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The belief for other subsets is zero. The plausibilities for subsets {B}, {B, F}, and {B, P} are all equivalent to one, because

 

The second example is an extension of the first. Suppose that there is a third observation that confirms {P} to the degree of 0.7, denoted by m_c, and let m_a m_b=m_d. The orthogonal sum m_c md is illustrated in Table 7.2. There are two null intersections, i.e. Ø. One contains the value 0.294, and the other 0.196. Therefore, the normalisation constant K and the final evidence combination results are computed by:

 

and for all other subsets, m_c m_d=0.

Both belief and plausibility can be derived in the similar way, as explained in example one, and so will not be duplicated here. Readers may also wish to combine bpa using the above examples, but in a different sequence. For example, one may compute the orthogonal sum first using evidence 1 and 3, and then combine to evidence 2. This exercise should show that the results of evidence combination are the same, irrespective of the ordering.

Table 7.2 Extended example of Dempster’s rule combination

md→ mc↓	md({B})=(0.42)	md({B, F})=(0.28)	md({B,P})=(0.18)	md(θ)=(0.12)
mc({P})(0.7)	Ø=0.294	Ø=0.196	{P}=0.126	{P}=0.084
mc(θ)(0.3)	{B}=0.126	{B, F}=0.084	{B, P}=0.054	θ=0.036

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