A trilevel analysis of uncertainty measuresin partition-based granular computing

Uncertainty measure is one of the most significant concepts and fundamental issues in granular computing. Nowadays, there have been extensive studies on various uncertainty measures for quantifying diverse properties and associations of granules and granular structures. However, there is a lack of a systematic study for uncertain measures. Based on a trilevel thinking framework, this paper presents a systematic review and analysis of uncertainty measures used in partition-based models of granular computing. At an object level, a granule level and a granular structure level, we categorize uncertainty measures for describing the properties and the associations of objects, granules, and partitions respectively. Moreover, we illustrate how to construct an uncertainty measure at a higher level from a lower level. At last, we discuss several potential directions to design other new uncertainty measures for partition-based granular computing.