ON THE RELATIONSHIP BETWEEN THE INFORMATION MEASURES AND THE BAYES PROBABILITY OF ERROR

Concave measures as a general class of efficiency measures and information measures as a special class of concave measures are defined and investigated. The relationship between any concave measure, information measure in particular, and the Bayes probability of error P//B is determined for any 2 less than equivalent to Q less than infinity , where Q denotes the number of categories in a multicategory information system. The so-called epsilon //0 and epsilon //m criteria are proposed as the similarity measures between the information measures and P//B. The problems of determination, for any 2 less than equivalent to Q less than infinity , of all the information measures with minimal epsilon //0 and epsilon //m criteria, called epsilon //0 -optimal and epsilon //m-optimal, are formulated and completely solved. The minimal values of epsilon //0 and epsilon //m criteria are evaluated as well.