A measurement theory view on the granularity of partitions

Measurement of granularity is one of the foundational issues in granular computing. This paper investigates a class of measures of granularity of partitions. The granularity of a set is defined by a strictly monotonic increasing transformation of the cardinality of the set. The granularity of a partition is defined as the expected granularity of all blocks of the partition with respect to the probability distribution defined by the partition. Many existing measures of granularity are instances of the proposed class. New measures of granularity of partitions are also introduced.