notation ▁of ▁lots ▁of ▁uncertainty . ▁So , ▁what ▁does ▁one ▁do ▁when ▁there ▁is ▁uncertainty ▁about ▁the ▁value ▁of ▁the ▁membership ▁function ? ▁The ▁answer ▁to ▁this ▁question ▁was ▁provided ▁in ▁ 1 9 7 5 ▁by ▁the ▁invent or ▁of ▁f uz zy ▁sets , ▁Prof . ▁Lot fi ▁A . ▁Z ade h , ▁when ▁he ▁proposed ▁more ▁s oph istic ated ▁kinds ▁of ▁f uz zy ▁sets , ▁the ▁first ▁of ▁which ▁he ▁called ▁a ▁type - 2 ▁f uz zy ▁set . ▁A ▁type - 2 ▁f uz zy ▁set ▁lets ▁us ▁incorpor ate ▁uncertainty ▁about ▁the ▁membership ▁function ▁into ▁f uz zy ▁set ▁theory , ▁and ▁is ▁a ▁way ▁to ▁address ▁the ▁above ▁criticism ▁of ▁type - 1 ▁f uz zy ▁sets ▁head - on . ▁And , ▁if ▁there ▁is ▁no ▁uncertainty , ▁then ▁a ▁type - 2 ▁f uz zy ▁set ▁reduces ▁to ▁a ▁type - 1 ▁f uz zy ▁set , ▁which ▁is ▁analog ous ▁to ▁probability ▁reducing ▁to ▁determin ism ▁when ▁un predict ability ▁van ishes . ▁ ▁In ▁order ▁to ▁symbol ically ▁distinguish ▁between ▁a ▁type - 1 ▁f uz zy ▁set ▁and ▁a ▁type - 2 ▁f uz zy ▁set , ▁a ▁til de ▁symbol ▁is ▁put ▁over ▁the ▁symbol ▁for ▁the ▁f uz zy ▁set ; ▁so , ▁A ▁denotes ▁a ▁type - 1 ▁f uz zy ▁set , ▁whereas ▁ Ã ▁denotes ▁the ▁compar able ▁type - 2 ▁f uz zy ▁set . ▁When ▁the ▁latter ▁is ▁done ,