Through　adding　a　discounted　factor,　Shapley　values　of　cooperative　games　are　extended　to　interval-valued　(IV)　cooperative　games.　The　main　purpose　of　this　paper　is　to　propose　the　concept　of　IV　discounted　Shapley　values　and　hereby　develop　a　simplified　method　for　computing　IV　discounted　Shapley　values　for　a　class　of　IV　cooperative　games.　In　this　method,　we　introduce　the　concept　of　discounted　Shapley　values　of　-cooperative　games　associated　with　IV　cooperative　games　for　any　attitude　factor　alpha　is　an　element　of[0,1]　and　find　a　weaker　coalition　monotonicity-like　condition　so　that　the　defined　discounted　Shapley　values　possess　the　monotonicity.　Hence　we　can　obtain　the　analytical　formula　of　IV　discounted　Shapley　value　of　any　IV　cooperative　game　with　the　coalition　monotonicity-like　through　utilizing　only　the　lower　and　upper　bounds　of　coalitions＇　IV　values.　The　proposed　method　utilizes　the　weaker　coalition　monotonicity-like　condition　rather　than　the　irreversible　interval　subtraction　and　hereby　can　effectively　overcome　some　irrational　issues.