Correlation　clustering　problem　is　a　clustering　problem　which　has　many　applications　such　as　protein　interaction　networks,　cross-lingual　link　detection,　communication　networks,　and　social　computing.　In　this　paper,　we　introduce　two　variants　of　correlation　clustering　problem:　correlation　clustering　problem　on　uncertain　graphs　and　correlation　clustering　problem　with　non-uniform　hard　constrained　cluster　sizes.　Both　problems　overcome　part　of　the　limitations　of　the　existing　variants　of　correlation　clustering　problem　and　have　practical　applications　in　the　real　world.　We　provide　a　constant　approximation　algorithm　and　two　approximation　algorithms　for　the　former　and　the　latter　problem,　respectively.