Fusion Rules

All fusion methods are methods on MassFunction.

combined = m1.dempster(m2)

All sources must belong to the same frame.

Every rule returns a new MassFunction; input sources are not modified.

Conjunctive / DSmC / Smets

m1.conjunctive(m2)
m1.dsmc(m2)
m1.smets(m2)

The unnormalized conjunctive rule intersects propositions and multiplies their masses. On a free DSmT frame this is the classic DSm rule, DSmC. On a DST frame, conflicting intersections accumulate on empty.

smets() is an alias for the same unnormalized behavior in the transferable belief model sense.

Use this rule when you want to inspect conflict explicitly instead of redistributing or normalizing it immediately.

Dempster

m1.dempster(m2)

Dempster’s rule removes empty-set conflict and normalizes the remaining masses. If conflict is total, TotalConflictError is raised.

This rule is appropriate when the frame is exclusive and normalized conflict handling is acceptable for the application.

Yager

m1.yager(m2)

Yager’s rule transfers total conflict to total ignorance.

This keeps the result normalized while representing conflict as uncertainty instead of assigning it to specific hypotheses.

DSmH / Dubois-Prade-style transfer

m1.dsmh(m2)
m1.dubois_prade(m2)

dsmh() transfers empty intersections to the union of the propositions involved in the conflict. If that union is empty under the model, the mass goes to total ignorance.

For static Shafer-style problems, this is the same transfer pattern normally associated with Dubois-Prade. Dynamic DSmH cases can differ, especially when a hypothesis becomes empty after evidence was assigned to it.

Use DSmH with Frame.hybrid(...) when constraints are part of the model.

PCR5 and PCR6

m1.pcr5(m2)
m1.pcr6(m2, m3)

PCR rules redistribute partial conflict only to the propositions involved in that conflict, proportionally to the masses that created it.

pcr5() accepts two sources. pcr6() supports two or more sources.

PCR rules are useful in high-conflict cases where assigning conflict to total ignorance would be too coarse.