On the relationship between the efficiency measures of multicategory information systems

The concepts of efficiency measures of multicategory information systems and similarity measures between two efficiency measures are introduced and developed. The relationship between two efficiency measures is defined by the corresponding setD, and the appropriate marginal functions are introduced. An earlier work of Ben-Bassat's dealing with the ranking of features according to feature selection criteria is generalized and refined. Consequently, a general similarity measure between two efficiency measures is established. It is analyzed in the case of monotonic marginal functions and, especially, when the setDis convex. Some important sufficient conditions forDto be convex are also given. Finally, two other similarity measures are defined and interpreted.