A rough set approach to measuring information granules

This article introduces an approach to measures of information granules based on rough set theory. Informally, an information granule is a representation of a multiset (or bag) of real-world objects that are somehow indistinguishable, or similar, or which cause the same functionality. Examples of measures of information granules based on the rough set theory are inclusion, closeness, size, and enclosure. All of these measures are based on rough inclusion. This paper is limited to a consideration of measures of inclusion based on a straightforward extension of classical rough membership functions and closeness based on measurement of separation of equivalence classes in a partition of the universe containing information granules. Measurement of sensor-based information granules has been motivated by recent studies of sensor signals. A sensor signal is a non-empty, finite set of sample sensor signal values temporally ordered. Classification of sensor signals requires measurements of sample signal values over subintervals of time. This article introduces a rough set approach to measuring information granule inclusion and closeness.