Due　to　stochasticity　and　uncertainty　of　malicious　Web　services　over　the　Internet,　it　becomes　difficult　to　select　reliable　services　while　meeting　non-functional　requirements　in　service-oriented　systems.　To　avoid　the　unreliable　real-world　process　of　obtaining　services,　this　paper　proposes　a　novel　service　selection　approach　via　two-phase　decisions　for　enhancing　the　reliability　of　service-oriented　systems.　In　the　first-phase　decision,　we　define　the　problem　of　finding　reliable　service　candidates　as　a　multiple　criteria　decision　making　(MCDM)　problem.　Then,　we　construct　a　decision　model　to　address　the　problem.　In　the　second-phase　decision,　we　define　the　problem　of　selecting　services　based　on　nonfunctional　requirements　as　an　optimization　problem.　Finally,　we　propose　a　convex　hull　based　approach　for　solving　the　optimization　problem.　Large-scale　and　real-world　experiments　are　conducted　to　show　the　advantages　of　the　proposed　approach.　The　evaluation　results　confirm　that　our　approach　achieves　higher　success　rate　and　less　computation　time　to　guarantee　the　reliability　when　compared　to　the　other　state-of-the-art　approaches.　(C)　2017　Elsevier　Inc.　All　rights　reserved.