), ncol=1, fancybox=True, shadow=True)
plt.axvline(x)
i = 0
while i <= range(10):
plt.axvline(i, ymin=0, ymax=10, color='g', licestyle='-.')
plt.plot(0, 1, marker='o', markersize=10, color='g')
plt.plot(1, 0.8, marker='o', markersize=10, color='g')
plt.plot(2, 0.6, marker='o', markersize=10, color='g')
plt.plot(3, 0.6, marker='o', markersize=10, color='g')
plt.plot(4, 0.8, marker='o', markersize=10, color='g')
plt.plot(5, 1, marker='o', markersize=10, color='g')
plt.plot(6, 0.8, marker='o', markersize=10, color='g')
plt.plot(7, 0.6, marker='o', markersize=10, color='g')
plt.plot(8, 0.4, marker='o', markersize=10, color='g')
plt.plot(9, 0.2, marker='o', markersize=10, color='g')
plt.plot(10, 0, marker='o', markersize=10, color='g')
plt.show()
sk.fuzzy_and(x, bajo, x, medio)
from skfuzzy import trapmf
from skfuzzy import smf as s_shape_mf
from skfuzzy import zmf as z_shape_mf
font = {'family': 'DejaVu Sans', 'weight': 'normal', 'size': 7}
plt.rc('font', **font)
universe = np.arange(0, 13)
mfA = kinked_curve_mf(universe, [(2, 0), (8, 0.5), (9, 0.25), (14, 0)])
mfB = kinked_curve_mf(universe, [(0, 1), (5, 0)])
mfC = kinked_curve_mf(universe, [(0, 0), (3, 1), (5, 0)])
B_and_C, mf_B_and_C = fuzz.fuzzy_or(universe, mfA, universe, mfB)
A_or_B_and_C, mf_A_or_B_and_C = fuzz.fuzzy_and(B_and_C, mf_B_and_C, universe,
mfC)
fig = plt.figure(figsize=(10, 8))
grid = gridspec.GridSpec(nrows=2, ncols=6)
axA = fig.add_subplot(grid[0, :2],
xlim=(0, max(universe)),
ylim=(0, 1),
title='A')
axB = fig.add_subplot(grid[0, 2:4], sharex=axA, sharey=axA, title='B')
axC = fig.add_subplot(grid[0, 4:], sharex=axA, sharey=axA, title='C')
axBC = fig.add_subplot(grid[1, :3], sharex=axA, sharey=axA, title='B^C')
axD = fig.add_subplot(grid[1, 3:], sharex=axA, sharey=axA, title='AvB^C')
fig.tight_layout()
plt.locator_params(nbins=len(universe))
def train_NEFPROX(system,
trainData,
valData,
inMFs,
outMFs,
iRange,
oRange,
inDataMFs='sing',
outDataMFs='sing',
sigma=0.0005,
nTrainMax=None,
nValMax=None,
maxIterations=500,
errConvergeCount=5,
TESTMODE=False):
""""
Trains a NEFPROX system (based on Nernberger, Nauck, Kruse -
"Neuro-fuzzy control based on the NEFCON-model: recent developments"
and on Nauck, Kruse - "Neuro-Fuzzy Systems for Function Approximation")
------ INPUTS ------
system : instance of nefprox
NEFPROX system to train
trainData : list
training data set
valData : list
separate validation data set... data in form:
[quant_inputs, qual_inputs, outputData]
with each data item ['function', 'var'] : [min,max]
(inputs for system are named 'function var')
inMFs : dict
dictionary of input MFs: {inputname : {ling1 : ([x,y], params), ling2 : ([x,y], params), ...},
inputname2 : {ling1: ([x,y], params), ... }, ... }
outMFs : dict
dictionary of output MFs: {ling1 : [x,y], ling2 : [xy], ...}
iRange : dict
dictionary of input ranges for MFs: {[input] : [x,y], ... }
oRange : dict
dictionary of output ranges for MFs: {[output] : [x,y], ... }
inDataMFs : string
type of MF for input data (given [min, max]), supports sing, trap and tri
outDataMFs : string
type of MF for output data (given [min,max]), supports sing, trap and tri
sigma : float
learning rate. modifies adjustments to MFs
nTrainMax : int
maximum number of training points to use
nValMax : int
maximum number of validation points to use
Note: As of 30May15 only setup to train fuzzy triangular MFs
"""
q = 0 #0 for quant data, 1 or qual data
out_name = outMFs.keys()[0]
#limit amount of data:
if nTrainMax <> None: trainData = trainData[:nTrainMax]
if nValMax <> None: valData = valData[:nValMax]
del_sysErr = 0.01 #percentage for system error to decrease
sysErrorLast = 9999
errDecreaseCount = 0
errConvergeCount = 0
errIncreaseCount = 0
convergeCount = 5 #for this number of turns to converge
bestSystem = system #track best system
bestError = sysErrorLast #track best error
iteration = 1 #track iterations through data
trackOptInfo = optInfo #track of optimization information
trackOptInfo.lenTrainData = len(trainData)
trackOptInfo.lenValidationData = len(valData)
#print "BUILDING DATA MFS"
#GET MFs FOR INPUT TRAINING DATA
trainData_MFs = copy.deepcopy(trainData)
for dataIt in trainData_MFs:
#create input MFs for each input
for inp in dataIt[q]:
if inDataMFs == 'sing': #create singleton MF
dataIt[q][inp] = sum(dataIt[q][inp]) / len(
dataIt[q][inp]) #get mean of range (or single value)
x_range = [
dataIt[q][inp] * 0.9, dataIt[q][inp] * 1.1,
(dataIt[q][inp] * 1.1 - dataIt[q][inp] * 0.9) / 100.
]
dataIt[q][inp] = list(
fuzzOps.singleton_to_fuzzy(
dataIt[q][inp], x_range)) #turn singleton value to MF
elif inDataMFs == 'tri': #create triangluar MF (min, avg, max)
x_range = np.arange(
dataIt[q][inp][0] * 0.9, dataIt[q][inp][1] * 1.1,
(dataIt[q][inp][1] * 1.1 - dataIt[q][inp][0] * 0.9) / 150)
y_vals = fuzz.trimf(x_range, [
dataIt[q][inp][0],
sum(dataIt[q][inp]) / len(dataIt[q][inp]),
dataIt[q][inp][1]
])
dataIt[q][inp] = [x_range, y_vals]
elif inDataMFs == 'trap': #create traoeziodal MF (min, min, max, max)
x_range = np.arange(
dataIt[q][inp][0] * 0.9, dataIt[q][inp][1] * 1.1,
(dataIt[q][inp][1] * 1.1 - dataIt[q][inp][0] * 0.9) / 150)
y_vals = fuzz.trimf(x_range, [
dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][0],
dataIt[q][inp][1]
])
dataIt[q][inp] = [x_range, y_vals]
#create output MFs
if outDataMFs == 'sing': #create singleton MF
dataIt[2] = sum(dataIt[2]) / len(
dataIt[2]) #get average for singleton value
x_range = [
dataIt[2] * 0.9, dataIt[2] * 1.1,
(dataIt[2] * 1.1 - dataIt[2] * 0.9) / 100.
