Example 01: Fuzzy numbers¶

Arithmetic on triangular, intuitionistic, Pythagorean and spherical numbers, a second operator family, scores and a weighted average.

Source¶

examples/01_fuzzy_numbers.py

"""Fuzzy numbers: arithmetic, operator families, scores and weighted aggregation."""

import math

from bulanik import IFN, PFN, TFN, SphericalFN
from bulanik.aggregate import wa

# Triangular numbers use interval-style arithmetic.
cost = TFN(1, 2, 3) + TFN(3, 4, 5)
print("TFN sum:", cost, "centroid score:", cost.score())

# Intuitionistic numbers: the algebraic sum is the probabilistic sum of mu.
a, b = IFN(0.6, 0.3), IFN(0.5, 0.4)
total = a + b
assert math.isclose(total.mu, 0.8, rel_tol=1e-9)
print("IFN sum:", total)

# Scalar multiplication, and the algebraic vs Einstein operator families.
print("2 x a  :", a * 2)
print("algebraic:", a.add(b, ops="algebraic"))
print("einstein :", a.add(b, ops="einstein"))

# Scores are named too; results report the name you picked.
print("score difference:", round(total.score("difference"), 4), "normalized:", round(total.score("normalized"), 4))

# Pythagorean and spherical numbers allow more room than intuitionistic ones.
p = PFN(0.8, 0.5)  # 0.64 + 0.25 <= 1, impossible as an IFN
s = SphericalFN(0.6, 0.3, 0.4)
print("PFN:", p, "score:", round(p.score(), 4), "| Spherical:", s, "score:", round(s.score(), 4))

# Weighted average of two opinions.
print("WA:", wa([a, b], [0.7, 0.3]))

Output¶

Run when this page is built:

TFN sum: TFN(l=4.0, m=6.0, u=8.0) centroid score: 6.0
IFN sum: IFN(mu=0.8, nu=0.12)
2 x a  : IFN(mu=0.84, nu=0.09)
algebraic: IFN(mu=0.8, nu=0.12)
einstein : IFN(mu=0.8461538461538461, nu=0.08450704225352113)
score difference: 0.68 normalized: 0.84
PFN: PFN(mu=0.8, nu=0.5) score: 0.39 | Spherical: SphericalFN(mu=0.6, nu=0.3, pi=0.4) score: 0.03
WA: IFN(mu=0.5723061600035249, nu=0.32704150727080533)

What to notice¶

The algebraic and Einstein families give different sums for the same two IFNs; the result always reports the operator used.
score() is a number you can sort on, but each type has its own default (centroid for triangular, difference for orthopair).
Weights are validated, and wa returns the same number type you put in.

Go further¶

Run it yourself: python examples/01_fuzzy_numbers.py.