Partner　selection　is　a　major　issue　in　the　formation　of　a　virtual　enterprise.　In　practice,　in　the　partner　selection　process,　the　information　about　the　candidates　and　their　performances　are　incomplete　and　uncertain.　Vague　sets　theory　is　one　of　the　methods　used　to　deal　with　uncertain　information.　In　this　paper,　a　new　method　based　on　vague　sets　is　proposed　to　deal　with　the　partner　selection　problem　in　the　formation　of　a　virtual　enterprise　while　the　factors　of　satisfaction　degree,　due　date,　cost　and　the　precedence　of　tasks　are　taken　into　account.　On　the　basis　of　the　agreement　index　of　satisfaction　degree,　the　formulated　partner　selection　problems　are　interpreted　so　as　to　maximize　the　minimum　agreement　index.　To　solve　the　problem,　an　improved　particle　swarm　optimization　(PSO)　algorithm　is　proposed.　Finally,　the　simulation　of　a　numerical　example　demonstrates　that　the　method　is　effective.　(C)　2011　Elsevier　Ltd.　All　rights　reserved.