evtools-dst 0.2.0

Evidence Theory Tools — utilities for Dempster-Shafer theory of belief functions

evtools

Evidence Theory Tools — a growing Python library of utilities for working with belief functions in the Dempster-Shafer theory of evidence.

Modules

Module	Description
evtools.dsvector	DSVector — unified container for any belief function representation
evtools.conversions	Low-level conversions between all standard representations via the Fast Möbius Transform

---

evtools.dsvector

DSVector is the central object of evtools. It represents any belief function as a vector on 2^Ω, in both sparse (dict) and dense (numpy array) forms. The sparse representation is the master; the dense array is computed on demand and cached.

Kind enum

Kind	Symbol	Name
Kind.M	m	Basic Belief Assignment (mass function)
Kind.BEL	bel	Belief function
Kind.PL	pl	Plausibility function
Kind.B	b	Commonality function
Kind.Q	q	Implicability function
Kind.V	v	Conjunctive weight function
Kind.W	w	Disjunctive weight function

Constructors

from evtools.dsvector import DSVector, Kind

# Human-friendly: name focal elements as strings
m = DSVector.from_focal(["a", "b", "c"], {"a": 0.3, "b,c": 0.5})

# From a dense numpy array
m = DSVector.from_dense(["a", "b", "c"], np.array([0, 0.3, 0, 0, 0.5, 0, 0, 0.2]))

# From a sparse dict of frozensets
m = DSVector.from_sparse(["a", "b", "c"], {
    frozenset({"a"}):          0.3,
    frozenset({"b", "c"}):    0.5,
    frozenset({"a","b","c"}): 0.2,
})

Conversions

pl  = m.to(Kind.PL)   # returns a new DSVector with kind=Kind.PL
bel = m.to_bel()      # shortcut
b   = m.to_b()        # commonality
q   = m.to_q()        # implicability
v   = m.to_v()        # conjunctive weights (requires subnormal BBA)
w   = m.to_w()        # disjunctive weights (requires subnormal BBA)

Accessing values

m.sparse                     # dict[frozenset, float]
m.dense                      # np.ndarray of length 2^n
m[frozenset({"a"})]          # value for a given subset (0.0 if absent)
for subset, value in m: ...  # iterate over non-zero focal elements

---

evtools.conversions

Low-level conversion functions between all standard representations, implemented using the Fast Möbius Transform (FMT) from Smets (2002) and Denoeux (2008). All functions operate on plain np.ndarray vectors of length 2^n.

Every conversion is available as a <source>to<target> function, e.g. mtob, pltom, qtow, beltov, etc.

import numpy as np
from evtools.conversions import mtob, mtopl, mtobel, mtow

m = np.array([0.0, 0.3, 0.5, 0.2])  # ∅, {a}, {b}, {a,b}

print(mtob(m))    # commonality function
print(mtopl(m))   # plausibility function
print(mtobel(m))  # belief function
print(mtow(m))    # disjunctive weight function

---

Installation

pip install evtools-dst

Or from source:

git clone https://github.com/daviddavkanmercier/evtools.git
cd evtools
pip install -e .

Running tests

pip install -e ".[dev]"
pytest tests/

References

• P. Smets. The application of the matrix calculus to belief functions, International Journal of Approximate Reasoning, 31(1–2):1–30, 2002.
• T. Denœux. Conjunctive and disjunctive combination of belief functions induced by non-distinct bodies of evidence, Artificial Intelligence, 172:234–264, 2008.
• D. Mercier, B. Quost, T. Denœux, Refined modeling of sensor reliability in the belief function framework using contextual discounting, Information Fusion, Vol. 9, Issue 2, pp 246-258, April 2008.

License

MIT