Apprendre Membership Functions | Membership Functions and Fuzzy Sets

A membership function is a mathematical tool at the core of fuzzy logic, allowing you to describe how strongly an element belongs to a fuzzy set. Rather than assigning a strict yes-or-no value as in classical logic, a membership function maps each element in a domain to a value between 0 and 1. This value represents the degree of membership or the "truth" that the element belongs to the fuzzy set. For instance, consider the fuzzy set representing medium temperature. Instead of saying a temperature is either medium or not, the membership function lets you express that 20°C is "somewhat medium" (e.g., 0.6), 25°C is "very medium" (e.g., 1.0), and 30°C is "barely medium" (e.g., 0.2). The shape of the membership function — such as triangular, trapezoidal, or Gaussian — determines how these degrees are assigned across the domain, making it possible to model vague or imprecise concepts in a mathematically precise way.


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def triangular_membership(x, a, b, c):
    """
    Triangular membership function using if-else logic.
    Parameters:
        x: input value (single float)
        a: left foot of triangle
        b: peak of triangle
        c: right foot of triangle
    Returns:
        Degree of membership between 0 and 1
    """
    if x <= a or x >= c:
        return 0.0
    elif a < x < b:
        return (x - a) / (b - a)
    elif b < x < c:
        return (c - x) / (c - b)
    elif x == b:
        return 1.0
    else:
        return 0.0

# Example: evaluate degrees for a few temperatures
values = [15, 20, 25, 30, 35]
results = [triangular_membership(v, a=15, b=25, c=35) for v in values]
print("Temperatures:", values)
print("Degrees of membership:", results)

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Section 2. Chapitre 1

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              123456789101112131415161718192021222324252627
            
def triangular_membership(x, a, b, c):
    """
    Triangular membership function using if-else logic.
    Parameters:
        x: input value (single float)
        a: left foot of triangle
        b: peak of triangle
        c: right foot of triangle
    Returns:
        Degree of membership between 0 and 1
    """
    if x <= a or x >= c:
        return 0.0
    elif a < x < b:
        return (x - a) / (b - a)
    elif b < x < c:
        return (c - x) / (c - b)
    elif x == b:
        return 1.0
    else:
        return 0.0

# Example: evaluate degrees for a few temperatures
values = [15, 20, 25, 30, 35]
results = [triangular_membership(v, a=15, b=25, c=35) for v in values]
print("Temperatures:", values)
print("Degrees of membership:", results)

Tout était clair ?

Merci pour vos commentaires !

Section 2. Chapitre 1