In　decision-making　analysis,　the　description　on　decision　makers＇　risk　attitude　under　uncertainty　is　a　focus　topic.　This　paper　presents　a　novel　decision　analysis　framework　that　considers　uncertainty　and　risk　using　the　cumulative　prospect　theory.　The　proposed　approach　describes　uncertain　preference　information　using　interval-valued　fuzzy　sets,　maintaining　this　representation　without　converting　intervals　into　crisp　numbers　throughout　the　entire　process.　To　quantify　the　distance　between　interval-valued　fuzzy　sets,　we　introduce　a　comprehensive　interval-valued　distance　model　that　accounts　for　multiple　situations　determined　based　on　the　relative　positions　between　intervals.　Afterwards,　some　related　theorems　about　the　proposed　interval-valued　distance　model　are　explored　mathematically.　Then,　with　the　aid　of　different　reference　points　and　interval-valued　distance　model,　the　overall　interval-valued　prospect　value　of　each　alternative　is　investigated.　Finally,　an　Enhanced　Minimax　Regret-based　(EMR)　approach　is　developed　to　compare　and　rank　the　obtained　overall　interval-valued　prospect　values.　An　illustrative　example,　accompanied　by　detailed　discussions,　is　provided　to　demonstrate　the　flexibility　and　superiority　of　the　proposed　decision　analysis　framework.　©　2024　Elsevier　B.V.