]
dataIt[2] = list(fuzzOps.singleton_to_fuzzy(
dataIt[2], x_range)) #turn singleton value to MF
elif outDataMFs == 'tri': #create singleton MF
x_range = np.arange(dataIt[2][0] * 0.9, dataIt[2][1] * 1.1,
(dataIt[2][1] * 1.1 - dataIt[2][0] * 0.9) /
150)
y_vals = fuzz.trimf(
x_range,
[dataIt[2][0],
sum(dataIt[2]) / len(dataIt[2]), dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
elif outDataMFs == 'trap': #create singleton MF
x_range = np.arange(dataIt[2][0] * 0.9, dataIt[2][1] * 1.1,
(dataIt[2][1] * 1.1 - dataIt[2][0] * 0.9) /
150)
y_vals = fuzz.trimf(
x_range,
[dataIt[2][0], dataIt[2][0], dataIt[2][1], dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
#GET MFs FOR VALIDATION DATA
valData_MFs = copy.deepcopy(valData)
for dataIt in valData_MFs:
#create input MFs for each input
for inp in dataIt[q]:
if inDataMFs == 'sing': #create singleton MF
dataIt[q][inp] = sum(dataIt[q][inp]) / len(
dataIt[q][inp]) #get mean of range (or single value)
x_range = [
dataIt[q][inp] * 0.9, dataIt[q][inp] * 1.1,
(dataIt[q][inp] * 1.1 - dataIt[q][inp] * 0.9) / 100.
]
dataIt[q][inp] = list(
fuzzOps.singleton_to_fuzzy(
dataIt[q][inp], x_range)) #turn singleton value to MF
elif inDataMFs == 'tri': #create triangluar MF (min, avg, max)
x_range = np.arange(
dataIt[q][inp][0] * 0.9, dataIt[q][inp][1] * 1.1,
(dataIt[q][inp][1] * 1.1 - dataIt[q][inp][0] * 0.9) / 150)
y_vals = fuzz.trimf(x_range, [
dataIt[q][inp][0],
sum(dataIt[q][inp]) / len(dataIt[q][inp]),
dataIt[q][inp][1]
])
dataIt[q][inp] = [x_range, y_vals]
elif inDataMFs == 'trap': #create traoeziodal MF (min, min, max, max)
x_range = np.arange(
dataIt[q][inp][0] * 0.9, dataIt[q][inp][1] * 1.1,
(dataIt[q][inp][1] * 1.1 - dataIt[q][inp][0] * 0.9) / 150)
y_vals = fuzz.trimf(x_range, [
dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][0],
dataIt[q][inp][1]
])
dataIt[q][inp] = [x_range, y_vals]
#create output MFs
if outDataMFs == 'sing': #create singleton MF
dataIt[2] = sum(dataIt[2]) / len(
dataIt[2]) #get average for singleton value
x_range = [
dataIt[2] * 0.9, dataIt[2] * 1.1,
(dataIt[2] * 1.1 - dataIt[2] * 0.9) / 100.
]
dataIt[2] = list(fuzzOps.singleton_to_fuzzy(
dataIt[2], x_range)) #turn singleton value to MF
elif outDataMFs == 'tri': #create singleton MF
x_range = np.arange(dataIt[2][0] * 0.9, dataIt[2][1] * 1.1,
(dataIt[2][1] * 1.1 - dataIt[2][0] * 0.9) /
150)
y_vals = fuzz.trimf(
x_range,
[dataIt[2][0],
sum(dataIt[2]) / len(dataIt[2]), dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
elif outDataMFs == 'trap': #create singleton MF
x_range = np.arange(dataIt[2][0] * 0.9, dataIt[2][1] * 1.1,
(dataIt[2][1] * 1.1 - dataIt[2][0] * 0.9) /
150)
y_vals = fuzz.trimf(
x_range,
[dataIt[2][0], dataIt[2][0], dataIt[2][1], dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
#Add all inputs and input MFs
for inp in inMFs:
if not inp in system.layer1:
system.layer1[inp] = None
for ling in inMFs[inp]:
cMF = inMFs[inp][ling]
system.inputMFs[(inp, ling)] = cMF
#Add all outputs and output MFs
for otp in outMFs:
if not otp in system.layer3:
system.layer3[otp] = None
for ling in outMFs[otp]:
cMF = outMFs[otp][ling]
system.outputMFs[(otp, ling)] = cMF
outputname = otp #should only be one output
###### MAIN TRAINING LOOP:
#iterate over data set until converged or max iterations performed
while errConvergeCount < convergeCount and iteration <= maxIterations:
#print "RANDOMIZING DATA"
trainRef = range(len(trainData)) #get indecies for data
random.shuffle(trainRef) #shuffle indecies
trainData2 = copy.deepcopy(trainData) #copy data
trainData_MFs2 = copy.deepcopy(trainData_MFs)
trainData = [trainData2[i]
for i in trainRef] #assign new order to data
trainData_MFs = [trainData_MFs2[i] for i in trainRef]
#print "LEARNING RULES"
#STRUCTURE LEARNING (learn rules)
rules = []
for dataIt in trainData_MFs: #for each learning data pair (s_i, t_i):
rule_ant = []
#for each input create input MF
for inp in dataIt[q]:
#find the MF (j) that returns the maximum degree of memebership for input
maxMF = (0.0, next(k for k in inMFs[inp[0] + '_' + inp[1]])
) #track firing strength and MF
for mfx in inMFs[inp[0] + '_' + inp[1]]:
union = fuzz.fuzzy_and(
inMFs[inp[0] + '_' + inp[1]][mfx][0],
inMFs[inp[0] + '_' + inp[1]][mfx][1],
dataIt[q][inp][0],
dataIt[q][inp][1]) #get union (AND) of two MFs
fs = max(union[1]) #get firing strength
if fs > maxMF[0]: maxMF = (fs, mfx)
rule_ant.append((inp[0] + '_' + inp[1],
maxMF[1])) #add to list of best input MFs
#find output MF that output belongs to with highest degree
maxMF = (0.0, outMFs[out_name].itervalues().next()
) #grab random MF to start
for mfx in outMFs[out_name]:
union = fuzz.fuzzy_and(
dataIt[2][0], dataIt[2][1], outMFs[out_name][mfx][0],
