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electretri.py
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# Module Created by: Prof. Valdecy Pereira, D.Sc.
# UFF - Universidade Federal Fluminense (Brazil)
# email: [email protected]
# GitHub Repository: <https://github.com/Valdecy>
import copy
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np
from sklearn.decomposition import TruncatedSVD
# Function: Concordance Matrices and Vectors
def concordance_matrices_vectors(performance_matrix, number_of_profiles, number_of_alternatives, B, P, Q, W):
n_rows = number_of_profiles * number_of_alternatives
n_cols = performance_matrix.shape[1]
# Concordance Matrix x_b
concordance_matrix = np.zeros((n_rows, n_cols))
count = B.shape[0] - 1
alternative = -number_of_alternatives
for i in range(0, concordance_matrix .shape[0]):
if (i > 0 and i % number_of_alternatives == 0):
count = count - 1
if (i > 0 and i % number_of_alternatives != 0):
alternative = alternative + 1
elif (i > 0 and i % number_of_alternatives == 0):
alternative = -number_of_alternatives
for j in range(0, concordance_matrix.shape[1]):
if (B[count, j] - performance_matrix[alternative, j] >= P[0, j]):
concordance_matrix[i, j] = 0
elif (B[count, j] - performance_matrix[alternative, j] < Q[0, j]):
concordance_matrix[i, j] = 1
else:
concordance_matrix[i, j] = (P[0, j] - B[count, j] + performance_matrix[alternative, j])/(P[0, j] - Q[0, j])
# Concordance Vector x_b
concordance_vector = np.zeros((n_rows, 1))
for i in range(0, concordance_vector.shape[0]):
for j in range(0, concordance_matrix.shape[1]):
concordance_vector[i, 0] = concordance_vector[i, 0] + concordance_matrix[i, j]*W[j]
if (W.sum(axis = 0) != 0):
concordance_vector[i, 0] = concordance_vector[i, 0]/W.sum(axis = 0)
# Concordance Matrix b_x
concordance_matrix_inv = np.zeros((n_rows, n_cols))
count = B.shape[0] - 1
alternative = -number_of_alternatives
for i in range(0, concordance_matrix_inv.shape[0]):
if (i > 0 and i % number_of_alternatives == 0):
count = count - 1
if (i > 0 and i % number_of_alternatives != 0):
alternative = alternative + 1
elif (i > 0 and i % number_of_alternatives == 0):
alternative = -number_of_alternatives
for j in range(0, concordance_matrix_inv.shape[1]):
if (-B[count, j] + performance_matrix[alternative, j] >= P[0, j]):
concordance_matrix_inv[i, j] = 0
elif (-B[count, j] + performance_matrix[alternative, j] < Q[0, j]):
concordance_matrix_inv[i, j] = 1
else:
concordance_matrix_inv[i, j] = (P[0, j] + B[count, j] - performance_matrix[alternative, j])/(P[0, j] - Q[0, j])
# Concordance Vector b_x
concordance_vector_inv = np.zeros((n_rows, 1))
for i in range(0, concordance_vector_inv.shape[0]):
for j in range(0, concordance_matrix_inv.shape[1]):
concordance_vector_inv[i, 0] = concordance_vector_inv[i, 0] + concordance_matrix_inv[i, j]*W[j]
if (W.sum(axis = 0) != 0):
concordance_vector_inv[i, 0] = concordance_vector_inv[i, 0]/W.sum(axis = 0)
return concordance_matrix, concordance_matrix_inv, concordance_vector, concordance_vector_inv
# Function: Discordance Matrices
def discordance_matrices(performance_matrix, number_of_profiles, number_of_alternatives, B, P, V):
n_rows = number_of_profiles * number_of_alternatives
n_cols = performance_matrix.shape[1]
# Discordance Matrix x_b
disconcordance_matrix = np.zeros((n_rows, n_cols))
count = B.shape[0] - 1
alternative = -number_of_alternatives
for i in range(0, disconcordance_matrix.shape[0]):
if (i > 0 and i % number_of_alternatives == 0):
count = count - 1
if (i > 0 and i % number_of_alternatives != 0):
alternative = alternative + 1
elif (i > 0 and i % number_of_alternatives == 0):
alternative = -number_of_alternatives
for j in range(0, disconcordance_matrix.shape[1]):
if (B[count, j] - performance_matrix[alternative, j] < P[0, j]):
disconcordance_matrix[i, j] = 0
elif (B[count, j] - performance_matrix[alternative, j] >= V[0, j]):
disconcordance_matrix[i, j] = 1
else:
disconcordance_matrix[i, j] = (-P[0, j] + B[count, j] - performance_matrix[alternative, j])/(V[0, j] - P[0, j])
# Discordance Matrix b_x
disconcordance_matrix_inv = np.zeros((n_rows, n_cols))
count = B.shape[0] - 1
