def compositionOfBinaryRelations(r1: FS.FuzzySet, r2: FS.FuzzySet):
domain1, domain2 = r1.getDomain(), r2.getDomain()
""":type: Domain.Domain"""
assert domain1.getNumberOfComponents() == 2 and domain2.getNumberOfComponents() == 2
domains1, domains2 = domain1.getDomains(), domain2.getDomains()
for i,j in zip(domains1[1], domains2[0]):
assert(i == j)
X = domains1[0]
Y = domains2[1]
composition = FS.MutableFuzzySet(DM.CompositeDomain.combine(DM.SimpleDomain([x for x in X]), DM.SimpleDomain([y for y in Y])))
for x in domains1[0]:
for z in domains2[1]:
mins = []
for y in domains1[1]:
mins.append( min(r1.getValueAt((x,y)), r2.getValueAt((y,z))) )
composition.set((x,z), max(mins))
return composition
def isUTimesURelation(set: FS.FuzzySet):
domain = set.getDomain()
""":type: Domain.Domain"""
if domain.getNumberOfComponents() != 2:
return False
domains = domain.getDomains()
for a, b in zip(domains[0], domains[1]):
if a != b:
return False
return True
def isReflexive(set: FS.FuzzySet):
if not Relations.isUTimesURelation(set):
return False
domain = set.getDomain()
""":type: Domain.Domain"""
domains = domain.getDomains()
for i in domains[0]:
if set.getValueAt((i, i)) != 1.0:
return False
return True
def isSymmetric(set: FS.FuzzySet):
if not Relations.isUTimesURelation(set):
return False
domain = set.getDomain()
""":type: Domain.Domain"""
domains = domain.getDomains()
for i in domains[0]:
for j in domains[0]:
if set.getValueAt((i,j)) != set.getValueAt((j,i)):
return False
return True
def isMinMaxTransitive(set: FS.FuzzySet):
if not Relations.isUTimesURelation(set):
return False
domain = set.getDomain()
""":type: Domain.Domain"""
domains = domain.getDomains()
for u in domains[0]:
for v in domains[0]:
tmp = []
for w in domains[0]:
tmp.append(min(set.getValueAt((u, w)), set.getValueAt((w, v))))
if set.getValueAt((u, v)) < max(tmp):
return False
return True
