To　solve　the　partner　selection　problem　with　fuzzy　completion　time　and　due　date　in　a　virtual　enterprise,　a　new　method　based　on　Vague　sets　was　proposed.　Based　on　the　concept　of　delivery　time　satisfiability　degree,　the　formulated　partner　selection　problem　was　interpreted　so　as　to　maximize　the　delivery　time　satisfiability　degree　index.　The　model　took　into　account　the　factors　of　delivery　time　satisfiability　degree,　cost　and　the　precedence　of　tasks.　Standard　particle　swarm　optimization(PSO)　algorithm　was　easily　trapped　in　local　optimum,　so　chaotic　searching　behavior　was　incorporated　into　standard　PSO　algorithm　and　a　CPSO　algorithm　was　proposed　to　solve　the　problem.　The　simulation　of　an　example　demonstrates　that　the　local　searching　capability　of　the　CPSO　algorithm　is　much　better　than　that　of　standard　PSO　algorithm.