alternative = -number_of_alternatives
for i in range(0, disconcordance_matrix_inv.shape[0]):
if (i > 0 and i % number_of_alternatives == 0):
count = count - 1
if (i > 0 and i % number_of_alternatives != 0):
alternative = alternative + 1
elif (i > 0 and i % number_of_alternatives == 0):
alternative = -number_of_alternatives
for j in range(0, disconcordance_matrix_inv.shape[1]):
if (-B[count, j] + performance_matrix[alternative, j] < P[0, j]):
disconcordance_matrix_inv[i, j] = 0
elif (-B[count, j] + performance_matrix[alternative, j] >= V[0, j]):
disconcordance_matrix_inv[i, j] = 1
else:
disconcordance_matrix_inv[i, j] = (-P[0, j] - B[count, j] + performance_matrix[alternative, j])/(V[0, j] - P[0, j])
return disconcordance_matrix, disconcordance_matrix_inv
# Function: Credibility Vectors
def credibility_vectors(number_of_profiles, number_of_alternatives, concordance_matrix, concordance_matrix_inv, concordance_vector, concordance_vector_inv, disconcordance_matrix, disconcordance_matrix_inv):
n_rows = number_of_profiles * number_of_alternatives
# Credibility Vector x_b
credibility_vector = np.zeros((n_rows, 1))
for i in range(0, credibility_vector.shape[0]):
credibility_vector[i, 0] = concordance_vector[i, 0]
for j in range(0, concordance_matrix.shape[1]):
if (disconcordance_matrix[i, j] > concordance_vector[i, 0]):
value = (1 - disconcordance_matrix[i, j])/(1 - concordance_vector[i, 0])
credibility_vector[i, 0] = credibility_vector[i, 0]*value
# Credibility Vector b_x
credibility_vector_inv = np.zeros((n_rows, 1))
for i in range(0, credibility_vector_inv.shape[0]):
credibility_vector_inv[i, 0] = concordance_vector_inv[i, 0]
for j in range(0, concordance_matrix_inv.shape[1]):
if (disconcordance_matrix_inv[i, j] > concordance_vector_inv[i, 0]):
value = (1 - disconcordance_matrix_inv[i, j])/(1 - concordance_vector_inv[i, 0])
credibility_vector_inv[i, 0] = credibility_vector_inv[i, 0]*value
return credibility_vector, credibility_vector_inv
# Function: Fuzzy Logic
def fuzzy_logic(number_of_profiles, number_of_alternatives, credibility_vector, credibility_vector_inv, cut_level):
n_rows = number_of_profiles * number_of_alternatives
fuzzy_vector = []
fuzzy_matrix = [[]]* number_of_alternatives
for i in range(0, n_rows):
if (credibility_vector[i, 0] >= cut_level and credibility_vector_inv[i, 0] >= cut_level):
fuzzy_vector.append('I')
elif (credibility_vector[i, 0] >= cut_level and credibility_vector_inv[i, 0] < cut_level):
fuzzy_vector.append('>')
elif (credibility_vector[i, 0] < cut_level and credibility_vector_inv[i, 0] >= cut_level):
fuzzy_vector.append('<')
elif (credibility_vector[i, 0] < cut_level and credibility_vector_inv[i, 0] < cut_level):
fuzzy_vector.append('R')
fm = [fuzzy_vector[x:x+number_of_alternatives] for x in range(0, len(fuzzy_vector), number_of_alternatives)]
for j in range(number_of_profiles-1, -1,-1):
for i in range(0, number_of_alternatives):
fuzzy_matrix[i] = fuzzy_matrix[i] + [fm[j][i]]
return fuzzy_matrix
# Function: Classification
def classification_algorithm(number_of_profiles, number_of_alternatives, fuzzy_matrix, rule, verbose = True):
classification = []
if (rule == 'pc'):
# Pessimist Classification
for i1 in range(0, number_of_alternatives):
class_i = number_of_profiles
count = 0
for i2 in range(0, number_of_profiles):
count = count + 1
if (fuzzy_matrix[i1][i2] == '>'):
class_i = int(number_of_profiles - count)
classification.append(class_i)
if (verbose == True):
print('a' + str(i1 + 1) + ' = ' + 'C' + str(class_i))
elif(rule == 'oc'):
# Optimistic Classification
for i1 in range(0, number_of_alternatives):
class_i = 0
count = 0
for i2 in range(number_of_profiles - 1, -1, -1):
count = count + 1
if (fuzzy_matrix[i1][i2] == '<'):
class_i = int(count)
classification.append(class_i)
if (verbose == True):
print('a' + str(i1 + 1) + ' = ' + 'C' + str(class_i))
return classification
# Function: Plot Projected Points
def plot_points(choix, data, classification):
plt.style.use('ggplot')
