212.

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7.4.4 Decision rules for evidential reasoning

Where a statistical classifier such as maximum likelihood is used, the label assigned to a given pixel is the one for which the class membership likelihood function is greatest. This is the most straightforward choice. However, in evidential reasoning, the decision rules are more complicated because the decision space involves two elements, i.e. belief and plausibility. According to Shafer (1979), there are three possible choices:

1	Belief driven:	Label is chosen on the basis of maximal belief
2	Plausibility driven:	Label is chosen on the basis of maximal plausibility
3	Mean of the interval:	Label is chosen on the basis of the maximal average of belief and plausibility values

These three choices may generate different results. If we look at the example given above, with three classes (Bare Soil {B}, Forest {F}, and Pasture {P}), it is possible to compute, the belief and plausibility values for each.

(7.30)

It is clear that if m({B})>m({F}), i.e. Bel{B}>Bel{F} then one can also conclude that Pl{B}>Pl{F}. In this situation, two of the decision rules (i.e. belief-driven and plausibility-driven) produce the same result. Thus, it shows that one still has just one choice to make the decision if one tends to perform the single-class labelling.

7.5 Dealing with source reliability

The methods described above show the promise for handling the multisource classification problem. The issue concerning the source weighting factors is not fully resolved, however. In practical circumstance, each available data source may not be fully certain and complete. Therefore, it is necessary to weight each of the sources so that the final classification reflects our knowledge of the reliability of each of the data sources.

The process for the determination of weighting factors is similar to that of computing reliability in consensus theory for managing different opinion sources (Winkler, 1968; McConway, 1980; French, 1985). The choice of source weighting factors will have a significant effect on the results of a multisource classification because the contribution of each source will be

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