TRAPMF

Generates a trapezoidal membership function for a given universe. The shape of the trapezoid is defined by four parameters: left foot, left ceiling, right ceiling, and right foot.

The membership value is 0 outside the feet, climbs linearly to 1 at the left ceiling, stays flat at 1 until the right ceiling, and falls linearly back to 0.

Excel Usage

=TRAPMF(x, a, b, c, d)

x (list[list], required): Array of independent universe variables.
a (float, required): Left foot of the trapezoid (membership begins to climb from zero).
b (float, required): Left ceiling of the trapezoid (membership attains 1).
c (float, required): Right ceiling of the trapezoid (membership begins to fall).
d (float, required): Right foot of the trapezoid (membership reattains zero).

Returns (list[list]): Array of membership values corresponding to the input universe.

Example 1: Trapezoidal membership with a flat top

Inputs:

x						a	b	c	d
0	1	2	3	4	5	1	2	3	4

Excel formula:

=TRAPMF({0,1,2,3,4,5}, 1, 2, 3, 4)

Expected output:

Result
0
0
1
1
0
0

Example 2: Trapezoidal membership at a plateau point

Inputs:

x	a	b	c	d
2.5	1	2	3	4

Excel formula:

=TRAPMF(2.5, 1, 2, 3, 4)

Expected output:

1

Example 3: Trapezoidal membership across both sloped edges

Inputs:

x						a	b	c	d
1	1.5	2	3	3.5	4	1	2	3	4

Excel formula:

=TRAPMF({1,1.5,2,3,3.5,4}, 1, 2, 3, 4)

Expected output:

Result
0
0.5
1
1
0.5
0

Example 4: Trapezoidal membership on a negative universe

Inputs:

x					a	b	c	d
-4	-3	-2	-1	0	-3	-2	-1	0

Excel formula:

=TRAPMF({-4,-3,-2,-1,0}, -3, -2, -1, 0)

Expected output:

Result
0
0
1
1
0

Python Code

Show Code

import numpy as np
from skfuzzy import trapmf as fuzz_trapmf

def trapmf(x, a, b, c, d):
    """
    Generate a trapezoidal fuzzy membership function.

    See: https://pythonhosted.org/scikit-fuzzy/api/skfuzzy.html#skfuzzy.trapmf

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (list[list]): Array of independent universe variables.
        a (float): Left foot of the trapezoid (membership begins to climb from zero).
        b (float): Left ceiling of the trapezoid (membership attains 1).
        c (float): Right ceiling of the trapezoid (membership begins to fall).
        d (float): Right foot of the trapezoid (membership reattains zero).

    Returns:
        list[list]: Array of membership values corresponding to the input universe.
    """
    try:
        def to1d(arr):
            if isinstance(arr, list):
                flat = []
                for row in arr:
                    row_list = row if isinstance(row, list) else [row]
                    for val in row_list:
                        try:
                            flat.append(float(val))
                        except (TypeError, ValueError):
                            continue
                return np.array(flat)
            return np.array([float(arr)])

        x_arr = to1d(x)
        if len(x_arr) == 0:
            return "Error: Input mapping array x cannot be empty"

        if not (a <= b <= c <= d):
            return "Error: Parameters must satisfy a <= b <= c <= d"

        result = fuzz_trapmf(x_arr, [a, b, c, d])
        return [[float(val)] for val in result]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Array of independent universe variables.

a *

Left foot of the trapezoid (membership begins to climb from zero).

b *

Left ceiling of the trapezoid (membership attains 1).

c *

Right ceiling of the trapezoid (membership begins to fall).

d *

Right foot of the trapezoid (membership reattains zero).