colors = {'A':'#bf77f6', 'B':'#fed8b1', 'C':'#d1ffbd', 'D':'#f08080', 'E':'#3a18b1', 'F':'#ff796c', 'G':'#04d8b2', 'H':'#ffb07c', 'I':'#aaa662', 'J':'#0485d1', 'K':'#fffe7a', 'L':'#b0dd16', 'M':'#85679', 'N':'#12e193', 'O':'#82cafc', 'P':'#ac9362', 'Q':'#f8481c', 'R':'#c292a1', 'S':'#c0fa8b', 'T':'#ca7b80', 'U':'#f4d054', 'V':'#fbdd7e', 'W':'#ffff7e', 'X':'#cd7584', 'Y':'#f9bc08', 'Z':'#c7c10c'}
classification_ = copy.deepcopy(classification)
color_leg = {}
if (data.shape[1] == 2):
data_proj = np.copy(data)
else:
tSVD = TruncatedSVD(n_components = 2, n_iter = 100, random_state = 42)
tSVD_proj = tSVD.fit_transform(data)
data_proj = np.copy(tSVD_proj)
#variance = sum(np.var(tSVD_proj, axis = 0) / np.var(tSVD_proj, axis = 0).sum())
class_list = list(set(classification_))
for i in range(0, len(classification_)):
classification_[i] = str(classification_[i])
for i in range(0, len(classification_)):
for j in range(0, len(class_list)):
classification_[i] = classification_[i].replace(str(class_list[j]), str(chr(ord('A') + class_list[j])))
class_list = list(set(classification_))
class_list.sort()
for i in range(0, len(class_list)):
color_leg[class_list[i]] = colors[class_list[i]]
patchList = []
for key in color_leg:
data_key = mpatches.Patch(color = color_leg[key], label = key)
patchList.append(data_key)
for i in range(0, data_proj.shape[0]):
plt.text(data_proj[i, 0], data_proj[i, 1], choix[i] , size = 10, ha = 'center', va = 'center', bbox = dict(boxstyle = 'round', ec = (0.0, 0.0, 0.0), fc = colors[classification_[i]],))
plt.gca().legend(handles = patchList, loc = 'center left', bbox_to_anchor = (1.05, 0.5))
axes = plt.gca()
xmin = np.amin(data_proj[:,0])
xmax = np.amax(data_proj[:,0])
axes.set_xlim([xmin*0.7, xmax*1])
ymin = np.amin(data_proj[:,1])
ymax = np.amax(data_proj[:,1])
if (ymin < ymax):
axes.set_ylim([ymin, ymax])
else:
axes.set_ylim([ymin*0.7, ymax*1])
#plt.show()
return plt
# Function: ELECTRE TRI-B
def electre_tri_b(choix, performance_matrix, W = [], Q = [], P = [], V = [], B = [], cut_level = 1.0, verbose = True, rule = 'pc', graph = False):
# Loading Parameters
if (isinstance(B[0], list)):
number_of_profiles = len(B)
else:
number_of_profiles = 1
number_of_alternatives = performance_matrix.shape[0]
p_vector = np.zeros((1, performance_matrix.shape[1]))
q_vector = np.zeros((1, performance_matrix.shape[1]))
v_vector = np.zeros((1, performance_matrix.shape[1]))
for i in range(0, p_vector.shape[1]):
p_vector[0][i] = P[i]
q_vector[0][i] = Q[i]
v_vector[0][i] = V[i]
w_vector = np.array(W)
b_matrix = np.array(B)
if (isinstance(B[0], list)):
b_matrix = np.array(B)
else:
b_matrix = np.zeros((1, performance_matrix.shape[1]))
for i in range(0, performance_matrix.shape[1]):
b_matrix[0][i] = B[i]
# Algorithm
concordance_matrix, concordance_matrix_inv, concordance_vector, concordance_vector_inv = concordance_matrices_vectors(performance_matrix = performance_matrix, number_of_profiles = number_of_profiles, number_of_alternatives = number_of_alternatives, B = b_matrix, P = p_vector, Q = q_vector, W = w_vector)
disconcordance_matrix, disconcordance_matrix_inv = discordance_matrices(performance_matrix = performance_matrix, number_of_profiles = number_of_profiles, number_of_alternatives = number_of_alternatives, B = b_matrix, P = p_vector, V = v_vector)
credibility_vector, credibility_vector_inv = credibility_vectors(number_of_profiles = number_of_profiles, number_of_alternatives = number_of_alternatives, concordance_matrix = concordance_matrix, concordance_matrix_inv = concordance_matrix_inv, concordance_vector = concordance_vector, concordance_vector_inv = concordance_vector_inv, disconcordance_matrix = disconcordance_matrix, disconcordance_matrix_inv = disconcordance_matrix_inv)
fuzzy_matrix = fuzzy_logic(number_of_profiles = number_of_profiles, number_of_alternatives = number_of_alternatives, credibility_vector = credibility_vector, credibility_vector_inv = credibility_vector_inv, cut_level = cut_level)
classification = classification_algorithm(number_of_profiles = number_of_profiles, number_of_alternatives = number_of_alternatives, fuzzy_matrix = fuzzy_matrix, rule = rule, verbose = verbose)
if (graph == True):
plot_points(choix,performance_matrix, classification)
return classification, plt
###############################################################################