TRIMF

Generates a triangular membership function for a given universe. The shape of the triangle is defined by three parameters: left foot, peak, and right foot.

The membership value is 0 outside the feet, climbs linearly to 1 at the peak, and falls linearly back to 0.

Excel Usage

=TRIMF(x, a, b, c)

x (list[list], required): Array of independent universe variables.
a (float, required): Left foot of the triangle (membership begins to climb from zero).
b (float, required): Peak of the triangle (membership equals 1).
c (float, required): Right foot of the triangle (membership reattains zero).

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

Example 1: Triangular membership with a centered peak

Inputs:

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

Excel formula:

=TRIMF({0,1,2,3,4}, 1, 2, 3)

Expected output:

Result
0
0
1
0
0

Example 2: Triangular membership at the peak point

Inputs:

x	a	b	c
2	1	2	3

Excel formula:

=TRIMF(2, 1, 2, 3)

Expected output:

1

Example 3: Triangular membership with a left shoulder

Inputs:

x					a	b	c
0	0.5	1	1.5	2	0	0	2

Excel formula:

=TRIMF({0,0.5,1,1.5,2}, 0, 0, 2)

Expected output:

Result
1
0.75
0.5
0.25
0

Example 4: Triangular membership with a right shoulder

Inputs:

x				a	b	c
0	1	1.5	2	0	2	2

Excel formula:

=TRIMF({0,1,1.5,2}, 0, 2, 2)

Expected output:

Result
0
0.5
0.75
1

Python Code

Show Code

import numpy as np
from skfuzzy import trimf as fuzz_trimf

def trimf(x, a, b, c):
    """
    Generate a triangular fuzzy membership function.

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

    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 triangle (membership begins to climb from zero).
        b (float): Peak of the triangle (membership equals 1).
        c (float): Right foot of the triangle (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):
            return "Error: Parameters must satisfy a <= b <= c"

        result = fuzz_trimf(x_arr, [a, b, c])
        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 triangle (membership begins to climb from zero).

b *

Peak of the triangle (membership equals 1).

c *

Right foot of the triangle (membership reattains zero).