In　this　paper,　we　define　the　concepts　of　interval-valued　cores　of　interval-valued　multiobjective　n-person　cooperative　games　and　satisfactory　degree　(or　ranking　indexes)　of　comparing　intervals　with　the　features　of　inclusion　and/or　overlap　relations.　Hereby,　the　interval-valued　cores　can　be　computed　by　developing　a　new　two-phase　method　based　on　the　auxiliary　nonlinear　programming　models.　The　proposed　method　can　provide　cooperative　chances　under　the　situations　of　inclusion　and/or　overlap　relations　between　intervals　in　which　the　traditional　interval　ranking　method　may　not　always　assure.　The　feasibility　and　applicability　of　the　models　and　method　proposed　in　this　paper　are　illustrated　with　a　numerical　example.　©　Springer　Nature　Singapore　Pte　Ltd.　2017.