5
Applying DSm Classic rule, which is a generalization of classical conjunctive rule from the 

![0_image_0.png](0_image_0.png)

fusion space (Θ, U ), called *power set*, when all hypotheses are supposed exclusive (i.e. all intersections are empty) to the fusion space (Θ, U , ∩), called *hyper-power set*, where hypotheses are not necessarily exclusive (i.e. there exist non-empty intersections), we just get: 
 A B C AU BU C A∩B A∩C B∩C 
mDSmC(.) 0.26 0.18 0.07 0.02 0.26 0.13 0.08 DSmC and the Conjunctive Rule have the same formula, but they work on different fusion spaces. 

Inagaki rule was defined on the fusion space (Θ, U ) . In this case, since all intersections are empty, the total conflicting mass, which is m12∩( A∩B) + m12∩( A∩C) + m12∩( B∩C) = 0.26 + 
+ 0.13 + 0.08 = 0.47, and this is redistributed to the masses of A, B, C, and AU BU C according to some weights w1, w2, w3, and w4 respectively, depending to each particular rule, where: 0 ≤ w1, w2, w3, w4 ≤ 1 and w1 + w2 + w3 + w4 = 1. Hence A B C AU BU C 
mInagaki(.) 0.26+0.47w1 0.18+0.47w2 0.07+0.47w3 0.02+0.47w4 Yet, Inagaki rule can also be straightly extended from the power set to the hyper-power set. Suppose in DWO the user finds out that the hypothesis B∩C is not plausible, therefore m12∩( B∩C) = 0.08 has to be transferred to the other non-empty elements: A, B, C, AU BU C, 
A∩B, A∩C, according to some weights v1, v2, v3, v4, v5, and v6 respectively, depending to the particular version of this rule is chosen, where: 
0 ≤ v1, v2, v3, v4, v5, v6 ≤ 1 and v1 + v2 + v3 + v4 + v5 + v6 = 1. Hence A B C AU BU C A∩B A∩C 
mDWO(.) 0.26+0.08v1 0.18+0.08v2 0.07+0.08v3 0.02+0.08v4 0.26+0.08v5 0.13+0.08v6 Now, since CPRIM is a particular case of DWO, but CPRIM is a class of fusion rules, let's consider a sub-particular case for example when the redistribution of m12∩( B∩C) = 0.08 is done proportionally with respect to the DSm cardinals of B and C which are both equal to 4. DSm 