Mass Functions

A mass function is a basic belief assignment over propositions in a frame.

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

Mass values must be finite, non-negative, and sum to one. Tiny floating-point drift near one is normalized; NaN, infinities, and real sum mismatches are rejected.

Meaning: mass on A is direct support for A. Mass on A | B is unresolved support for either A or B.

Accepted keys

Keys may be Proposition objects, atom names, string expressions, or iterables of atom names:

frame.mass({"A": 0.4, "B": 0.2, "A | B": 0.4})
frame.mass({A: 0.4, B: 0.2, A | B: 0.4})

Inspect values

m.items()
m.focal()
m.to_dict()
m.total_mass
m.conflict

items() returns (proposition, value) pairs sorted by proposition label. focal() returns only propositions with non-zero mass. to_dict() is useful for display, logging, and simple serialization.

m.conflict is the mass assigned to the empty proposition. It is usually zero for a valid source, but it can appear after unnormalized combination on a constrained model.

DSm generalized bbas assume m(empty) = 0. MassFunction can also carry the unnormalized conflict produced by smets(); methods that mathematically require closed-world source bbas, such as PCR5/PCR6 and static Dubois-Prade, reject such inputs explicitly.

Decision transforms such as pignistic() and pignistic_regions() ignore empty-set conflict and rescale the remaining mass by default. Pass normalize_conflict=False to inspect raw unnormalized TBM scores.

Query support

m.mass(A)
m.belief(A)
m.plausibility(A)
m.commonality(A)

  • mass(A) returns the direct assigned mass.

  • belief(A) sums non-empty masses of propositions contained in A. Excluding the universal empty set has no effect for a DSm gbba and keeps the usual TBM interpretation when a Smets result carries conflict.

  • plausibility(A) sums masses of propositions intersecting A.

  • commonality(A) sums masses of propositions that contain A.

For DST, belief(A) <= plausibility(A) gives the usual lower and upper support interval for A.

Dictionary output

Use to_dict() when you want compact string keys:

combined = m1.pcr5(m2)
print(combined.to_dict())

By default, keys look like "A|B". Pass string_keys=False if you need Proposition keys.

For JSON, CSV, and LaTeX exports, see the import/export guide.