Size relation of uncertain sets with application to clustering

Along with increasing and extension of uncertain set theory in decision making, ordering and ranking of uncertain sets have significantly become relevant, that is, an uncertain set needs to be evaluated and compared with the others. This paper introduces the size relation between two uncertain sets. It derives a formula to calculate the uncertain measure that an uncertain set is less than or equal to another one. Moreover, some examples are given to illustrate the size relation of uncertain sets. Finally, clustering is proposed as an application.