outMFs[out_name][mfx][1]) #get union (AND) of two MFs
fs = max(union[1]
) #get "firing strength" (yes I know it's an output)
if fs > maxMF[0]: maxMF = (fs, mfx)
rules.append([sorted(rule_ant), maxMF[1], maxMF[0]]) #antecendent
#METHOD 2: for creating rule base
#create rule grid, averaging rule "degree" for each consequent. keep the consequent
#with the highest average "degree"
rule_grid = {}
for rule in rules:
if rule[2] > 0.0 and len(rule[0]) > 0:
antX = tuple(sorted(a for a in rule[0]))
if not antX in rule_grid: #if rule isn't in grid add it
rule_grid[antX] = {
rule[1]: (rule[2], 1)
} #add new dict with consequent giving (total degree, number of data points)
else:
if not rule[1] in rule_grid[
antX]: #if consequent isn't already accounted for
rule_grid[antX][rule[1]] = (rule[2], 1)
else:
rule_grid[antX][rule[1]] = \
(rule_grid[antX][rule[1]][0] + rule[2],#add to the rule dgree and
rule_grid[antX][rule[1]][1] + 1) #update the number of data points
for rule in rule_grid: #for each rule grid get the average degree for each consequent
for cons in rule_grid[rule]:
rule_grid[rule][cons] = (rule_grid[rule][cons][0]/ \
rule_grid[rule][cons][1], rule_grid[rule][cons][1])
for rule in rule_grid: #for each rule grid get the average degree for each consequent
rule_deg = 0.0
rule_cons = ''
for cons in rule_grid[rule]:
if rule_grid[rule][cons][
0] > rule_deg: #capture consequent with hightest average "degree"
rule_deg = rule_grid[rule][cons][0]
rule_cons = cons
rule_grid[rule] = [rule_cons, rule_deg]
#Translate Rule Grid into NEFPROX
system.layer2 = {}
system.connect1to2 = {}
system.connect2to3 = {}
for rule in rule_grid:
if len(system.layer2) > 0:
nodeNo = max([int(ruleNo) for ruleNo in system.layer2
]) + 1.0 #get new node number/name
else:
nodeNo = 0
system.connect1to2[nodeNo] = {antIn: 0.0
for antIn in rule
} #create antecedent dict for rule
system.layer2[nodeNo] = None
system.connect2to3[nodeNo] = {
(outputname, rule_grid[rule][0]): None
}
#PARAMETER LEARNING (adjust MFs)
trainingError = 0.0
trainingActPre = [[], []] #[[actuals], [prediteds]]
time1 = datetime.now()
for i in range(
len(trainData)
): #for each learning data pair (s_i, t_i) in raw training data:
#progress report
time2 = datetime.now()
if (time2 - time1).seconds > 60.0:
print round(100.0 * (float(i) / float(len(trainData))),
1), '% done learning parameters.'
time1 = datetime.now()
#import pdb; pdb.set_trace()
#sys.exit("Test Finish")
#build input object
if inDataMFs == 'sing': #if crisp inputs use avg of original data
inData = {
inp[0] + '_' + inp[1]:
sum(trainData[i][q][inp]) / len(trainData[i][q][inp])
for inp in trainData[i][q]
}
else: #otherwise use input
inData = {
inp[0] + '_' + inp[1]: trainData_MFs[i][q][inp]
for inp in trainData_MFs[i][q]
}
output = system.run(
inData) #pass input through system to get result
output = output[output.keys()
[0]] #should only be one output value, get it.
#get delta value: d = t_i - o_i for each output unit (should only be one)
if not outDataMFs == 'sing' and isinstance(
output, list): #if both output and data are fuzzy
raise StandardError(
'Still have to convert data with output range to MF')
err = fuzzy_error.fuzErrorAC(trainData_MFs[i], output)
elif outDataMFs == 'sing' and isinstance(
output, float): #if both output and data are crisp
err = sum(trainData[i][2]) / len(trainData[i][2]) - output
trainingError = trainingError + err**2
trainingActPre[0].append(
sum(trainData[i][2]) / len(trainData[i][2]))
trainingActPre[1].append(output)
elif not outDataMFs == 'sing' and isinstance(
output, float): #if both output is fuzzy and data is crisp
raise StandardError('You have not created a case for this yet')
elif outDataMFs == 'sing' and isinstance(
output, list): #if both output is crisp and data is fuzzy
raise StandardError('You have not created a case for this yet')
#back propagate error through system
system.backpropagate(err, sigma, dataIt[2], iRange, oRange)
trackOptInfo.trackError[0].append(
(trainingError / len(trainData))**0.5) #save RMS training error
#CHECK SYSTEM ERROR: with Validation data
sysError = 0.0
sysActPre = [[], []] #[[actuals], [prediteds]]
for i in range(len(valData)): #for each learning data pair (s_i, t_i):
#build input object
if inDataMFs == 'sing': #if crisp inputs use avg of original data
inData = {
inp[0] + '_' + inp[1]:
sum(valData[i][q][inp]) / len(valData[i][q][inp])
for inp in valData[i][q]
}
else: #otherwise use input
inData = {
inp[0] + '_' + inp[1]: valData_MFs[i][q][inp]
for inp in valData_MFs[i][q]
}
output = system.run(
inData) #pass input through system to get result
output = output[output.keys()
[0]] #should only be one output value, get it.
