a measure of
variety such that uncertainty (H) is zero when all elements are in the same category. H increases with both the number of categories and their equiprobability. The uncertainty resulting from two or more sets of categories is the sum of the uncertainties of the sets of categories taken independently. H = the sum of P sub i times the log of P sub i, where P sub i is the probability of an element being in the Its category. Since the categories must be specified by an
observer , the uncertainty of a system may be different as seen by different observers. Because of an unfortunate use of terminology in systems analysis discourse, the word "uncertainty" has both a precise technical meaning and its loose natural meaning of an event or situation that is not certain. In
decision theory and statistics, a precise distinction is made between a situation of
risk and one of certainty. There is an uncontrollable random event inherent in both of these situations. The distinction is that in a
risk y situation the uncontrollable random event comes from a known probability distribution, whereas in an uncertain situation the probability distribution is unknown. (IIASA)
The (average) number of binary
decisions a decision maker has to make in order to select one out of a set of mutually exclusive alternatives, a measure of an observer's ignorance or lack of
information (
see bit ). Since the categories within which events are observed are always specified by an observer, the notion of uncertainty emphasizes the cognitive dimension of information processes, specifically in the form of measures of
variety, statistical entropy including
noise and
equivocation . (
Krippendorff )
