def generate_MFs(inp, outp):
"""
Generates input MFs from input data in the form: {'var': {'ling':[Xvals_MF1], 'ling':[Xvals_MF2], ...},
'var': {'ling':[Xvals_MF1], 'ling':[Xvals_MF2], ...}, ... }
"""
inParams = copy.deepcopy(inp)
outParams = copy.deepcopy(outp)
for var in inParams:
#x_min = min([min(inParams[var][ling]) for ling in inParams[var]])
#x_max = max([max(inParams[var][ling]) for ling in inParams[var]])
#x = np.arange(x_min,x_max,float((x_max-x_min)/100.0)) #generage x values for MF
for ling in inParams[var]: #for each MF
#if len(inParams[var][ling]) == 3: y = fuzz.trimf( x, inParams[var][ling]) #if 3 values -> triangular
#elif len(inParams[var][ling]) == 4: y = fuzz.trapmf(x, sorted(inParams[var][ling])) #if 4 values -> trapezoidal
inParams[var][ling] = fuzzyOps.paramsToMF(inParams[var][ling])
for var in outParams:
#x_min = min([min(outParams[var][ling]) for ling in outParams[var]])
#x_max = max([max(outParams[var][ling]) for ling in outParams[var]])
#x = np.arange(x_min,x_max,float((x_max-x_min)/100.0)) #generage x values for MF
for ling in outParams[var]: #for each MF
#if len(outParams[var][ling]) == 3: y = fuzz.trimf( x, outParams[var][ling]) #if 3 values -> triangular
#elif len(outParams[var][ling]) == 4: y = fuzz.trapmf(x, sorted(outParams[var][ling])) #if 4 values -> trapezoidal
outParams[var][ling] = fuzzyOps.paramsToMF(outParams[var][ling])#[x,y]
return inParams, outParams
def generate_MFs(inp, outp):
"""
Generates input MFs from input data in the form: {'var': {'ling':[Xvals_MF1], 'ling':[Xvals_MF2], ...},
'var': {'ling':[Xvals_MF1], 'ling':[Xvals_MF2], ...}, ... }
"""
inParams = copy.deepcopy(inp)
outParams = copy.deepcopy(outp)
for var in inParams:
#x_min = min([min(inParams[var][ling]) for ling in inParams[var]])
#x_max = max([max(inParams[var][ling]) for ling in inParams[var]])
#x = np.arange(x_min,x_max,float((x_max-x_min)/100.0)) #generage x values for MF
for ling in inParams[var]: #for each MF
#if len(inParams[var][ling]) == 3: y = fuzz.trimf( x, inParams[var][ling]) #if 3 values -> triangular
#elif len(inParams[var][ling]) == 4: y = fuzz.trapmf(x, sorted(inParams[var][ling])) #if 4 values -> trapezoidal
inParams[var][ling] = fuzzyOps.paramsToMF(inParams[var][ling])
for var in outParams:
#x_min = min([min(outParams[var][ling]) for ling in outParams[var]])
#x_max = max([max(outParams[var][ling]) for ling in outParams[var]])
#x = np.arange(x_min,x_max,float((x_max-x_min)/100.0)) #generage x values for MF
for ling in outParams[var]: #for each MF
#if len(outParams[var][ling]) == 3: y = fuzz.trimf( x, outParams[var][ling]) #if 3 values -> triangular
#elif len(outParams[var][ling]) == 4: y = fuzz.trapmf(x, sorted(outParams[var][ling])) #if 4 values -> trapezoidal
outParams[var][ling] = fuzzyOps.paramsToMF(
outParams[var][ling]) #[x,y]
return inParams, outParams
def plotMF_OPT(MFstructIn, MFstructOut, varList, inRanges, outRanges, varMins=None, varMaxs=None):
"""
Plot membership functions in optimization problem
"""
inMFsMin, outMFsMin = None, None
inMFsMax, outMFsMax = None, None
inMFs, outMFs = deparameterize(list(MFstructIn), list(MFstructOut), list(varList))
if not varMins == None:
inMFsMin, outMFsMin = deparameterize(list(MFstructIn), list(MFstructOut), list(varMins))
if not varMaxs == None:
inMFsMax, outMFsMax = deparameterize(list(MFstructIn), list(MFstructOut), list(varMaxs))
#plot
#plt.close('all')
#plt.clf() #start a fresh figure if one is open
plt.figure(figsize=(10, 6))
i = 1
for inp in inMFs:
plt.subplot(len(inMFs) + len(outMFs), 1, i)
for mf in inMFs[inp]:
vals = fuzzyOps.paramsToMF(inMFs[inp][mf])
