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### Combinations of OMPs

By definition, OMPs are combinations of BPQs. The implicit value of an OMP equals the combination of its constituent BPQs . This property allows OMPs to be defined as functions such that an OMP is a function where is the set of BPQs, is the set of natural numbers and equals the number of occurrences of in .

For example, let denote the OMP associated with the scenario model that contains three logistic population growth models (), two Holling predation model () and one competition model (). Therefore,

and hence:

By describing OMPs as functions, the concept of combinations of OMPs becomes clear. For two OMPs and , the combined preference is defined as:

Note that the combination operator is assumed to be commutative, associative and strictly monotonic ( ). The latter assumption is made to better reflect the ideas underpinning conventional utility calculi [1].

Next: Partial ordering of OMPs Up: Order-of-magnitude preferences (OMPs) Previous: Representation of OMPs
Jeroen Keppens 2004-03-01