Znum

A Python library for Z-number arithmetic and multi-criteria decision making (MCDM).

A Z-number is a fuzzy number with two components:

• A: The main fuzzy set values (restriction on values)
• B: The confidence/belief values (reliability of A)

Znum supports full mathematical operations (addition, subtraction, multiplication, division, power), comparison operators, and includes implementations of TOPSIS and PROMETHEE optimization methods.

Installation

pip install znum

Quick Start

from znum import Znum

# Create Z-numbers
z1 = Znum([1, 2, 3, 4], [0.1, 0.2, 0.3, 0.4])
z2 = Znum([2, 4, 8, 10], [0.5, 0.6, 0.7, 0.8])

# Arithmetic operations
z3 = z1 + z2
z4 = z1 * z2
z5 = z1 - z2
z6 = z1 / z2

# Comparison
print(z1 > z2)  # False
print(z1 < z2)  # True

# Power
z7 = z1 ** 2

MCDM Methods

TOPSIS

from znum import Znum, Topsis, MCDMUtils

# Create weights, alternatives, and criteria types
weights = [Znum([0.2, 0.3, 0.4, 0.5], [0.1, 0.2, 0.3, 0.4])]
alternatives = [[Znum([7, 8, 9, 10], [0.6, 0.7, 0.8, 0.9])]]
criteria_types = [MCDMUtils.CriteriaType.BENEFIT]

table = [weights, *alternatives, criteria_types]
topsis = Topsis(table)
result = topsis.solve()

# Access results
best_idx = topsis.index_of_best_alternative
worst_idx = topsis.index_of_worst_alternative
ranking = topsis.ordered_indices

PROMETHEE

from znum import Znum, Promethee, MCDMUtils

table = [weights, *alternatives, criteria_types]
promethee = Promethee(table)
sorted_alternatives = promethee.solve()

# Access results
best_idx = promethee.index_of_best_alternative
worst_idx = promethee.index_of_worst_alternative
ranking = promethee.ordered_indices

Development

# Install dependencies
pip install -e ".[dev]"

# Run tests
pytest

References

• Zadeh, L.A. (2011). A Note on Z-numbers. Information Sciences, 181(14), 2923–2932. doi:10.1016/j.ins.2011.02.022
• Li, Y., Herrera-Viedma, E., Pérez, I.J. et al. (2023). The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution. Information Sciences, 647, 119477. doi:10.1016/j.ins.2023.119477

License

MIT