#get delta value: d = t_i - o_i for each output unit (should only be one)
if not outDataMFs == 'sing' and isinstance(
output, list): #if both output and data are fuzzy
raise StandardError(
'Still have to convert data with output range to MF')
err = fuzzy_error.fuzErrorAC(valData_MFs[i][2], output)
elif outDataMFs == 'sing' and isinstance(
output, float): #if both output and data are crisp
err = (sum(valData[i][2]) / len(valData[i][2]) - output)**2
sysActPre[0].append(sum(valData[i][2]) / len(valData[i][2]))
sysActPre[1].append(output)
elif not outDataMFs == 'sing' and isinstance(
output, float): #if both output is fuzzy and data is crisp
raise StandardError('You have not created a case for this yet')
elif outDataMFs == 'sing' and isinstance(
output, list): #if both output is crisp and data is fuzzy
raise StandardError('You have not created a case for this yet')
sysError = sysError + err #sum up error
sysError = (sysError / len(valData)
)**0.5 #total system error = (1/2N)sum( (t_i - o_i)^2 )
trackOptInfo.trackError[1].append(sysError) #track validation error
#ONLY TEST MODE
if TESTMODE:
plt.figure()
plt.scatter(trainingActPre[0], trainingActPre[1])
plt.scatter(sysActPre[0], sysActPre[1])
plt.legend(["Training", "Validation"])
plt.show()
#check error progress
change_sysError = (
(sysErrorLast - sysError) / sysErrorLast
) #get normalized change in error (negative is an increase)
if iteration > 1:
if change_sysError > 0: sigma = sigma * 1.03
elif change_sysError < 0: sigma = sigma * 0.5
if change_sysError <= del_sysErr and \
change_sysError >= 0:
errConvergeCount = errConvergeCount + 1 #add to count if error change is small enough
else:
errConvergeCount = 0 #otherwise reset it
"""
if change_sysError > 0:
errDecreaseCount = errDecreaseCount + 1
errIncreaseCount = errIncreaseCount + 1 #add to count if error increases
#errIncreaseCount = 0 #otherwise reset it
else:
errIncreaseCount = errIncreaseCount + 1 #add to count if error increases
errDecreaseCount = 0
if errDecreaseCount >= 4:
sigma = sigma*1.1 #if error increases x times, increase the learning rate
errIncreaseCount = 0
errDecreaseCount = 0
elif errIncreaseCount >= 4:
sigma = sigma*0.9 #if fluctuations or increases
errIncreaseCount = 0
errDecreaseCount = 0
"""
if abs(sysError) < bestError: #track best syste
bestSystem = copy.deepcopy(system)
bestError = abs(sysError)
sysErrorLast = sysError #track last error
iteration = iteration + 1
trackOptInfo.learning_rate.append(sigma) #track learnin rate
print 'system error:', round(sysError,
6), ' delta system error:', round(
change_sysError, 6),
print ' decrease/increase count:', errDecreaseCount, '/', errIncreaseCount, " learning rate:", round(
sigma, 8)
#capture opt info
trackOptInfo.iterations = iteration
return bestSystem, trackOptInfo
def train_NEFPROX(system, trainData, valData, inMFs, outMFs, iRange, oRange,
inDataMFs='sing', outDataMFs='sing', sigma=0.0005,
nTrainMax=None, nValMax=None, maxIterations=500, errConvergeCount=5,
TESTMODE=False):
""""
Trains a NEFPROX system (based on Nernberger, Nauck, Kruse -
"Neuro-fuzzy control based on the NEFCON-model: recent developments"
and on Nauck, Kruse - "Neuro-Fuzzy Systems for Function Approximation")
------ INPUTS ------
system : instance of nefprox
NEFPROX system to train
trainData : list
training data set
valData : list
separate validation data set... data in form:
[quant_inputs, qual_inputs, outputData]
with each data item ['function', 'var'] : [min,max]
(inputs for system are named 'function var')
inMFs : dict
dictionary of input MFs: {inputname : {ling1 : ([x,y], params), ling2 : ([x,y], params), ...},
inputname2 : {ling1: ([x,y], params), ... }, ... }
outMFs : dict
dictionary of output MFs: {ling1 : [x,y], ling2 : [xy], ...}
iRange : dict
dictionary of input ranges for MFs: {[input] : [x,y], ... }
oRange : dict
dictionary of output ranges for MFs: {[output] : [x,y], ... }
inDataMFs : string
type of MF for input data (given [min, max]), supports sing, trap and tri
outDataMFs : string
type of MF for output data (given [min,max]), supports sing, trap and tri
sigma : float
learning rate. modifies adjustments to MFs
nTrainMax : int
maximum number of training points to use
nValMax : int
maximum number of validation points to use
Note: As of 30May15 only setup to train fuzzy triangular MFs
"""
q = 0 #0 for quant data, 1 or qual data
out_name = outMFs.keys()[0]
#limit amount of data:
if nTrainMax <> None: trainData = trainData[:nTrainMax]
if nValMax <> None: valData = valData[:nValMax]
del_sysErr = 0.01 #percentage for system error to decrease
sysErrorLast = 9999
errDecreaseCount = 0
errConvergeCount = 0
errIncreaseCount = 0
convergeCount = 5 #for this number of turns to converge
bestSystem = system #track best system
bestError = sysErrorLast #track best error
iteration = 1 #track iterations through data
trackOptInfo = optInfo #track of optimization information
trackOptInfo.lenTrainData = len(trainData)
trackOptInfo.lenValidationData = len(valData)
#print "BUILDING DATA MFS"
#GET MFs FOR INPUT TRAINING DATA
trainData_MFs = copy.deepcopy(trainData)
for dataIt in trainData_MFs:
#create input MFs for each input
for inp in dataIt[q]:
if inDataMFs == 'sing': #create singleton MF
dataIt[q][inp] = sum(dataIt[q][inp])/len(dataIt[q][inp]) #get mean of range (or single value)
x_range = [dataIt[q][inp]*0.9, dataIt[q][inp]*1.1, (dataIt[q][inp]*1.1 - dataIt[q][inp]*0.9)/100.]
dataIt[q][inp] = list(fuzzOps.singleton_to_fuzzy(dataIt[q][inp], x_range)) #turn singleton value to MF
elif inDataMFs == 'tri': #create triangluar MF (min, avg, max)
x_range = np.arange(dataIt[q][inp][0]*0.9, dataIt[q][inp][1]*1.1, (dataIt[q][inp][1]*1.1 - dataIt[q][inp][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[q][inp][0], sum(dataIt[q][inp])/len(dataIt[q][inp]), dataIt[q][inp][1]])
dataIt[q][inp] = [x_range, y_vals]
elif inDataMFs == 'trap': #create traoeziodal MF (min, min, max, max)
x_range = np.arange(dataIt[q][inp][0]*0.9, dataIt[q][inp][1]*1.1, (dataIt[q][inp][1]*1.1 - dataIt[q][inp][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][1]])
dataIt[q][inp] = [x_range, y_vals]
#create output MFs
if outDataMFs == 'sing': #create singleton MF
dataIt[2] = sum(dataIt[2])/len(dataIt[2]) #get average for singleton value
x_range = [dataIt[2]*0.9, dataIt[2]*1.1, (dataIt[2]*1.1 - dataIt[2]*0.9)/100.]
