Renewable　energy　is　considered　as　a　promising　solution　to　alleviate　the　exploitation　of　fossil　fuel　energy　and　to　keep　sustainable　development.　Hence,　renewable　energy　investments　are　attracting　more　and　more　attention.　To　solve　the　renewable　energy　investment　problems　under　uncertain　environment,　this　paper　proposes　a　new　multi-criteria　risk　decision-making　method　based　on　interval　type-2　fuzzy　sets　(IT2FSs)　and　regret　theory.　First,　to　describe　the　uncertainty　of　real-world　situation,　the　evaluation　information　is　expressed　by　linguistic　terms　and　encoded　into　IT2FSs.　Second,　a　new　interval　type-2　fuzzy　projection　model　is　proposed　to　measure　the　relationships　between　alternatives　under　interval　type-2　fuzzy　environment.　Then,　to　determine　the　criteria　weights,　a　new　interval　type-2　fuzzy　entropy　weight　determination　model　is　developed.　Moreover,　some　new　rules　are　provided　to　explore　the　difference　between　alternatives　under　different　spaces　(i.e.,　positive　space　and　negative　space).　Finally,　the　regret　theory　is　extended　to　describe　the　psychological　behavior　of　decision　makers　and　select　the　optimal　alternative　under　risk　and　uncertainty　environment.　A　case　study　including　comparative　analysis　is　provided　to　manifest　the　feasibility　and　advantages　of　the　proposed　method.　©　2022　Elsevier　Ltd