▁the ▁resulting ▁type - 2 ▁f uz zy ▁set ▁is ▁called ▁a ▁general ▁type - 2 ▁f uz zy ▁set ▁( to ▁distinguish ▁it ▁from ▁the ▁special ▁interval ▁type - 2 ▁f uz zy ▁set ). ▁ ▁Prof . ▁Z ade h ▁didn ' t ▁stop ▁with ▁type - 2 ▁f uz zy ▁sets , ▁because ▁in ▁that ▁ 1 9 7 6 ▁paper ▁he ▁also ▁generalized ▁all ▁of ▁this ▁to ▁type - n ▁f uz zy ▁sets . ▁The ▁present ▁article ▁focus es ▁only ▁on ▁type - 2 ▁f uz zy ▁sets ▁because ▁they ▁are ▁the ▁next ▁step ▁in ▁the ▁logical ▁pro gression ▁from ▁type - 1 ▁to ▁type - n ▁f uz zy ▁sets , ▁where ▁n ▁= ▁ 1 , ▁ 2 , ▁… ▁. ▁Although ▁some ▁research ers ▁are ▁beginning ▁to ▁explore ▁higher ▁than ▁type - 2 ▁f uz zy ▁sets , ▁as ▁of ▁early ▁ 2 0 0 9 , ▁this ▁work ▁is ▁in ▁its ▁inf ancy . ▁ ▁The ▁membership ▁function ▁of ▁a ▁general ▁type - 2 ▁f uz zy ▁set , ▁ Ã , ▁is ▁three - dimensional ▁( Fig . ▁ 1 ), ▁where ▁the ▁third ▁dimension ▁is ▁the ▁value ▁of ▁the ▁membership ▁function ▁at ▁each ▁point ▁on ▁its ▁two - dimensional ▁domain ▁that ▁is ▁called ▁its ▁foot print ▁of ▁uncertainty ▁( FO U ). ▁ ▁For ▁an ▁interval ▁type - 2 ▁f uz zy ▁set ▁that ▁third - dim ension ▁value ▁is ▁the ▁same ▁( e . g ., ▁ 1 ) ▁everywhere ,