def test_when_then_rule_cuts_output_at_input_membership():
small_mf = Gaussian(150, 4)
cheap_center = 175
cheap_mf = Triangle(150, cheap_center, 200)
input_variable = FuzzyVariable("size", {
"small": FuzzySet(small_mf),
"large": FuzzySet(Gaussian(180, 4))
})
output_variable = FuzzyVariable(
"clothing cost", {
"cheap": FuzzySet(cheap_mf),
"expansive": FuzzySet(Triangle(200, 250, 400))
})
rule = when("size", "small").then("clothing cost", "cheap").compile(
{"size": input_variable}, {"clothing cost": output_variable})
assert rule({
"size": 150
}).membership(cheap_center) == pytest.approx(small_mf(150))
assert rule({
"size": 20
}).membership(cheap_center) == pytest.approx(small_mf(20))
assert rule({
"size": 140
}).membership(cheap_center) == pytest.approx(small_mf(140))
def test_r_sets_example():
# R Sets is R library
system = MamdaniSystem.empty()
system.add_input(
"service", {
"poor": Gaussian(0, 1.5),
"good": Gaussian(5, 1.5),
"excellent": Gaussian(10, 1.5),
})
system.add_input("food", {
"rancid": Trapezoid(-2, 0, 2, 4),
"delicious": Trapezoid(7, 9, 11, 13),
})
system.add_output(
"tip", {
"cheap": Triangle(0, 5, 10),
"average": Triangle(7.5, 12.5, 17.5),
"generous": Triangle(15, 20, 25),
})
system.add_rule(
when("service", "poor").or_is("food", "rancid").then("tip", "cheap"))
system.add_rule(when("service", "good").then("tip", "average"))
system.add_rule(
when("service",
"excellent").or_is("food", "delicious").then("tip", "generous"))
system_output = system.run({"service": 3, "food": 8}, (0, 25))
assert system_output["tip"] == pytest.approx(14.89, 0.1)
def draw_system(logic, title):
mf1 = Triangle(0, 3, 6)
mf2 = Gaussian(4.5, 1)
mf3 = Triangle(3, 6, 9)
mf1_or2_or3 = logic.t_conorm(logic.t_conorm(mf1, mf2), mf3)
mf1_and2_and3 = logic.t_norm(logic.t_norm(mf1, mf2), mf3)
universe = np.linspace(0, 10, 1000)
plt.plot(universe, [mf1(x) for x in universe], "--")
plt.plot(universe, [mf2(x) for x in universe], "--")
plt.plot(universe, [mf3(x) for x in universe], "--")
plt.plot(universe, [mf1_or2_or3(x) for x in universe], label="T-Conorm")
plt.plot(universe, [mf1_and2_and3(x) for x in universe], label="T-Norm")
plt.xlabel("x")
plt.ylabel(r"$\mu$(x)")
plt.title(title)
plt.legend()
from yvain.fuzzy_system import MamdaniSystem, when
from yvain.membership_functions import Gaussian, Trapezoid, Triangle
if __name__ == '__main__':
system = MamdaniSystem.empty()
system.add_input(
"service", {
"poor": Gaussian(0, 1.5),
"good": Gaussian(5, 1.5),
"excellent": Gaussian(10, 1.5),
})
system.add_input("food", {
"rancid": Trapezoid(-2, 0, 2, 4),
"delicious": Trapezoid(7, 9, 11, 13),
})
system.add_output(
"tip", {
"cheap": Triangle(0, 5, 10),
"average": Triangle(7.5, 12.5, 17.5),
"generous": Triangle(15, 20, 25),
})
system.add_rule(
when("service", "poor").or_is("food", "rancid").then("tip", "cheap"))
system.add_rule(when("service", "good").then("tip", "average"))
system.add_rule(
when("service",
"excellent").or_is("food", "delicious").then("tip", "generous"))
print(system.run({"service": 3, "food": 8}, (0, 25)))
from docs.source.plots.membership_functions.membership_plot import draw_mf
from yvain.membership_functions import Gaussian
import matplotlib.pyplot as plt
if __name__ == '__main__':
mu, sigma = 5, 2
draw_mf(Gaussian(mu=5, sigma=2), 0, 10, f"Gaussian(mu={mu}, sigma={sigma})")
plt.vlines(mu, ymin=0, ymax=1, colors="gray",
linestyles="--")
import matplotlib.pyplot as plt
import numpy as np
from yvain.logical_systems import Zadeh
from yvain.membership_functions import Triangle, Gaussian
if __name__ == '__main__':
mf1 = Triangle(0, 3, 6)
mf2 = Gaussian(4.5, 1)
mf3 = Triangle(3, 6, 9)
logic = Zadeh()
mf1_or2_or3 = logic.t_conorm(logic.t_conorm(mf1, mf2), mf3)
mf1_and2_and3 = logic.t_norm(logic.t_norm(mf1, mf2), mf3)
universe = np.linspace(0, 10, 1000)
plt.subplot(2, 1, 1)
plt.plot(universe, [mf1(x) for x in universe])
plt.plot(universe, [mf2(x) for x in universe])
plt.plot(universe, [mf3(x) for x in universe])
plt.ylabel(r"$\mu$(x)")
plt.subplot(2, 1, 2)
plt.plot(universe, [mf1(x) for x in universe], "--")
plt.plot(universe, [mf2(x) for x in universe], "--")
plt.plot(universe, [mf3(x) for x in universe], "--")
plt.plot(universe, [mf1_or2_or3(x) for x in universe], label="T-Conorm")
plt.plot(universe, [mf1_and2_and3(x) for x in universe], label="T-Norm")
import matplotlib.pyplot as plt
import numpy as np
from yvain.logical_systems import Zadeh
from yvain.membership_functions import Gaussian
if __name__ == '__main__':
mf = Gaussian(4.5, 1)
logic = Zadeh()
mf_negated = logic.complement(mf)
universe = np.linspace(0, 10, 1000)
plt.plot(universe, [mf(x) for x in universe], label="gaussian mf")
plt.plot(universe, [mf_negated(x) for x in universe], "--", label="complementary mf")
plt.xlabel("x")
plt.ylabel(r"$\mu$(x)")
plt.legend()
from yvain.logical_systems import *
from yvain.membership_functions import Triangle, Gaussian
import pytest
_TRIANGLE_UNIVERSE = [
Triangle(0, 5, 10),
Triangle(5, 10, 15),
Triangle(10, 15, 20)
]
_GAUSSIAN_UNIVERSE = [Gaussian(5, 2), Gaussian(7, 1), Gaussian(10, 4)]
_LOGICS = [
Zadeh(),
Drastic(),
Product(),
Lukasiewicz(),
Fodor(),
Frank(2),
ShweizerSklar(2),
Yager(2),
Dombi(2)
]
@pytest.mark.parametrize("logic", _LOGICS)
def test_demorgan_triple(logic):
ors = _TRIANGLE_UNIVERSE[0]
ands = logic.complement(_TRIANGLE_UNIVERSE[0])
for mf in _TRIANGLE_UNIVERSE[1:]: