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electre1.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 math
import matplotlib.pyplot as plt
import numpy as np
import sys
from collections import defaultdict
# Function: Cycle Finder
# (autor:Luke Harold Miles, code at https://gist.github.com/qpwo/272df112928391b2c83a3b67732a5c25)
def simple_cycles(G):
def _unblock(thisnode, blocked, B):
stack = set([thisnode])
while stack:
node = stack.pop()
if node in blocked:
blocked.remove(node)
stack.update(B[node])
B[node].clear()
G = {v: set(nbrs) for (v,nbrs) in G.items()}
sccs = strongly_connected_components(G)
while sccs:
scc = sccs.pop()
startnode = scc.pop()
path = [startnode]
blocked = set()
closed = set()
blocked.add(startnode)
B = defaultdict(set)
stack = [ (startnode,list(G[startnode])) ]
while stack:
thisnode, nbrs = stack[-1]
if nbrs:
nextnode = nbrs.pop()
if nextnode == startnode:
yield path[:]
closed.update(path)
elif nextnode not in blocked:
path.append(nextnode)
stack.append( (nextnode, list(G[nextnode])) )
closed.discard(nextnode)
blocked.add(nextnode)
continue
if not nbrs:
if thisnode in closed:
_unblock(thisnode, blocked, B)
else:
for nbr in G[thisnode]:
if thisnode not in B[nbr]:
B[nbr].add(thisnode)
stack.pop()
path.pop()
remove_node(G, startnode)
H = subgraph(G, set(scc))
sccs.extend(strongly_connected_components(H))
# Function: SCC
def strongly_connected_components(graph):
index_counter = [0]
stack = []
lowlink = {}
index = {}
result = []
def _strong_connect(node):
index[node] = index_counter[0]
lowlink[node] = index_counter[0]
index_counter[0] += 1
stack.append(node)
successors = graph[node]
for successor in successors:
if successor not in index:
_strong_connect(successor)
lowlink[node] = min(lowlink[node],lowlink[successor])
elif successor in stack:
lowlink[node] = min(lowlink[node],index[successor])
if lowlink[node] == index[node]:
connected_component = []
while True:
successor = stack.pop()
connected_component.append(successor)
if successor == node: break
result.append(connected_component[:])
for node in graph:
if node not in index:
_strong_connect(node)
return result
# Function: Remove Node
def remove_node(G, target):
del G[target]
for nbrs in G.values():
nbrs.discard(target)
# Function: Subgraph
def subgraph(G, vertices):
return {v: G[v] & vertices for v in vertices}
###############################################################################
# Function: Concordance Matrix
def concordance_matrix(dataset, W):
concordance = np.zeros((dataset.shape[0], dataset.shape[0]))
for i in range(0, concordance.shape[0]):
for j in range(0, concordance.shape[1]):
value = 0
for k in range(0, dataset.shape[1]):
if (dataset[i,k] >= dataset[j,k]):
value = value + W[k]
concordance[i,j] = value
if (np.sum(W) != 0):
concordance = concordance/np.sum(W)
return concordance
# Function: Discordance Matrix
def discordance_matrix(dataset):
delta = np.max(np.amax(dataset, axis = 0) - np.amin(dataset, axis = 0))
discordance = np.zeros((dataset.shape[0], dataset.shape[0]))
for i in range(0, discordance.shape[0]):
for j in range(0, discordance.shape[1]):
discordance[i,j] = np.max((dataset[j,:] - dataset[i,:]))/delta
if (discordance[i,j] < 0):
discordance[i,j] = 0
return discordance
# Function: Dominance Matrix
def dominance_matrix(concordance, discordance, c_hat = 0.75, d_hat = 0.50):
dominance = np.zeros((concordance.shape[0], concordance.shape[0]))
for i in range (0, dominance.shape[0]):
for j in range (0, dominance.shape[1]):
