def composition_of_binary_relations(r1, r2):
dom1 = r1.get_domain()
dom2 = r2.get_domain()
size1_x = dom1.get_component(0).get_cardinality()
size1_y = dom1.get_component(1).get_cardinality()
size2_x = dom2.get_component(0).get_cardinality()
size2_y = dom2.get_component(1).get_cardinality()
if size1_x != size2_y:
raise DomainsDimensionError(
"Invalid domain dimensions for composition.")
rows = [[
r1.get_value_at(dom1.element_for_index(j + i * size1_y))
for j in range(size1_y)
] for i in range(size1_x)]
columns = [[
r2.get_value_at(dom2.element_for_index(i + j * size2_y))
for j in range(size2_x)
] for i in range(size2_y)]
new_domain = Domain.combine(dom1.get_component(0),
dom2.get_component(1))
new_fset = MutableFuzzySet(new_domain)
for i, elem in enumerate(new_domain):
mins = [
min(x, y)
for x, y in zip(rows[i // size1_x], columns[i % size2_y])
]
new_fset.set(elem, max(mins))
return new_fset
def main():
u = Domain.int_range(1, 6)
u2 = Domain.combine(u, u)
r1 = MutableFuzzySet(u2)
r1.set((1, 1), 1)
r1.set((2, 2), 1)
r1.set((3, 3), 1)
r1.set((4, 4), 1)
r1.set((5, 5), 1)
r1.set((3, 1), 0.5)
r1.set((1, 3), 0.5)
r2 = MutableFuzzySet(u2)
r2.set((1, 1), 1)
r2.set((2, 2), 1)
r2.set((3, 3), 1)
r2.set((4, 4), 1)
r2.set((5, 5), 1)
r2.set((3, 1), 0.5)
r2.set((1, 3), 0.1)
r3 = MutableFuzzySet(u2)
r3.set((1, 1), 1)
r3.set((2, 2), 1)
r3.set((3, 3), 0.3)
r3.set((4, 4), 1)
r3.set((5, 5), 1)
r3.set((1, 2), 0.6)
r3.set((2, 1), 0.6)
r3.set((2, 3), 0.7)
r3.set((3, 2), 0.7)
r3.set((3, 1), 0.5)
r3.set((1, 3), 0.5)
r4 = MutableFuzzySet(u2)
r4.set((1, 1), 1)
r4.set((2, 2), 1)
r4.set((3, 3), 1)
r4.set((4, 4), 1)
r4.set((5, 5), 1)
r4.set((1, 2), 0.4)
r4.set((2, 1), 0.4)
r4.set((2, 3), 0.5)
r4.set((3, 2), 0.5)
r4.set((3, 1), 0.4)
r4.set((1, 3), 0.4)
print("R1:")
print("UxU:", Relations.is_u_times_u_relation(r1))
print("Reflexive:", Relations.is_reflexive(r1))
print("Symmetric:", Relations.is_symmetric(r1))
print("\nR2:")
print("UxU:", Relations.is_u_times_u_relation(r2))
print("Reflexive:", Relations.is_reflexive(r2))
print("Symmetric:", Relations.is_symmetric(r2))
print("\nR3:")
print("UxU:", Relations.is_u_times_u_relation(r3))
print("Reflexive:", Relations.is_reflexive(r3))
print("Symmetric:", Relations.is_symmetric(r3))
print("Max-min transitive:", Relations.is_max_min_transitive(r3))
print("\nR4:")
print("UxU:", Relations.is_u_times_u_relation(r4))
print("Reflexive:", Relations.is_reflexive(r4))
print("Symmetric:", Relations.is_symmetric(r4))
print("Max-min transitive:", Relations.is_max_min_transitive(r4))
u = Domain.int_range(1, 5)
r = MutableFuzzySet(Domain.combine(u, u))
r.set((1, 1), 1)
r.set((2, 2), 1)
r.set((3, 3), 1)
r.set((4, 4), 1)
r.set((1, 2), 0.3)
r.set((2, 1), 0.3)
r.set((2, 3), 0.5)
r.set((3, 2), 0.5)
r.set((3, 4), 0.2)
r.set((4, 3), 0.2)
r2 = r
print("Početna relacija je neizrazita relacija ekvivalencije?",
Relations.is_fuzzy_equivalence(r2))
print()
for i in range(3):
r2 = Relations.composition_of_binary_relations(r2, r)
print("Broj odrađenih kompozicija:" + str(i + 1) + ". Relacija je:")
Debug.print(r2)
print("Ova relacija je neizrazita relacija ekvivalencije?")
print(Relations.is_fuzzy_equivalence(r2))
print()
u1 = Domain.int_range(1, 5)
u2 = Domain.int_range(1, 4)
u3 = Domain.int_range(1, 5)
r1 = MutableFuzzySet(Domain.combine(u1, u2))
r1.set((1, 1), 0.3)
r1.set((1, 2), 1)
r1.set((3, 3), 0.5)
r1.set((4, 3), 0.5)
r2 = MutableFuzzySet(Domain.combine(u2, u3))
r2.set((1, 1), 1)
r2.set((2, 1), 0.5)
r2.set((2, 2), 0.7)
r2.set((3, 3), 1)
r2.set((3, 4), 0.4)
r1r2 = Relations.composition_of_binary_relations(r1, r2)
Debug.print(r1r2)