Due　to　the　complicated　data　dependencies　between　the　tasks　in　a　workflow　application　and　the　heterogeneous　resources　in　edge-cloud　environments,　it　is　difficult　to　select　an　optimal　tasks-servers　solution　for　scheduling　workflow　applications　in　the　complex　environments.　Current　research　on　workflow　applications　scheduling　is　mainly　concentrated　on　certain　conditions,　ignoring　the　fact　that　the　scheduling　environments　usually　fluctuate.　In　this　article,　we　deal　with　reducing　the　execution　cost　of　multiple　workflow　applications　within　the　corresponding　deadline　constraints　and　improving　the　network　robustness　in　fuzzy　edge-cloud　environments.　Triangular　Fuzzy　Numbers　(TFNs)　are　employed　to　describe　the　computing　capacity　of　servers　and　the　bandwidth　between　them　in　uncertain　environments.　Specially,　a　novel　Scheduling　Strategy　based　on　Particle　Swarm　Optimization　algorithm　employing　the　Quadratic　Penalty　Function　(SSPSO_QPF)　is　proposed　for　scheduling　multiple　workflow　applications.　Compared　with　other　classic　scheduling　strategies,　simulation　results　demonstrate　that　the　proposed　strategy　can　generate　feasible　scheduling　schemes　even　with　the　strict　deadline　constraints,　and　significantly　reduce　the　fuzzy　execution　cost　of　multiple　workflow　applications.　©　2013　IEEE.