by the policemen. This situation corresponds to set up a hybrid model M with the constraint θ3 M= ∅.

16 Let's examine the result of the fusion in such situation obtained by the Smets', Yager's, Dubois & Prade's and hybrid DSm rules of combinations. First note that, based on the free DSm model, one would get by applying the classic DSm rule (denoted here by index **DSmC**) the following fusion result m**DSmC**(θ1) = 0.21 m**DSmC**(θ2) = 0.11 m**DSmC**(θ3) = 0.06 m**DSmC**(θ1 ∪ θ2) = 0.03 m**DSmC**(θ1 ∩ θ2) = 0.21 m**DSmC**(θ1 ∩ θ3) = 0.13 m**DSmC**(θ2 ∩ θ3) = 0.14 m**DSmC**(θ3 ∩ (θ1 ∪ θ2)) = 0.11 But because of the exclusivity constraints (imposed here by the use of Shafer's model and by the nonexistential constraint θ3 M= ∅), the total conflicting mass is actually given by k12 = 0.06 + 0.21 + 0.13 + 0.14 +
0.11 = 0.65.

- If one applies **Dempster's rule** [24] (denoted here by index DS), one gets:
mDS(∅) = 0 mDS(θ1) = 0.21/[1 − k12] = 0.21/[1 − 0.65] = 0.21/0.35 = 0.600000 mDS(θ2) = 0.11/[1 − k12] = 0.11/[1 − 0.65] = 0.11/0.35 = 0.314286 mDS(θ1 ∪ θ2) = 0.03/[1 − k12] = 0.03/[1 − 0.65] = 0.03/0.35 = 0.085714
- If one applies **Smets' rule** [39,40] (i.e. the non normalized version of Dempster's rule with the conflicting mass transferred onto the empty set), one gets:
mS(∅) = m(∅) = 0.65 (conflicting mass)
mS(θ1) = 0.21 mS(θ2) = 0.11 mS(θ1 ∪ θ2) = 0.03
- If one applies **Yager's rule** [48–50], one gets:
mY (∅) = 0 mY (θ1) = 0.21 mY (θ2) = 0.11 mY (θ1 ∪ θ2) = 0.03 + k12 = 0.03 + 0.65 = 0.68
- If one applies **Dubois & Prade's rule** [12], one gets because θ3 M= ∅ :
mDP (∅) = 0 (by definition of Dubois & Prade's rule)
mDP (θ1) = [m1(θ1)m2(θ1) + m1(θ1)m2(θ1 ∪ θ2)
+ m2(θ1)m1(θ1 ∪ θ2)]
+ [m1(θ1)m2(θ3) + m2(θ1)m1(θ3)]
= [0.1 · 0.5 + 0.1 · 0.1 + 0.5 · 0.3] + [0.1 · 0.3 + 0.5 · 0.2] = 0.21 + 0.13 = 0.34 mDP (θ2) = [0.4 · 0.1 + 0.4 · 0.1 + 0.1 · 0.3] + [0.4 · 0.3 + 0.1 · 0.2]
= 0.11 + 0.14 = 0.25