PIECEMF

Piecewise linear membership function (particularly used in FIRE filters).

Piecewise definition: - y = 0 for x <= a - y = b(x - a)/c(b - a) for a <= x <= b - y = x/c for b <= x <= c - y = 1 for c <= x

Excel Usage

=PIECEMF(x, a, b, c)

x (list[list], required): Array of independent universe variables.
a (float, required): First breakpoint of the piecewise function.
b (float, required): Second breakpoint of the piecewise function.
c (float, required): Third breakpoint of the piecewise function.

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

Example 1: Piecewise membership with ordered breakpoints

Inputs:

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

Excel formula:

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

Expected output:

Result
0
0
0.666667
1
1
1

Example 2: Piecewise membership on the upper plateau

Inputs:

x	a	b	c
3	1	2	3

Excel formula:

=PIECEMF(3, 1, 2, 3)

Expected output:

1

Example 3: Piecewise membership across the rising segment

Inputs:

x					a	b	c
1	1.5	2	2.5	3	1	2	3

Excel formula:

=PIECEMF({1,1.5,2,2.5,3}, 1, 2, 3)

Expected output:

Result
0
0.333333
0.666667
0.833333
1

Example 4: Piecewise membership with wider support

Inputs:

x							a	b	c
0	1	2	3	4	5	6	1	3	5

Excel formula:

=PIECEMF({0,1,2,3,4,5,6}, 1, 3, 5)

Expected output:

Result
0
0
0.3
0.6
0.8
1
1

Python Code

Show Code

import numpy as np
from skfuzzy import piecemf as fuzz_piecemf

def piecemf(x, a, b, c):
    """
    Generate a piecewise linear fuzzy membership function.

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

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

    Args:
        x (list[list]): Array of independent universe variables.
        a (float): First breakpoint of the piecewise function.
        b (float): Second breakpoint of the piecewise function.
        c (float): Third breakpoint of the piecewise function.

    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_piecemf(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 *

First breakpoint of the piecewise function.

b *

Second breakpoint of the piecewise function.

c *

Third breakpoint of the piecewise function.