This　paper　proposes　a　representation　theorem　for　an　arbitrary　interval-valued　fuzzy　J-equivalence　relations.　Firstly,　we　present　a　note　on　representations　of　fuzzy　T-equivalence　relations　in　which　the　representation　theorem　should　be　applied　to　a　fuzzy　similarity　measure　better.　Secondly,　an　representation　theorem　is　proposed　that　the　interval-valued　fuzzy　J-equivalence　relations　can　be　generated　by　a　family　of　similar　interval-valued　fuzzy　subsets.　Then　some　interval-valued　fuzzy　J-equivalence　relations　are　presented.