evidencelib 1.0.0

Computational belief functions for DST and DSmT.

evidencelib

Python library for belief-function calculations in Dempster-Shafer theory (DST) and Dezert-Smarandache theory (DSmT).

evidencelib provides a compact quantitative core for finite frames: symbolic propositions, basic belief assignments, evidence fusion rules, belief measures, and pignistic decision support.

Documentation is available on Read the Docs.

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Installation

You can install evidencelib using pip:

pip install evidencelib

For local development:

git clone https://github.com/itaprac/evidencelib.git
cd evidencelib
python3.10 -m venv .venv
source .venv/bin/activate
pip install -e ".[dev,docs]"

Run the test suite:

python -m pytest -q

Build the documentation locally:

python -m sphinx -W -b html docs docs/_build/html

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Available Functionality

The library contains:

Models

Constructor	Description
Frame.dst(...)	Shafer's classical DST model with exhaustive and mutually exclusive hypotheses.
Frame.dsmt(...)	Free DSm model where hypotheses may overlap.
Frame.hybrid(...)	Constrained DSm model with explicit emptiness or exclusivity constraints.

Proposition Algebra

Operation	Meaning
A | B	Union / disjunction, A ∪ B.
A & B	Intersection / conjunction, A ∩ B.
frame.proposition("A ∩ (B ∪ C)")	Parse a proposition from text.
frame.elements()	Generate the model's power set or hyper-power set.

Belief Measures

Method	Description
mass(A)	Direct mass assigned to a proposition.
belief(A)	Sum of masses contained in A.
plausibility(A)	Sum of masses intersecting A.
commonality(A)	Sum of masses containing A.
conflict	Mass assigned to the empty proposition.

Fusion Rules

Method	Description
conjunctive(...)	Unnormalized conjunctive rule.
dsmc(...)	Classic DSm rule on a free DSm frame.
smets(...)	TBM/Smets rule, keeping conflict on the empty proposition.
dempster(...)	Normalized Dempster rule.
yager(...)	Yager rule, moving conflict to total ignorance.
dsmh(...)	Hybrid DSm rule for constrained models.
dubois_prade(...)	Static Dubois-Prade-style conflict transfer.
pcr5(...)	PCR5 for two sources.
pcr6(...)	PCR6 for two or more sources.

Decision Support

Method	Description
pignistic()	Singleton pignistic scores.
pignistic_regions()	Probability distribution over disjoint model regions.
decision()	Singleton with the largest pignistic score.

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Usage Example

from evidencelib import Frame

frame = Frame.dst(["A", "B"])
A, B = frame.symbols()

m1 = frame.mass({
    A: 0.6,
    A | B: 0.4,
})

m2 = frame.mass({
    B: 0.3,
    A | B: 0.7,
})

print(m1.dempster(m2).to_dict())
print(m1.pcr5(m2).to_dict())

Output:

{"A": 0.5121951219512195, "A|B": 0.34146341463414637, "B": 0.14634146341463414}
{"A": 0.54, "A|B": 0.28, "B": 0.18}

Free DSmT example:

frame = Frame.dsmt(["A", "B"])
A, B = frame.symbols()

m = frame.mass({
    A: 0.2,
    B: 0.3,
    A & B: 0.4,
    A | B: 0.1,
})

print(m.pignistic())
print(m.pignistic_regions())

In DSmT, singleton hypotheses can overlap, so pignistic() returns decision scores that do not necessarily sum to one. Use pignistic_regions() for a probability distribution over disjoint Venn regions.

More examples are available in the examples/ directory and in the documentation.

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References

• Shafer, G. (1976). A Mathematical Theory of Evidence. Princeton University Press.
• Smarandache, F., & Dezert, J. (eds.). Advances and Applications of DSmT for Information Fusion.
• Dezert, J., & Smarandache, F. An Introduction to DSmT.
• Zadeh, L. A. (1986). A simple view of the Dempster-Shafer theory of evidence and its implication for the rule of combination. AI Magazine, 7(2), 85-90.

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License

evidencelib is released under the MIT License.