fuzzy_set.trapezoidal_fuzzy_number module

class fuzzy_set.trapezoidal_fuzzy_number.TrapezoidalFuzzyNumber(x1: float, x2: float, x3: float, x4: float)

Bases: FuzzyNumber

A Trapezoidal Fuzzy Number (TFN) is a Fuzzy Number (FN) which is piecewise linear and continuous. Thus, it has a trapezoidal shape. As a consequence, a TFN is fully characterized by a quadruple of real numbers, denoted by \([x_1, x_2, x_3, x_4]\), where:

• \(x_1 \le ... \le x_4\);

• \([x_1, x_4]\) is the support of the TFN;

• \([x_2, x_3]\) is the core of the TFN.

Trapezoidal Fuzzy Numbers support arithmetic operators, i.e., +, -, *, /. See Reliability Range Through Upgraded Operation with TFN.

Example:

>>> from fuzzy_set import TrapezoidalFuzzyNumber
>>> t1 = TrapezoidalFuzzyNumber(1, 3, 8, 10)
>>> t2 = TrapezoidalFuzzyNumber(2, 5, 7, 8)
>>> t1 + t2
TrapezoidalFuzzyNumber<(3, 8, 15, 18)>
>>> t1 - t2
TrapezoidalFuzzyNumber<(-7, -4, 3, 8)>
>>> t1 * t2
TrapezoidalFuzzyNumber<(2, 15, 56, 80)>
>>> t1 / t2
TrapezoidalFuzzyNumber<(0.125, 0.42857142857142855, 1.6, 5.0)>

Example:

import matplotlib.pyplot as plt
from operator import __add__, __sub__, __mul__, __truediv__
(fig, axs) = plt.subplots(2, 2)
for (ij, (op, opname)) in {
    (0, 0): (__add__, "+"),
    (0, 1): (__sub__, "-"),
    (1, 0): (__mul__, "\cdot"),
    (1, 1): (__truediv__, "/"),
}.items():
    ax = axs[ij]
    title = f"$a_1 {opname} a_2$"
    ax.set_title(title)
    t1.plot(ax=ax, label="$a_1$")
    t2.plot(ax=ax, label="$a_2$")
    op(t1, t2).plot(ax=axs[ij], label=title)
    ax.grid()
    ax.legend()
    ax.legend(bbox_to_anchor=(1, 0.5), loc="center left")
plt.tight_layout()