dataIt[2] = list(fuzzOps.singleton_to_fuzzy(dataIt[2], x_range)) #turn singleton value to MF
elif outDataMFs == 'tri': #create singleton MF
x_range = np.arange(dataIt[2][0]*0.9, dataIt[2][1]*1.1, (dataIt[2][1]*1.1 - dataIt[2][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[2][0], sum(dataIt[2])/len(dataIt[2]), dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
elif outDataMFs == 'trap': #create singleton MF
x_range = np.arange(dataIt[2][0]*0.9, dataIt[2][1]*1.1, (dataIt[2][1]*1.1 - dataIt[2][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[2][0], dataIt[2][0], dataIt[2][1], dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
#GET MFs FOR VALIDATION DATA
valData_MFs = copy.deepcopy(valData)
for dataIt in valData_MFs:
#create input MFs for each input
for inp in dataIt[q]:
if inDataMFs == 'sing': #create singleton MF
dataIt[q][inp] = sum(dataIt[q][inp])/len(dataIt[q][inp]) #get mean of range (or single value)
x_range = [dataIt[q][inp]*0.9, dataIt[q][inp]*1.1, (dataIt[q][inp]*1.1 - dataIt[q][inp]*0.9)/100.]
dataIt[q][inp] = list(fuzzOps.singleton_to_fuzzy(dataIt[q][inp], x_range)) #turn singleton value to MF
elif inDataMFs == 'tri': #create triangluar MF (min, avg, max)
x_range = np.arange(dataIt[q][inp][0]*0.9, dataIt[q][inp][1]*1.1, (dataIt[q][inp][1]*1.1 - dataIt[q][inp][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[q][inp][0], sum(dataIt[q][inp])/len(dataIt[q][inp]), dataIt[q][inp][1]])
dataIt[q][inp] = [x_range, y_vals]
elif inDataMFs == 'trap': #create traoeziodal MF (min, min, max, max)
x_range = np.arange(dataIt[q][inp][0]*0.9, dataIt[q][inp][1]*1.1, (dataIt[q][inp][1]*1.1 - dataIt[q][inp][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][0], dataIt[q][inp][1]])
dataIt[q][inp] = [x_range, y_vals]
#create output MFs
if outDataMFs == 'sing': #create singleton MF
dataIt[2] = sum(dataIt[2])/len(dataIt[2]) #get average for singleton value
x_range = [dataIt[2]*0.9, dataIt[2]*1.1, (dataIt[2]*1.1 - dataIt[2]*0.9)/100.]
dataIt[2] = list(fuzzOps.singleton_to_fuzzy(dataIt[2], x_range)) #turn singleton value to MF
elif outDataMFs == 'tri': #create singleton MF
x_range = np.arange(dataIt[2][0]*0.9, dataIt[2][1]*1.1, (dataIt[2][1]*1.1 - dataIt[2][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[2][0], sum(dataIt[2])/len(dataIt[2]), dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
elif outDataMFs == 'trap': #create singleton MF
x_range = np.arange(dataIt[2][0]*0.9, dataIt[2][1]*1.1, (dataIt[2][1]*1.1 - dataIt[2][0]*0.9)/150)
y_vals = fuzz.trimf(x_range, [dataIt[2][0], dataIt[2][0], dataIt[2][1], dataIt[2][1]])
dataIt[2] = [x_range, y_vals]
#Add all inputs and input MFs
for inp in inMFs:
if not inp in system.layer1:
system.layer1[inp] = None
for ling in inMFs[inp]:
cMF = inMFs[inp][ling]
system.inputMFs[(inp, ling)] = cMF
#Add all outputs and output MFs
for otp in outMFs:
if not otp in system.layer3:
system.layer3[otp] = None
for ling in outMFs[otp]:
cMF = outMFs[otp][ling]
system.outputMFs[(otp, ling)] = cMF
outputname = otp #should only be one output
###### MAIN TRAINING LOOP:
#iterate over data set until converged or max iterations performed
while errConvergeCount < convergeCount and iteration <= maxIterations:
#print "RANDOMIZING DATA"
trainRef = range(len(trainData)) #get indecies for data
random.shuffle(trainRef) #shuffle indecies
trainData2 = copy.deepcopy(trainData) #copy data
trainData_MFs2 = copy.deepcopy(trainData_MFs)
trainData = [trainData2[i] for i in trainRef] #assign new order to data
trainData_MFs = [trainData_MFs2[i] for i in trainRef]
#print "LEARNING RULES"
#STRUCTURE LEARNING (learn rules)
rules = []
for dataIt in trainData_MFs: #for each learning data pair (s_i, t_i):
rule_ant = []
#for each input create input MF
for inp in dataIt[q]:
#find the MF (j) that returns the maximum degree of memebership for input
maxMF = (0.0, next(k for k in inMFs[inp[0] + '_' + inp[1]])) #track firing strength and MF
for mfx in inMFs[inp[0] + '_' + inp[1]]:
union = fuzz.fuzzy_and(inMFs[inp[0] + '_' + inp[1]][mfx][0], inMFs[inp[0] + '_' + inp[1]][mfx][1],
dataIt[q][inp][0], dataIt[q][inp][1]) #get union (AND) of two MFs
fs = max(union[1]) #get firing strength
if fs > maxMF[0]: maxMF = (fs, mfx)
rule_ant.append((inp[0]+'_'+inp[1], maxMF[1])) #add to list of best input MFs
#find output MF that output belongs to with highest degree
maxMF = (0.0, outMFs[out_name].itervalues().next()) #grab random MF to start
for mfx in outMFs[out_name]:
union = fuzz.fuzzy_and(dataIt[2][0], dataIt[2][1],
outMFs[out_name][mfx][0], outMFs[out_name][mfx][1]) #get union (AND) of two MFs
fs = max(union[1]) #get "firing strength" (yes I know it's an output)
if fs > maxMF[0]: maxMF = (fs, mfx)
rules.append([sorted(rule_ant), maxMF[1], maxMF[0]]) #antecendent
#METHOD 2: for creating rule base
#create rule grid, averaging rule "degree" for each consequent. keep the consequent
#with the highest average "degree"
rule_grid = {}
for rule in rules:
if rule[2] > 0.0 and len(rule[0]) > 0:
antX = tuple(sorted(a for a in rule[0]))
if not antX in rule_grid: #if rule isn't in grid add it
rule_grid[antX] = {rule[1]: (rule[2], 1)} #add new dict with consequent giving (total degree, number of data points)
else:
if not rule[1] in rule_grid[antX]: #if consequent isn't already accounted for
rule_grid[antX][rule[1]] = (rule[2], 1)
