This　paper　introduces　a　consensus　reaching　process　(CRP)　able　to　smooth　disagreements　between　the　experts　who　participate　in　a　multi-criteria　group　decision-making　problem　in　order　to　obtain　a　solution　in　which　experts　agree.　To　deal　with　the　lack　of　information　and　uncertainty　inherent　in　this　type　of　problems,　the　experts＇　preferences　are　modeled　by　means　of　interval-valued　hesitant　fuzzy　sets　(IVHFS),　which　allow　both　representing　uncertainty　and　any　doubts　experts　may　have　when　giving　their　assessments　over　the　alternatives.　The　proposal　makes　use　of　an　extension　of　the　ordered　weight　averaging　operator　under　an　IVHFS　which　performs　aggregations　reasonably.　In　addition,　the　CRP　incorporates　a　feedback　mechanism　that　provides　precise　and　individual　suggestions　to　the　experts　for　increasing　the　level　of　agreement　within　the　group.　Finally,　the　proposal　is　validated　by　solving　a　practical　study　related　to　the　selection　of　renewable　energies　in　China　under　several　scenarios.