Znum

Z-number arithmetic and multi-criteria decision making for Python.

A Z-number \(Z = (A, B)\) extends ordinary fuzzy numbers with a reliability component:

• A — a trapezoidal fuzzy number restricting the possible values of a variable
• B — a trapezoidal fuzzy number measuring the reliability (confidence) of A

Znum provides full arithmetic, comparison operators, and two MCDM solvers (TOPSIS and PROMETHEE) — all operating natively on Z-numbers.

Features

• Full arithmetic: +, -, *, /, ** between Z-numbers and scalars
• Comparison operators: <, >, <=, >=, == using fuzzy dominance
• Sorting: Works with Python's sorted(), min(), max()
• TOPSIS: Hellinger and Simple distance methods
• PROMETHEE: Pairwise preference with net flow ranking
• Crisp values: Znum.crisp(x) for exact numbers with full reliability

Quick example

from znum import Znum

# Fuzzy Z-numbers
z1 = Znum(A=[1, 2, 3, 4], B=[0.6, 0.7, 0.8, 0.9])
z2 = Znum(A=[2, 3, 5, 7], B=[0.5, 0.6, 0.7, 0.8])

# Arithmetic
z3 = z1 + z2
z4 = z1 * z2

# Comparison
print(z1 < z2)  # True

# Crisp (exact) values
five = Znum.crisp(5)
ten = Znum.crisp(10)
print(five + ten)  # Znum(A=[15.0, 15.0, 15.0, 15.0], B=[1.0, 1.0, 1.0, 1.0])

Requirements

• Python >= 3.10
• NumPy >= 1.24
• highspy >= 1.7.0

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