Considering　both　cardinal　characteristics　and　double　powers,　the　anti-symmetric　interval　excess　value　is　defined.　The　least　square　pre-nucleolus　for　interval　cooperative　games　is　presented　by　making　a　single-objective　programming　model.　We　obtain　the　analytic　expression　of　least　square　pre-nucleolus　using　Lagrange　multiplier　method,　and　construct　an　effective　quadratic　programming　model　to　derive　the　least　square　pre-nucleolus　of　incomplete　interval　cooperative　games.　In　addition,　the　application　of　least　square　pre-nucleolus　in　land　pollution　control　is　provided　to　show　the　validity　of　the　proposed　solution　concepts.　©　2020　-　IOS　Press　and　the　authors.　All　rights　reserved.