MachineLearningLab2
Andrey Ryabov

Solution

1. Let's create Crisp Sets with Linguistic variables. Also add Mamdani inferencing multipliers for every Crisp Set.

Temperature = ["Cold", "Medium", "Hot"]         # degree
TemperatureMultiplier = [3, 1, 3]

Rain = ["Drizzling", "Raining", "Showering"]    # drops/s
RainMultiplier = [1.1, 2, 3]

WindSpeed = ["Quite", "Feels", "BlowsAway"]     # m/s
WindMultiplier = [1, 2, 5]

Path = ["Easy", "Medium", "Hard"]               # multiplier

2. Now write the function which prepares coefficient weights for part of linear function.

def getWeight(x, left, right, inverted=False):
    if x <= left: return 1 if inverted else 0
    if x >= right: return 0 if inverted else 1
    if inverted:
        return 1 - (x - left) / (right - left)
    return (x - left) / (right - left)

3. Here create the function which prepares coefficient weights for part of linear function, but triangulary shaped.

def getTriangleWeight(x, left, center, right, inverted=False):
    return getWeight(x, left, center, inverted) if x <= center else getWeight(x, center, right, not inverted)

4. Temperature, Rain, WindSpeed Fuzzy Sets.

def tempFuncWeights(x):
    return (getWeight(x, 0, 10, True), getTriangleWeight(x, 7, 15, 27), getWeight(x, 27, 31))

def rainFuncWeights(x):
    return (getTriangleWeight(x, 0, 1, 2), getWeight(x, 0, 4), getWeight(x, 0, 7))

def windFuncWeights(x):
    return (getWeight(x, 0, 2, True), getTriangleWeight(x, 2, 4, 7), getWeight(x, 7, 15))

5. A simple function for First of Maximum method calculation.

def FoM(tuple):                # First of Maximum
    maxValue = max(tuple)
    if tuple[0] == maxValue:
        return (maxValue, 0)
    if tuple[1] == maxValue:
        return (maxValue, 1)
    return (maxValue, 2)

6. Finally, write the defuzzification function using FoM (First of Maximum) method. Also this defuzzification function works with Mamdani inferencing shown in p.1.

def calcDefuzzificatedValue(w1, w2, w3):
    res1 = FoM(w1)[0] * TemperatureMultiplier[FoM(w1)[1]]
    res2 = FoM(w2)[0] * RainMultiplier[FoM(w2)[1]]
    res3 = FoM(w3)[0] * WindMultiplier[FoM(w3)[1]]

    return res1 + res2 + res3

7. The other code just shows how my implementation works.

xses = (10, 5, 15)
print("How hard to go on a trip with (Temperature =", xses[0], ", Rain =", xses[1], " WindSpeed =", xses[2], ") ==", 
    calcDefuzzificatedValue(tempFuncWeights(xses[0]), rainFuncWeights(xses[1]), windFuncWeights(xses[2])))

x = np.linspace(0, 31, 10)
y = np.linspace(0, 7, 10)
windSpeed = 15

X, Y = np.meshgrid(x, y)

Z = [[calcDefuzzificatedValue(tempFuncWeights(i), rainFuncWeights(j), windFuncWeights(windSpeed)) for i in x] for j in y]

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.set_xlabel("Temperature, degrees")
ax.set_ylabel("Rain, drops/s")
ax.set_zlabel("How hard to go on a trip with {}, m/s wind speed".format(windSpeed))
ax.contour3D(X, Y, Z, 100, cmap='viridis')
plt.show()

Results

1. An output text.

2. Images of my Mamdani inferencing.

or from another side

Code of solution

main.py

import numpy as np
import matplotlib.pyplot as plt

Temperature = ["Cold", "Medium", "Hot"]         # degree
TemperatureMultiplier = [3, 1, 3]

Rain = ["Drizzling", "Raining", "Showering"]    # drops/s
RainMultiplier = [1.1, 2, 3]

WindSpeed = ["Quite", "Feels", "BlowsAway"]     # m/s
WindMultiplier = [1, 2, 5]

Path = ["Easy", "Medium", "Hard"]               # multiplier

def getWeight(x, left, right, inverted=False):
    if x <= left: return 1 if inverted else 0
    if x >= right: return 0 if inverted else 1
    if inverted:
        return 1 - (x - left) / (right - left)
    return (x - left) / (right - left)

def getTriangleWeight(x, left, center, right, inverted=False):
    return getWeight(x, left, center, inverted) if x <= center else getWeight(x, center, right, not inverted)

def tempFuncWeights(x):
    return (getWeight(x, 0, 10, True), getTriangleWeight(x, 7, 15, 27), getWeight(x, 27, 31))

def rainFuncWeights(x):
    return (getTriangleWeight(x, 0, 1, 2), getWeight(x, 0, 4), getWeight(x, 0, 7))

def windFuncWeights(x):
    return (getWeight(x, 0, 2, True), getTriangleWeight(x, 2, 4, 7), getWeight(x, 7, 15))

def calcDefuzzificatedValue(w1, w2, w3):
    res1 = FoM(w1)[0] * TemperatureMultiplier[FoM(w1)[1]]
    res2 = FoM(w2)[0] * RainMultiplier[FoM(w2)[1]]
    res3 = FoM(w3)[0] * WindMultiplier[FoM(w3)[1]]

    return res1 + res2 + res3

def FoM(tuple):                # First of Maximum
    maxValue = max(tuple)
    if tuple[0] == maxValue:
        return (maxValue, 0)
    if tuple[1] == maxValue:
        return (maxValue, 1)
    return (maxValue, 2)

xses = (10, 5, 15)
print("How hard to go on a trip with (Temperature =", xses[0], ", Rain =", xses[1], " WindSpeed =", xses[2], ") ==", 
    calcDefuzzificatedValue(tempFuncWeights(xses[0]), rainFuncWeights(xses[1]), windFuncWeights(xses[2])))

x = np.linspace(0, 31, 10)
y = np.linspace(0, 7, 10)
windSpeed = 15

X, Y = np.meshgrid(x, y)

Z = [[calcDefuzzificatedValue(tempFuncWeights(i), rainFuncWeights(j), windFuncWeights(windSpeed)) for i in x] for j in y]

fig = plt.figure()
ax = plt.axes(projection='3d')
ax.set_xlabel("Temperature, degrees")
ax.set_ylabel("Rain, drops/s")
ax.set_zlabel("How hard to go on a trip with {}, m/s wind speed".format(windSpeed))
ax.contour3D(X, Y, Z, 100, cmap='viridis')
plt.show()