Sir, while solving DST problem while finding m5 (i already have m1,m2,m3,m4) i got 2 plausibility cases , what should we do in this case? earlier if there was i plausibility case we used to calc plausibility and divide everything with it but in this case i got 2 plausibility cases please help
Ok so here i will explain you few steps u can try and also a example to be more specific , hope u understand- Step 1: Understand the Two Plausibility Cases Each plausibility case corresponds to a different subset or hypothesis in the frame of discernment. For each case, calculate the plausibility value based on the combination of the masses 𝑚1, 𝑚2, 𝑚3, 𝑚4 Step 2: Determine if the Cases Overlap If the two plausibility cases overlap (i.e., they pertain to subsets that are not mutually exclusive), combine the plausibility values by adding them. This is because their joint plausibility contributes to the overall belief in the union of these subsets. If the cases are disjoint (i.e., they pertain to subsets that have no common elements), handle them as separate hypotheses. You would then assign their masses separately and normalize afterward. Step 3: Normalize the Masses Add up all the resulting masses, including those from the two plausibility cases. Normalize by dividing each mass by the sum of the plausibilities to ensure the total mass equals 1. Example: Let’s say: 𝑚1(𝐴)=0.3 𝑚2(𝐴)=0.4 𝑚3(𝐵)=0.2 𝑚4(𝐶)=0.1 𝑚5 has two plausibility cases: Case 1: Plausibility for 𝐴∪𝐵= 0.6 Case 2: Plausibility for 𝐶 = 0.4 Steps: 1.Combine A∪B and 𝐶 if possible, or treat them as separate. 2.Calculate the total plausibility sum: Total Plausibility= 0.6+0.4=1.0 3.Normalize: 𝑚5(𝐴∪𝐵)=0.6/1.0=0.6 𝑚5(C)=0.4/1.0=0.4
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Sir, while solving DST problem while finding m5 (i already have m1,m2,m3,m4) i got 2 plausibility cases , what should we do in this case?
earlier if there was i plausibility case we used to calc plausibility and divide everything with it
but in this case i got 2 plausibility cases
please help
Ok so here i will explain you few steps u can try and also a example to be more specific , hope u understand-
Step 1: Understand the Two Plausibility Cases
Each plausibility case corresponds to a different subset or hypothesis in the frame of discernment.
For each case, calculate the plausibility value based on the combination of the masses
𝑚1, 𝑚2, 𝑚3, 𝑚4
Step 2: Determine if the Cases Overlap
If the two plausibility cases overlap (i.e., they pertain to subsets that are not mutually exclusive), combine the plausibility values by adding them. This is because their joint plausibility contributes to the overall belief in the union of these subsets.
If the cases are disjoint (i.e., they pertain to subsets that have no common elements), handle them as separate hypotheses. You would then assign their masses separately and normalize afterward.
Step 3: Normalize the Masses
Add up all the resulting masses, including those from the two plausibility cases.
Normalize by dividing each mass by the sum of the plausibilities to ensure the total mass equals 1.
Example:
Let’s say:
𝑚1(𝐴)=0.3
𝑚2(𝐴)=0.4
𝑚3(𝐵)=0.2
𝑚4(𝐶)=0.1
𝑚5 has two plausibility cases:
Case 1: Plausibility for
𝐴∪𝐵= 0.6
Case 2: Plausibility for 𝐶 = 0.4
Steps:
1.Combine A∪B and 𝐶 if possible, or treat them as separate.
2.Calculate the total plausibility sum:
Total Plausibility=
0.6+0.4=1.0
3.Normalize:
𝑚5(𝐴∪𝐵)=0.6/1.0=0.6
𝑚5(C)=0.4/1.0=0.4
@engineerskaadda78 Thankyou for the quick reply, it's very helpful 👍🏻