▁type - 1 ▁f uz zy ▁set ) ▁and ▁then ▁compute ▁the ▁center ▁of ▁gravity ▁of ▁the ▁membership ▁function ▁for ▁that ▁set ; ▁compute ▁a ▁weight ed ▁average ▁of ▁the ▁center ▁of ▁grav ities ▁of ▁each ▁of ▁the ▁fired ▁rule ▁consequ ent ▁membership ▁functions ; ▁etc . ▁ ▁Things ▁are ▁somewhat ▁more ▁complicated ▁for ▁an ▁interval ▁type - 2 ▁F LS , ▁because ▁to ▁go ▁from ▁an ▁interval ▁type - 2 ▁f uz zy ▁set ▁to ▁a ▁number ▁( us ually ) ▁requires ▁two ▁steps ▁( Fig . ▁ 3 ). ▁The ▁first ▁step , ▁called ▁type - redu ction , ▁is ▁where ▁an ▁interval ▁type - 2 ▁f uz zy ▁set ▁is ▁reduced ▁to ▁an ▁interval - valu ed ▁type - 1 ▁f uz zy ▁set . ▁There ▁are ▁as ▁many ▁type - redu ction ▁methods ▁as ▁there ▁are ▁type - 1 ▁def uzz ification ▁methods . ▁An ▁algorithm ▁developed ▁by ▁K arn ik ▁and ▁M end el ▁now ▁known ▁as ▁the ▁K M ▁Algorithm ▁is ▁used ▁for ▁type - redu ction . ▁Although ▁this ▁algorithm ▁is ▁iter ative , ▁it ▁is ▁very ▁fast . ▁ ▁The ▁second ▁step ▁of ▁Output ▁Process ing , ▁which ▁occurs ▁after ▁type - redu ction , ▁is ▁still ▁called ▁def uzz ification . ▁Because ▁a ▁type - redu ced ▁set ▁of ▁an ▁interval ▁type - 2 ▁f uz zy ▁set ▁is ▁always ▁a ▁finite ▁interval ▁of ▁numbers , ▁the ▁def uzz ified ▁value ▁is ▁just ▁the ▁average ▁of ▁the ▁two ▁end - points ▁of ▁this ▁interval