if (concordance[i,j] >= c_hat and discordance[i,j] <= d_hat and i != j):
dominance[i, j] = 1
return dominance
# Function: Find Cycles and Unites it as a Single Criteria
def johnson_algorithm_cycles(dominance):
graph = {}
value = [[] for i in range(dominance.shape[0])]
keys = range(dominance.shape[0])
for i in range(0, dominance.shape[0]):
for j in range(0, dominance.shape[0]):
if (dominance[i,j] == 1):
value[i].append(j)
for i in keys:
graph[i] = value[i]
s1 = list(simple_cycles(graph))
for k in range(0, len(s1)):
for j in range(0, len(s1[k]) -1):
dominance[s1[k][j], s1[k][j+1]] = 0
dominance[s1[k][j+1], s1[k][j]] = 0
s2 = s1[:]
for m in s1:
for n in s1:
if set(m).issubset(set(n)) and m != n:
s2.remove(m)
break
for i in range(0, dominance.shape[0]):
count = 0
for j in range(0, len(s2[k])):
if (dominance[i, s2[k][j]] > 0):
count = count + 1
if (count > 0):
for j in range(0, len(s2[k])):
dominance[i, s2[k][j]] = 1
return dominance
# Function: Electre I
def electre_i(dataset, W, remove_cycles = False, c_hat = 0.75, d_hat = 0.50, graph = True):
kernel = []
dominated = []
concordance = concordance_matrix(dataset, W)
discordance = discordance_matrix(dataset)
dominance = dominance_matrix(concordance, discordance, c_hat = c_hat, d_hat = d_hat)
if (remove_cycles == True):
dominance = johnson_algorithm_cycles(dominance)
row_sum = np.sum(dominance, axis = 0)
kernel = np.where(row_sum == 0)[0].tolist()
for j in range(0, dominance.shape[1]):
for i in range(0, len(kernel)):
if (dominance[kernel[i], j] == 1):
if (j not in dominated):
dominated.append(j)
limit = len(kernel)
for j in range(0, dominance.shape[1]):
for i in range(0, limit):
if (dominance[kernel[i], j] == 0 and np.sum(dominance[:,j], axis = 0) > 0):
if (j not in dominated and j not in kernel):
kernel.append(j)
kernel = ['a' + str(alt + 1) for alt in kernel]
dominated = ['a' + str(alt + 1) for alt in dominated]
if (graph == True):
for i in range(0, dominance.shape[0]):
radius = 1
node_x = radius*math.cos(math.pi * 2 * i / dominance.shape[0])
node_y = radius*math.sin(math.pi * 2 * i / dominance.shape[0])
if ('a' + str(i+1) in kernel):
plt.text(node_x, node_y, 'a' + str(i+1), size = 12, ha = 'center', va = 'center', bbox = dict(boxstyle = 'round', ec = (0.0, 0.0, 0.0), fc = (0.8, 1.0, 0.8),))
else:
plt.text(node_x, node_y, 'a' + str(i+1), size = 12, ha = 'center', va = 'center', bbox = dict(boxstyle = 'round', ec = (0.0, 0.0, 0.0), fc = (1.0, 0.8, 0.8),))
for i in range(0, dominance.shape[0]):
for j in range(0, dominance.shape[1]):
node_xi = radius*math.cos(math.pi * 2 * i / dominance.shape[0])
node_yi = radius*math.sin(math.pi * 2 * i / dominance.shape[0])
node_xj = radius*math.cos(math.pi * 2 * j / dominance.shape[0])
node_yj = radius*math.sin(math.pi * 2 * j / dominance.shape[0])
if (dominance[i, j] == 1):
if ('a' + str(i+1) in kernel):
plt.arrow(node_xi, node_yi, node_xj - node_xi, node_yj - node_yi, head_width = 0.01, head_length = 0.2, overhang = 0.0, color = 'black', linewidth = 0.9, length_includes_head = True)
else:
plt.arrow(node_xi, node_yi, node_xj - node_xi, node_yj - node_yi, head_width = 0.01, head_length = 0.2, overhang = 0.0, color = 'red', linewidth = 0.9, length_includes_head = True)
axes = plt.gca()
axes.set_xlim([-radius, radius])
axes.set_ylim([-radius, radius])
plt.axis('off')
#plt.show()
return concordance, discordance, dominance, kernel, dominated,plt
###############################################################################