There　are　not　effective　and　practical　methods　for　interval-valued　(IV)　cooperative　games　due　to　the　invertible　interval　subtraction.　This　paper　focuses　on　developing　a　fast　and　simplified　approach　to　computing　IV　egalitarian　Shapley　values　for　such　a　rather　large　subclass　of　IV　cooperative　games.　In　this　method,　through　adding　some　weaker　coalition　monotonicity-like　conditions,　it　is　proven　that　egalitarian　Shapley　value　is　monotonic　and　non-decreasing.　Hence,　the　IV　egalitarian　Shapley　value　of　IV　cooperative　games　can　be　directly　obtained　by　determining　its　lower　and　upper　bounds,　respectively.　The　method　proposed　in　this　paper　does　not　use　the　Moore＇s　interval　subtraction　and　hereby　can　effectively　avoid　the　issues　resulted　from　it.　Furthermore,　some　important　properties　of　the　IV　egalitarian　Shapley　values　of　IV　cooperative　games　are　discussed.　The　feasibility　and　applicability　of　the　method　proposed　in　this　paper　are　illustrated　with　real　numerical　examples.