Recommender　systems　aim　to　identify　items　that　a　user　may　like.　In　this　paper,　we　discuss　a　three-way　decision　approach　which　provides　a　more　meaningful　way　to　recommend　items　to　a　user.　Besides　recommended　items　and　not　recommended　items,　the　proposed　model　adds　a　set　of　items　that　are　possibly　recommended　to　users.　In　the　model,　we　focus　on　two　issues.　One　is　the　computation　of　required　thresholds　to　define　the　three　sets　based　on　the　decision-theoretic　rough　set　model.　The　other　is　the　notion　of　user　preference　on　the　three　sets　which　forms　the　basis　of　a　ranking　strategy,　and　then　a　pair-wise　preference　learning　algorithm　using　gradient　descent　is　adopted　for　inferring　latent　vectors　for　users　and　items.　Working　with　a　sigmoid　function　of　a　product　of　a　user　and　item　latent　vector,　we　estimate　the　probability　that　the　user　prefers　the　item　to　make　recommendations.　Experimental　results　show　that　the　proposed　method　improves　recommendation　quality　from　the　cost-sensitive　view.　(C)　2017　Elsevier　Inc.　All　rights　reserved.