plt.plot(vals[0], vals[1], lw=2.0)
if inMFsMin <> None:
vals = fuzzyOps.paramsToMF(inMFsMin[inp][mf])
plt.plot(vals[0], vals[1], '--', lw=0.8)
if inMFsMax <> None:
vals = fuzzyOps.paramsToMF(inMFsMax[inp][mf])
plt.plot(vals[0], vals[1], ':', lw=0.8)
plt.plot([inRanges[inp][0], inRanges[inp][0]], [0.,1.], '-k', lw=3.0)
plt.plot([inRanges[inp][1], inRanges[inp][1]], [0.,1.], '-k', lw=3.0)
plt.ylabel('INPUT'+ str(inRanges[inp]))
i = i+1
plt.yticks([0.0,1.0])
for otp in outMFs:
plt.subplot(len(inMFs) + len(outMFs), 1, i)
for mf in outMFs[otp]:
vals = fuzzyOps.paramsToMF(outMFs[otp][mf])
plt.plot(vals[0], vals[1], lw=2.0)
if outMFsMin <> None:
vals = fuzzyOps.paramsToMF(outMFsMin[otp][mf])
plt.plot(vals[0], vals[1], '--', lw=0.8, )
if outMFsMax <> None:
vals = fuzzyOps.paramsToMF(outMFsMax[otp][mf])
plt.plot(vals[0], vals[1], ':', lw=0.8, )
plt.plot([outRanges[otp][0], outRanges[otp][0]], [0.,1.], '-k', lw=3.0)
plt.plot([outRanges[otp][1], outRanges[otp][1]], [0.,1.], '-k', lw=3.0)
plt.ylabel('OUTPUT')
i = i+1
elif point[2] < min(outRange):
err = point[2] - min(outRange)
elif point[2] > max(outRange):
err = point[2] - max(outRange)
truthRange = point[2]
error.append([truthRange, outRange, err])
return error
if __name__ == '__main__':
#testerror functions
import matplotlib.pyplot as plt
A = fuzzyOps.paramsToMF([6.,7.,8.])
B = fuzzyOps.paramsToMF([5.5,7.4,8.7])
C = fuzzyOps.paramsToMF([1.5,2.8,4.1])
D = fuzzyOps.paramsToMF([12.,14.,16.])
A_A_int = fuzErrorInt(A, A)
A_B_int = fuzErrorInt(A, B)
A_C_int = fuzErrorInt(A, C)
A_D_int = fuzErrorInt(A, D)
print "INT ERRORS:", A_A_int, A_B_int, A_C_int, A_D_int
#A = fuzzyOps.paramsToMF([3.,4.,5.])
#B = fuzzyOps.paramsToMF([3.5,4.2,5.7])
#C = fuzzyOps.paramsToMF([1.5,2.8,4.1])
#D = fuzzyOps.paramsToMF([16.,17.,19.])
def plotMF_OPT(MFstructIn,
MFstructOut,
varList,
inRanges,
outRanges,
varMins=None,
varMaxs=None):
"""
Plot membership functions in optimization problem
"""
inMFsMin, outMFsMin = None, None
inMFsMax, outMFsMax = None, None
inMFs, outMFs = deparameterize(list(MFstructIn), list(MFstructOut),
list(varList))
if not varMins == None:
inMFsMin, outMFsMin = deparameterize(list(MFstructIn),
list(MFstructOut), list(varMins))
if not varMaxs == None:
inMFsMax, outMFsMax = deparameterize(list(MFstructIn),
list(MFstructOut), list(varMaxs))
#plot
#plt.close('all')
#plt.clf() #start a fresh figure if one is open
plt.figure(figsize=(10, 6))
i = 1
for inp in inMFs:
plt.subplot(len(inMFs) + len(outMFs), 1, i)
for mf in inMFs[inp]:
vals = fuzzyOps.paramsToMF(inMFs[inp][mf])
plt.plot(vals[0], vals[1], lw=2.0)
if inMFsMin <> None:
vals = fuzzyOps.paramsToMF(inMFsMin[inp][mf])
plt.plot(vals[0], vals[1], '--', lw=0.8)
if inMFsMax <> None:
vals = fuzzyOps.paramsToMF(inMFsMax[inp][mf])
plt.plot(vals[0], vals[1], ':', lw=0.8)
plt.plot([inRanges[inp][0], inRanges[inp][0]], [0., 1.],
'-k',
lw=3.0)
plt.plot([inRanges[inp][1], inRanges[inp][1]], [0., 1.],
'-k',
lw=3.0)
plt.ylabel('INPUT' + str(inRanges[inp]))
i = i + 1
plt.yticks([0.0, 1.0])
for otp in outMFs:
plt.subplot(len(inMFs) + len(outMFs), 1, i)
for mf in outMFs[otp]:
vals = fuzzyOps.paramsToMF(outMFs[otp][mf])
plt.plot(vals[0], vals[1], lw=2.0)
if outMFsMin <> None:
vals = fuzzyOps.paramsToMF(outMFsMin[otp][mf])
plt.plot(
vals[0],
vals[1],
'--',
lw=0.8,
)
if outMFsMax <> None:
vals = fuzzyOps.paramsToMF(outMFsMax[otp][mf])
plt.plot(
vals[0],
vals[1],
':',
lw=0.8,
)
plt.plot([outRanges[otp][0], outRanges[otp][0]], [0., 1.],
'-k',
lw=3.0)
plt.plot([outRanges[otp][1], outRanges[otp][1]], [0., 1.],
'-k',
lw=3.0)
plt.ylabel('OUTPUT')
i = i + 1
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