Granular Structures Induced by Interval Sets and Rough Sets
An interval set is a family of sets restricted by a upper bound and lower bound. Interval-set algebras are concrete models of granular computing. The triarchic theory of granular computing focuses on a multilevel and multi-view granular structure. This paper discusses granular structures of interval sets under inclusion relations between two interval sets from a measurement-theoretic perspective and set-theoretic perspective, respectively. From a measurement-theoretic perspective, this paper discusses preferences on two objects represented by interval sets under inclusion relations on interval sets. From a set-theoretic perspective, this paper uses different inclusion relations and operations on interval sets to construct multilevel and multi-view granular structures.
KeywordsGranular computing Granular structure Interval set
Authors thanks Prof. Yiyu Yao from the University of Regina for his constructive suggestions on this paper.
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