else:
rule_grid[antX][rule[1]] = \
(rule_grid[antX][rule[1]][0] + rule[2],#add to the rule dgree and
rule_grid[antX][rule[1]][1] + 1) #update the number of data points
for rule in rule_grid: #for each rule grid get the average degree for each consequent
for cons in rule_grid[rule]:
rule_grid[rule][cons] = (rule_grid[rule][cons][0]/ \
rule_grid[rule][cons][1], rule_grid[rule][cons][1])
for rule in rule_grid: #for each rule grid get the average degree for each consequent
rule_deg = 0.0
rule_cons = ''
for cons in rule_grid[rule]:
if rule_grid[rule][cons][0] > rule_deg: #capture consequent with hightest average "degree"
rule_deg = rule_grid[rule][cons][0]
rule_cons = cons
rule_grid[rule] = [rule_cons, rule_deg]
#Translate Rule Grid into NEFPROX
system.layer2 = {}
system.connect1to2 = {}
system.connect2to3 = {}
for rule in rule_grid:
if len(system.layer2) > 0: nodeNo = max([int(ruleNo) for ruleNo in system.layer2]) + 1.0 #get new node number/name
else: nodeNo = 0
system.connect1to2[nodeNo] = {antIn:0.0 for antIn in rule} #create antecedent dict for rule
system.layer2[nodeNo] = None
system.connect2to3[nodeNo] = {(outputname, rule_grid[rule][0]): None}
#PARAMETER LEARNING (adjust MFs)
trainingError = 0.0
trainingActPre = [[],[]] #[[actuals], [prediteds]]
time1 = datetime.now()
for i in range(len(trainData)): #for each learning data pair (s_i, t_i) in raw training data:
#progress report
time2 = datetime.now()
if (time2-time1).seconds > 60.0:
print round(100.0*(float(i)/float(len(trainData))),1), '% done learning parameters.'
time1=datetime.now()
#import pdb; pdb.set_trace()
#sys.exit("Test Finish")
#build input object
if inDataMFs == 'sing': #if crisp inputs use avg of original data
inData = {inp[0]+'_'+inp[1]: sum(trainData[i][q][inp])/len(trainData[i][q][inp]) for inp in trainData[i][q]}
else: #otherwise use input
inData = {inp[0]+'_'+inp[1]: trainData_MFs[i][q][inp] for inp in trainData_MFs[i][q]}
output = system.run(inData) #pass input through system to get result
output = output[output.keys()[0]] #should only be one output value, get it.
#get delta value: d = t_i - o_i for each output unit (should only be one)
if not outDataMFs=='sing' and isinstance(output, list): #if both output and data are fuzzy
raise StandardError('Still have to convert data with output range to MF')
err = fuzzy_error.fuzErrorAC(trainData_MFs[i], output)
elif outDataMFs=='sing' and isinstance(output, float): #if both output and data are crisp
err = sum(trainData[i][2])/len(trainData[i][2]) - output
trainingError = trainingError + err**2
trainingActPre[0].append(sum(trainData[i][2])/len(trainData[i][2]))
trainingActPre[1].append(output)
elif not outDataMFs=='sing' and isinstance(output, float): #if both output is fuzzy and data is crisp
raise StandardError('You have not created a case for this yet')
elif outDataMFs=='sing' and isinstance(output, list): #if both output is crisp and data is fuzzy
raise StandardError('You have not created a case for this yet')
#back propagate error through system
system.backpropagate(err, sigma, dataIt[2], iRange, oRange)
trackOptInfo.trackError[0].append( (trainingError/len(trainData))**0.5 ) #save RMS training error
#CHECK SYSTEM ERROR: with Validation data
sysError = 0.0
sysActPre = [[],[]] #[[actuals], [prediteds]]
for i in range(len(valData)): #for each learning data pair (s_i, t_i):
#build input object
if inDataMFs == 'sing': #if crisp inputs use avg of original data
inData = {inp[0]+'_'+inp[1]: sum(valData[i][q][inp])/len(valData[i][q][inp]) for inp in valData[i][q]}
else: #otherwise use input
inData = {inp[0]+'_'+inp[1]: valData_MFs[i][q][inp] for inp in valData_MFs[i][q]}
output = system.run(inData) #pass input through system to get result
output = output[output.keys()[0]] #should only be one output value, get it.
#get delta value: d = t_i - o_i for each output unit (should only be one)
if not outDataMFs=='sing' and isinstance(output, list): #if both output and data are fuzzy
raise StandardError('Still have to convert data with output range to MF')
err = fuzzy_error.fuzErrorAC(valData_MFs[i][2], output)
elif outDataMFs=='sing' and isinstance(output, float): #if both output and data are crisp
err = (sum(valData[i][2])/len(valData[i][2]) - output)**2
sysActPre[0].append(sum(valData[i][2])/len(valData[i][2]))
sysActPre[1].append(output)
elif not outDataMFs=='sing' and isinstance(output, float): #if both output is fuzzy and data is crisp
raise StandardError('You have not created a case for this yet')
elif outDataMFs=='sing' and isinstance(output, list): #if both output is crisp and data is fuzzy
raise StandardError('You have not created a case for this yet')
sysError = sysError + err #sum up error
sysError = (sysError/len(valData))**0.5 #total system error = (1/2N)sum( (t_i - o_i)^2 )
trackOptInfo.trackError[1].append( sysError ) #track validation error
#ONLY TEST MODE
if TESTMODE:
plt.figure()
plt.scatter(trainingActPre[0],trainingActPre[1])
plt.scatter(sysActPre[0], sysActPre[1])
plt.legend(["Training", "Validation"])
plt.show()
#check error progress
change_sysError = ((sysErrorLast - sysError)/sysErrorLast) #get normalized change in error (negative is an increase)
if iteration > 1:
if change_sysError > 0: sigma = sigma*1.03
elif change_sysError < 0: sigma = sigma*0.5
