Exhaustiveness
Exhaustiveness is probably the most important property for a set of indicators that are supposed to represent a process.
A set of indicators is considered non-exhaustive when:
• The representation does not consider one or more (important) dimensions of the process; i.e., the set is incomplete since some indicators are missing (see Fig. 4.13).
• One or more indicators do not map distinguished empirical manifestations into distinguished symbolic manifestations; it can therefore be asserted that the mapping resolution is lower than necessary (see Fig. 4.14).
The property of exhaustiveness can also be explained as follows. If a set of indicators is unable to discriminate two process states (“a” and “b”) with some distinguished empirical manifestations, then it is not exhaustive. This condition may be expressed in formal terms as follows:
If ∀j ∈ F, Ij(a) ≈ Ij(b)
and if some empirical manifestations in state “a” are distinguished from those in state “b”,
then the set of indicators is not exhaustive, being:
a and b states of the process;
F set (family) of indicators.
