In　this　paper,　an　important　solution　concept　of　interval-valued　(IV)　cooperative　games　with　fuzzy　coalitions,　called　the　IV　least　square　prenucleolus,　is　proposed.　Firstly,　we　determine　the　fuzzy　coalitions’　values　by　using　Choquet　integral　and　hereby　obtain　the　IV　cooperative　games　with　fuzzy　coalitions　in　Choquet　integral　forms.　Then,　we　develop　a　simplified　method　to　compute　the　IV　least　square　prenucleolus　of　a　special　subclass　of　IV　cooperative　games　with　fuzzy　coalitions　in　Choquet　integral　forms.　In　this　method,　we　give　some　weaker　coalition　size　monotonicity-like　conditions,　which　can　always　ensure　that　the　least　square　prenucleolus　of　our　defined　cooperative　games　with　fuzzy　coalitions　in　Choquet　integral　form　are　monotonic　and　non-decreasing　functions　of　fuzzy　coalitions’　values.　Hereby,　the　lower　and　upper　bounds　of　the　proposed　IV　least　square　prenucleolus　can　be　directly　obtained　via　utilizing　the　lower　and　upper　bounds　of　the　IV　coalitions　values,　respectively.　In　addition,　we　investigate　some　important　properties　of　the　IV　least　square　prenucleolus.　The　feasibility　and　applicability　of　the　method　proposed　in　this　paper　are　illustrated　with　numerical　examples.　©　Springer　Nature　Singapore　Pte　Ltd.　2017.