On the relationship between the separability measures and the Bayes probability of error

The information measures, as a special class of efficiency measures of muiticategory information systems, and their relations to the Bayes probability of error have been recently defined and investigated. Another class of efficiency measures called the separability measures is introduced in this paper. The relationship between any separability measure and is determined for any , where denotes the number of categories in a multicategory information system. As before, and criteria are proposed as the similarity measures between the separability measures and . The problems of determination, for any , of all the separability measures with minimal and criteria, called -optimal and -Optimal, are defined and completely solved, respectively. The minimal values of and criteria are evaluated as well. It is proved that the information measures are for each more similar to than the separability measures with respect to the minimal values of both and criteria. It is pointed out that the average conditional quadratic entropy is not only an information measure but also a separability measure, which is, for each -optimal and very close to -optimal separability measures with respect to the criterion.