if change_sysError <= del_sysErr and \
change_sysError >= 0: errConvergeCount = errConvergeCount + 1 #add to count if error change is small enough
else: errConvergeCount = 0 #otherwise reset it
"""
if change_sysError > 0:
errDecreaseCount = errDecreaseCount + 1
errIncreaseCount = errIncreaseCount + 1 #add to count if error increases
#errIncreaseCount = 0 #otherwise reset it
else:
errIncreaseCount = errIncreaseCount + 1 #add to count if error increases
errDecreaseCount = 0
if errDecreaseCount >= 4:
sigma = sigma*1.1 #if error increases x times, increase the learning rate
errIncreaseCount = 0
errDecreaseCount = 0
elif errIncreaseCount >= 4:
sigma = sigma*0.9 #if fluctuations or increases
errIncreaseCount = 0
errDecreaseCount = 0
"""
if abs(sysError) < bestError: #track best syste
bestSystem = copy.deepcopy(system)
bestError = abs(sysError)
sysErrorLast = sysError #track last error
iteration = iteration + 1
trackOptInfo.learning_rate.append(sigma) #track learnin rate
print 'system error:', round(sysError,6), ' delta system error:', round(change_sysError,6),
print ' decrease/increase count:', errDecreaseCount, '/', errIncreaseCount, " learning rate:", round(sigma,8)
#capture opt info
trackOptInfo.iterations = iteration
return bestSystem, trackOptInfo
ax0.legend()
ax1.plot(x_servicio, servicio_bajo, 'b', linewidth=1.5, label='Pobre')
ax1.plot(x_servicio, servicio_medio, 'g', linewidth=1.5, label='Aceptable')
ax1.plot(x_servicio, servicio_alto, 'r', linewidth=1.5, label='Asombrosa')
ax1.set_title('Calidad de Servicio')
ax1.legend()
ax2.plot(x_tip, tip_bajo, 'b', linewidth=1.5, label='Bajo')
ax2.plot(x_tip, tip_medio, 'g', linewidth=1.5, label='Medio')
ax2.plot(x_tip, tip_alto, 'r', linewidth=1.5, label='Alto')
ax2.set_title('Cantidad de propina')
ax2.legend()
#probando operacion and
probando_and = fuzz.fuzzy_and(x_calidad, calidad_alta, x_servicio,
servicio_alto)
# desaparece los cuadros de arriba y derecha (mas kawaii)
for ax in (ax0, ax1, ax2):
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.get_xaxis().tick_bottom()
ax.get_yaxis().tick_left()
plt.tight_layout()
#Se eligieron reglas para definir el conjunto , tal como se explica a continuacion
"""
.. image:: PLOT2RST.current_figure
Fuzzy rules
def feedforward(self, inputs):
"""
------INPUTS------
inputs : dict
the set of outputs from previous nodes in form
{nodeName: value, nodeName: value, ...} (or inputs for input
nodes)
"""
#INPUT FEED FORWARD (fuzzify inputs)
for inp in self.layer1:
try:
if inp in inputs: #check if input is given
if not isinstance(inputs[inp], list):
MF = fuzzOps.paramsToMF([inputs[inp]]) #get fuzzy MF for singleton
self.layer1[inp] = MF
else:
self.layer1[inp] = inputs[inp]
else:
print "Not all inputs given!!!"
self.layer3[self.layer3.keys()[0]] = None #set system output to None
except:
raise StandardError("NEFPROX input error!")
#RULE FEED FORWARD (gets min (t-norm) firing strength of weights/MFterms and inputs)
for rule in self.layer2: #for each rule
for inp in self.connect1to2[rule]: #for each input in antecedent
fs = max(fuzz.fuzzy_and(self.inputMFs[inp][0], self.inputMFs[inp][1],
self.layer1[inp[0]][0], self.layer1[inp[0]][1])[1])
self.connect1to2[rule][inp] = fs
self.layer2[rule] = min([self.connect1to2[rule][inp] for inp in self.connect1to2[rule]])
#OUTPUT FEED FORWARD (apply minimum of firing strength and output MF (reduce output MF), then aggregate)
outMFs = []
for rule in self.connect2to3: #for each rule
cons = self.connect2to3[rule].keys()[0] #get consequent for single output
if self.layer2[rule] > 0.0: #only for active rules (save time)
outMF = copy.deepcopy(self.outputMFs[cons][:2])
outMF[1] = np.asarray([ min(self.layer2[rule], outMF[1][i]) for i in range(len(outMF[1])) ])
#apply minimum of firing strength and output MF (reduce output MF)
self.connect2to3[rule][cons] = outMF
outMFs.append(outMF)
else: #for inactive rules, applied MF is 0.0 for all
self.connect2to3[rule][cons] = [np.asarray([0.0, 0.0]), np.asarray([0.0,0.0])]
#once all rules are reduced with MFs aggregate
if len(outMFs) > 0: #check for no rules fired
while len(outMFs) > 1: #get maximum (union) of all MFs (aggregation)
outMFs0 = outMFs.pop(0)
outMFs[0][0], outMFs[0][1] = fuzz.fuzzy_or(outMFs0[0], outMFs0[1],
outMFs[0][0], outMFs[0][1])
if self.defuzz == None: pass
elif self.defuzz == 'centroid': outMFs[0] = fuzz.defuzz(outMFs[0][0],outMFs[0][1],'centroid')
elif self.defuzz == 'bisector': outMFs[0] = fuzz.defuzz(outMFs[0][0],outMFs[0][1],'bisector')
elif self.defuzz == 'mom': outMFs[0] = fuzz.defuzz(outMFs[0][0],outMFs[0][1],'mom') #mean of maximum
elif self.defuzz == 'som': outMFs[0] = fuzz.defuzz(outMFs[0][0],outMFs[0][1],'som') #min of maximum
elif self.defuzz == 'lom': outMFs[0] = fuzz.defuzz(outMFs[0][0],outMFs[0][1],'lom') #max of maximum
self.layer3[cons[0]] = outMFs[0]
else:#if no rules fire, then output is None
if self.defuzz == None:
self.layer3[cons[0]] = [[0.0,0.0],[0.0,0.0]] #result 0.0 in fuzzy MF form
else:
self.layer3[cons[0]] = 0.0 #result 0.0 as crisp if some defuzz method specified
return True
def backpropagate(self, error, LR, data, inRanges, outRanges):
"""
------INPUTS------
"""
#BACKPROP THROUGH OUTPUT NODE:
if not isinstance(data, list):
dataFuzz = fuzzOps.paramsToMF[[data]] #get fuzzy version of data for FS
else:
dataFuzz = copy.deepcopy(data)
