pybelief

Finite-frame Dempster-Shafer belief functions with sparse bitmask storage.

Installation

pip install pybelief

Quick start

from pybelief import MassFunction

frame = ["a", "b", "c"]

# Create mass functions using label sets
m1 = MassFunction(frame, named_focal_elements={
    frozenset({"a"}): 0.3,
    frozenset({"a", "b"}): 0.2,
    frozenset({"a", "b", "c"}): 0.5,
})

m2 = MassFunction(frame, named_focal_elements={
    frozenset({"b"}): 0.5,
    frozenset({"a", "b"}): 0.2,
    frozenset({"a", "b", "c"}): 0.3,
})

# Query belief, plausibility, commonality
m1.belief({"a"})          # 0.3
m1.plausibility({"b"})    # 0.7
m1.commonality({"a"})     # 1.0

# Combine sources
m12 = m1 & m2                    # Dempster's rule
m12 = m1 | m2                    # Conjunctive (TBM)
m12 = m1.combine_yager(m2)       # Yager's rule

# Decision making
m1.pignistic()            # {'a': 0.567, 'b': 0.267, 'c': 0.167}

Bitmask convention

Element i of the frame maps to bit i. For frame = ["a", "b", "c"]:

You can use either bitmasks or label sets in all API calls:

m.belief(0b011)          # bitmask
m.belief({"a", "b"})     # label set — same result

API overview

Construction

Transforms

Operations

Measures

Performance

Focal elements are stored sparsely. Combination runs in O(|F1| x |F2|) — fast when mass functions are sparse. Full transforms use the fast zeta transform in O(n * 2^n). Practical for frames up to ~20 elements.

Citation

If you use pybelief in your research, please cite:

@software{afifi2025pybelief,
  author    = {Afifi, Sohaib},
  title     = {pybelief: Finite-Frame Dempster--Shafer Belief Functions in Python},
  year      = {2025},
  url       = {https://github.com/sohaibafifi/pybelief},
}

License

MIT