Database
[{"Value":1,Time:ISODate("2016-05-18T16:00:00Z"),UpperBound:1,LowerBound:2},{"Value":2,Time:ISODate("2014-05-18T16:00:00Z"),UpperBound:3,LowerBound:4},{"Value":2,Time:ISODate("2019-05-18T16:00:00Z"),UpperBound:5,LowerBound:6}]
Query
db.collection.aggregate([{"$project":{Time:1,UpperBound:1,LowerBound:1,"Value":{"$cond":[{$and:[{$lt:["$Time",ISODate("2015-05-18T16:00:00Z")]},{$gt:["$Time",ISODate("2013-05-18T16:00:00Z")]}]},"$Value","$$REMOVE"]}}}])