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.