Optimal Scale Selections In Consistent Generalized Multi-Scale Decision Tables

A generalized multi-scale information table is an attribute-value system in which each object under each attribute is represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser labeled value. In such table, diverse attributes have different numbers of levels of scales. In this paper, information granules and optimal scale selections in consistent generalized multi-scale decision tables are studied. The concept of scale combinations in generalized multi-scale information tables is first reviewed. Representation of information granules in generalized multi-scale information tables is then shown. Lower and upper approximations with reference to different levels of granulations in multi-scale information tables are further defined and their properties are presented. Finally, belief and plausibility functions in the Dempster-Shafer theory of evidence are used to characterize optimal scale selections in consistent generalized multi-scale decision tables.