Although　medical　waste　usually　accounts　for　a　small　fraction　of　urban　municipal　waste,　its　proper　disposal　has　been　a　challenging　issue　as　it　often　contains　infectious,　radioactive,　or　hazardous　waste.　This　article　proposes　a　two-level　hierarchical　multicriteria　decision　model　to　address　medical　waste　disposal　method　selection　(MWDMS),　where　disposal　methods　are　assessed　against　different　criteria　as　intuitionistic　fuzzy　preference　relations　and　criteria　weights　are　furnished　as　real　values.　This　paper　first　introduces　new　operations　for　a　special　class　of　intuitionistic　fuzzy　values,　whose　membership　and　non-membership　information　is　cross　ratio　based]0,　1[-values.　New　score　and　accuracy　functions　are　defined　in　order　to　develop　a　comparison　approach　for]0,　1[-valued　intuitionistic　fuzzy　numbers.　A　weighted　geometric　operator　is　then　put　forward　to　aggregate　a　collection　of]0,　1[-valued　intuitionistic　fuzzy　values.　Similar　to　Saaty’s　1–9　scale,　this　paper　proposes　a　cross-ratio-based　bipolar　0.1–0.9　scale　to　characterize　pairwise　comparison　results.　Subsequently,　a　two-level　hierarchical　structure　is　formulated　to　handle　multicriteria　decision　problems　with　intuitionistic　preference　relations.　Finally,　the　proposed　decision　framework　is　applied　to　MWDMS　to　illustrate　its　feasibility　and　effectiveness.　©　2016　by　the　authors;　licensee　MDPI,　Basel,　Switzerland.