Theory Notes

This page maps the main DST and DSmT concepts to evidencelib objects.

DST

Dempster-Shafer theory works on a frame of discernment Theta whose hypotheses are exhaustive and mutually exclusive. In evidencelib this is:

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

The generated proposition space is the power set 2^Theta. Intersections such as A & B collapse to empty.

DSmT

The free DSm model keeps hypotheses exhaustive but does not require them to be exclusive:

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

The generated proposition space is the hyper-power set: expressions built from atoms using union and intersection. For small frames:

  • |Theta| = 2 gives 5 elements,

  • |Theta| = 3 gives 19 elements,

  • |Theta| = 4 gives 167 elements.

Frame.elements() has a safety limit because these spaces grow quickly.

Hybrid Models

A hybrid DSm model adds explicit constraints:

frame = Frame.hybrid(["A", "B", "C"], exclusive=True, empty=["C"])

This can represent static exclusivity constraints and dynamic situations where new knowledge makes a hypothesis or intersection empty.

Pignistic Output

In DST, singleton hypotheses are disjoint, so pignistic singleton probabilities sum to one.

In free DSmT, singleton hypotheses can overlap. pignistic() returns singleton event scores for decisions, while pignistic_regions() returns a distribution over disjoint Venn regions.