Interval-Value Nested Sets Category

Interval—value　nested　sets　category　is　discussed　in　the　paper.　There　are　three　parts　in　this　paper.　The　first　part　is　foreword.　.We　mainly　introduce　the　significance　of　interval—value　nested　sets　category.　The　second　part　:preliminary　of　knowledge.　We　discuss　all　kinds　of　properties　of　category.　Fuzzy　sets　and　Topos　theories　have　intimate　connections.　From　the　theory　of　nested　sets.　We　introduce　three　new　categories　in　the　third　part　which　called　HSEB1,HSEB2　and　HSEB3.　Their　topoi　properties　are　investigated.　Firstly,　category　HSEB1　is　Cartesian　Closed,　but　it　has　not　SC,　so　it　is　not　a　Topos.　Next,　we　obtain　category　HSEB2　is　a　Topos.　Lastly　the　properties　of　HSEB3　are　investigated　HSEB3　is　not　Cartesian　Closed.　It　has　Terminal　object,Equalizer　and　Exponentials　in　some　conditions,and　it　also　has　Middle　object,but　not　SC.　The　　category　like　that　is　not　a　Wtopos.　We　can　make　clearly　the　difference　between　Topos　and　Wtopos　through　studying　on　it.　On　such　basis,we　can　study　on　what　is　Wtopos　and　their　properties.　In　this　paper　,　we　generalizer　nested　sets　from　one　dimension　to　two　dimension.　On　the　base　of　one　dimension　nested　sets , 　we　can　reduce　the　fluctuation　and　indefiniteness　of　decision　information.