Portfolio　selection　can　be　regarded　as　a　type　of　multi-objective　decision　problem.　However,　traditional　solution　methods　rarely　discussed　the　decision　maker＇s　nonsatisfaction　and　hesitation　degrees　with　regard　to　multiple　objectives　and　they　require　many　extra　binary　variables,　which　lead　to　tedious　computational　burden.　Based　on　the　above,　the　aim　of　this　paper　is　to　develop　a　new　and　unified　intuitionistic　fuzzy　multi-objective　linear　programming　(IFMOLP)　model　for　such　portfolio　selection　problems.　The　nonmembership　functions　are　constructed　by　the　pessimistic,　optimistic,　and　mixed　approaches　so　as　to　perfect　the　traditional　intuitionistic　fizzy　(IF)　inequalities　and　IF　theory.　The　decision　maker＇s　hesitation　degrees　with　regard　to　multiple　objectives　are　represented　by　using　IF　inequalities,　and　the　new　IFMOLP　model　based　on　IF　inequalities　is　proposed.　The　IFMOLP　problems　are　solved　by　the　S-shaped　membership　functions　without　extra　binary　variables　required　by　the　piecewise-linear　method.　Finally,　the　portfolio　selection　model　under　IF　environments　based　on　IFMOLP　is　established,　and　a　real　example　is　analyzed　to　demonstrate　its　validity　and　superiority.　The　developed　unified　IFMOLP　model　and　method　can　not　only　effectively　solve　multi-objective　decision　problems　with　nonsatisfaction　and　hesitation　degrees　but　also　remarkably　reduce　the　complexity　of　the　nondeterministic　polynomial-hard　problems.　©　2021　World　Scientific　Publishing　Company.