data = fuzz.defuzz(data[0], data[1], 'centroid') #get crisp version of data
for rule in self.connect2to3: #for each rule to output connectionMF
if self.layer2[rule] > 0.0: #if rule is firing > 0.0
outKey = self.connect2to3[rule].keys()[0] #get connection (outName,ling)
fs = max(fuzz.fuzzy_and(self.outputMFs[outKey][0], self.outputMFs[outKey][1],
dataFuzz[0], dataFuzz[1])[1])
#get "firing strength" of individual MF (result of MF for data: W(R,y_i)(t_i))
#GET CONSTRAINTS:
#Triangular: MFs must overlap (or touch other MFs)
[minP, maxP] = outRanges[outKey[0]]
if len(self.outputMFs[outKey][2]) == 2:
raise StandardError("haven't programmed this")
if len(self.outputMFs[outKey][2]) == 3:
all_params = [self.outputMFs[ling][2] for ling in self.outputMFs]
all_params.sort(key=lambda x: x[1]) #sort params by orderer of b value
min_ps = all_params[max(0, all_params.index(self.outputMFs[outKey][2]) - 1)] #get MF just < the one changing
if min_ps == self.outputMFs[outKey][2]:
min_op = [minP, minP, minP] #adjust if MF is minimum one
max_ps = all_params[min(len(all_params) - 1, all_params.index(self.outputMFs[outKey][2]) + 1)]#get MF just > the one changing
if max_ps == self.outputMFs[outKey][2]:
max_op = [maxP, maxP, maxP] #adjust if MF is maximum one
else:
raise StandardError("haven't programmed this")
if fs > 0: #for W(R,y_i)(t_i) > 0
if len(self.outputMFs[outKey][2]) == 2: #gaussian MF adjustment
raise StandardError("haven't programmed this")
elif len(self.outputMFs[outKey][2]) == 3: #triangular MF adjustment
[a,b,c] = self.outputMFs[outKey][2][:] #get params
del_b = LR*error*(c - a)*self.layer2[rule]*(1-fs)
del_a = LR*(c - a)*self.layer2[rule] + del_b
del_c = -1*LR*(c - a)*self.layer2[rule] + del_b
b = min( max(b+del_b, min_ps[1]), max_ps[1] ) #bound b by nearest b's
a = min(b, min( max(a+del_a, min_ps[0]), min_ps[2] )) #bound a by nearest a and c and keep a < b
c = max(b, min( max(c+del_c, max_ps[0]), max_ps[2] )) #bound c by nearest a and c and keep c > b
self.outputMFs[outKey][2] = [a,b,c] #update params
elif len(self.outputMFs[outKey][2]) == 4: #trapezoidal MF adjustment
raise StandardError("haven't programmed this")
else: #for W(R,y_i)(t_i) = 0
if len(self.outputMFs[outKey][2]) == 2: #gaussian MF adjustment
raise StandardError("haven't programmed this")
elif len(self.outputMFs[outKey][2]) == 3: #triangular MF adjustment
[a,b,c] = self.outputMFs[outKey][2][:] #get params
del_b = LR*error*(c - a)*self.layer2[rule]*(1-fs)
del_a = np.sign(data-b)*LR*(c - a)*self.layer2[rule] + del_b
del_c = np.sign(data-b)*LR*(c - a)*self.layer2[rule] + del_b
b = min( max(b+del_b, min_ps[1]), max_ps[1] ) #bound b by nearest b's
a = min(b, min( max(a+del_a, min_ps[0]), min_ps[2] )) #bound a by nearest a and c and keep a < b
c = max(b, min( max(c+del_c, max_ps[0]), max_ps[2] )) #bound c by nearest a and c and keep c > b
self.outputMFs[outKey][2] = [a,b,c] #update params
elif len(self.outputMFs[outKey][2]) == 4: #trapezoidal MF adjustment
raise StandardError("haven't programmed this")
newMF = fuzzOps.paramsToMF(self.outputMFs[outKey][2]) #get updated MF
self.outputMFs[outKey][0] = newMF[0] #update MF
self.outputMFs[outKey][1] = newMF[1] #update MF
#BACKPROP THROUGH RULE NODES:
for rule in self.layer2:
#get Rule Error: E_R = o_R(1-o_R) * sum(2*W(R,y)(t_i) - 1) * abs(error)
# note: only one output node:
outKey = self.connect2to3[rule].keys()[0] #get connection (outName,ling)
fs = max(fuzz.fuzzy_and(self.outputMFs[outKey][0], self.outputMFs[outKey][1],
dataFuzz[0], dataFuzz[1])[1])
E_R = self.layer2[rule]*(1-self.layer2[rule]) * (2*fs-1) * abs(error) #rule error
for input in self.connect1to2[rule]:
o_x = fuzz.defuzz(self.layer1[input[0]][0], self.layer1[input[0]][1], 'centroid') #crisp version of input
if self.connect1to2[rule][input] > 0.0: #if FS from that input > 0
if fs > 0: #for W(R,y_i)(t_i) > 0
if len(self.outputMFs[outKey][2]) == 2: #gaussian MF adjustment
raise StandardError("haven't programmed this")
elif len(self.outputMFs[outKey][2]) == 3: #triangular MF adjustment
[a,b,c] = self.inputMFs[input][2][:] #get params
del_b = LR*E_R*(c - a)*(1-self.connect1to2[rule][input])*np.sign(o_x - b)
del_a = -LR*E_R*(c - a)*(1-self.connect1to2[rule][input])+del_b
del_c = LR*E_R*(c - a)*(1-self.connect1to2[rule][input])+del_b
#print 'LR', LR, 'E_R', E_R, 'c-a', c-a, '1-W(x,R)(ox)', (1-self.connect1to2[rule][input])
#print 'rule dels:', [del_a, del_b, del_c]
self.inputMFs[input][2] = [min(self.inputMFs[input][2][0]+del_a, self.inputMFs[input][2][1]+del_b),
self.inputMFs[input][2][1]+del_b,
max(self.inputMFs[input][2][2]+del_c, self.inputMFs[input][2][1]+del_b) ] #update params
elif len(self.outputMFs[outKey][2]) == 4: #trapezoidal MF adjustment
raise StandardError("haven't programmed this")
newMF = fuzzOps.paramsToMF(self.inputMFs[input][2]) #get updated MF
self.inputMFs[input][0] = newMF[0] #update MF
self.inputMFs[input][1] = newMF[1] #update MF
def firing_strength(self, input_name, input_, input_sys):
if not isinstance(input_, list): #if a singleton and not a list
fs = self.fuzzy_single_AND(input_, [input_sys.MFs[input_name][0],input_sys.MFs[input_name][1]])
return fs
x_min,y_min = fuzz.fuzzy_and(input_sys.MFs[input_name][0],input_sys.MFs[input_name][1],input_[0],input_[1]) #use AND operator to get minimum of two functions
return max(y_min)
