evidencelib 1.0.1

Computational belief functions for DST and DSmT.

evidencelib

evidencelib is a Python library for belief-function calculations in Dempster-Shafer theory (DST) and Dezert-Smarandache theory (DSmT). It provides a compact, zero-dependency quantitative core for reasoning under uncertainty using belief functions.

• Documentation: https://evidencelib.readthedocs.io
• Source Code: https://github.com/itaprac/evidencelib
• PyPI: https://pypi.org/project/evidencelib/
• Issue Tracker: https://github.com/itaprac/evidencelib/issues

---

Features

• Multiple models — Shafer's classical DST, free DSmT, and constrained hybrid DSm models
• Proposition algebra — symbolic construction of unions, intersections, and parsing from strings
• Fusion rules — Dempster, Yager, Smets/TBM, Dubois-Prade, Hybrid DSm, PCR5, PCR6
• Belief measures — mass, belief, plausibility, commonality, conflict
• Decision support — pignistic transformation over singletons and disjoint Venn regions
• Zero dependencies — pure Python, no external packages required
• Fully typed — type hints throughout the codebase

---

Installation

pip install evidencelib

Requires Python 3.10 or later.

---

Quick Start

Basic DST Example

from evidencelib import Frame

# Create a frame with mutually exclusive hypotheses
frame = Frame.dst(["Alive", "Dead"])
Alive, Dead = frame.symbols()

# Define a basic belief assignment
m = frame.mass({
    Alive: 0.2,
    Dead: 0.5,
    Alive | Dead: 0.3,
})

# Query belief measures
print(m.belief(Alive))        # 0.2
print(m.plausibility(Alive))  # 0.5
print(m.pignistic())          # {"Alive": 0.35, "Dead": 0.65}
print(m.decision())           # "Dead"

Combining Evidence

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})

# Dempster's rule
print(m1.dempster(m2).to_dict())
# {"A": 0.512, "A|B": 0.341, "B": 0.146}

# PCR6
print(m1.pcr6(m2).to_dict())
# {"A": 0.54, "A|B": 0.28, "B": 0.18}

DSmT with Overlapping Hypotheses

from evidencelib import Frame

# Free DSm model — hypotheses may overlap
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())          # singleton scores (may not sum to 1)
print(m.pignistic_regions())  # probability over disjoint Venn regions

---

API Overview

Frames

Constructor	Description
Frame.dst(atoms)	Shafer's model — exhaustive and mutually exclusive hypotheses
Frame.dsmt(atoms)	Free DSm model — hypotheses may overlap
Frame.hybrid(atoms, empty=..., exclusive=...)	Constrained DSm model with explicit constraints

Propositions

Operation	Description
A | B	Union / disjunction
A & B	Intersection / conjunction
frame.proposition("A ∩ (B ∪ C)")	Parse from string
frame.elements()	Generate power set or hyper-power set

Belief Measures

Method	Description
mass(A)	Direct mass assigned to proposition A
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
dempster(...)	Dempster's normalized rule
smets(...)	TBM/Smets rule — keeps conflict on empty set
yager(...)	Yager's rule — transfers conflict to total ignorance
dsmc(...)	Classic DSm conjunctive rule
dsmh(...)	Hybrid DSm rule for constrained models
dubois_prade(...)	Dubois-Prade 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 Venn regions
decision()	Singleton with the largest pignistic probability

---

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 tests:

python -m pytest -q

Build documentation:

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

---

Examples

See the examples/ directory for complete scripts:

• basic_dst.py — simple DST frame and belief measures
• rules_dst.py — comparing fusion rules
• zadeh.py — Zadeh's classic counterexample
• dsmt_fusion.py — DSmT evidence fusion
• hybrid_dsmt.py — constrained hybrid DSm model

---

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.

---

License

MIT License — see LICENSE for details.