With　the　rapid　development　of　Internet　of　Everything　(IoE)　and　the　popularization　of　4G/5G　wireless　networks,　edge　computing　has　gradually　become　the　mainstream.　In　actual　edge　environment,　some　factors　have　an　uncertain　impact　on　scientific　workflow　scheduling,　such　as　CPU　load　and　bandwidth　fluctuations　of　servers.　Aiming　at　scientific　workflow　scheduling　under　uncertain　edge　environment,　based　on　fuzzy　theory,　triangular　fuzzy　numbers　(TFNs)　were　used　to　represent　task　computation　time　and　data　transmission　time.　In　addition,　an　Adaptive　Discrete　Fuzzy　GA-based　Particle　Swarm　Optimization　(ADFGA-PSO)　is　proposed　to　reduce　the　fuzzy　execution　cost　while　satisfying　the　scientific　workflow’s　deadline.　The　uncertainty　of　workflow　scheduling　was　introduced,　which　caused　by　server　execution　performance　fluctuations　during　task　computation　and　bandwidth　fluctuations　during　data　transmission.　Meanwhile,　two-dimensional　discrete　particle　is　adopted　to　encode　the　fuzzy　scheduling　strategy　of　workflow,　and　the　two-point　crossover　operator,　neighborhood　mutation　and　adaptive　multipoint　mutation　operator　of　genetic　algorithm　(GA)　were　introduced　to　improve　the　diversity　of　population　and　avoid　the　local　optimum.　Experimental　results　show　that　compared　with　other　algorithms,　ADFGA-PSO　can　obtain　better　fuzzy　execution　cost　for　deadline-constrained　workflow　scheduling　under　uncertain　edge　environment.　©　2021,　Springer　Nature　Singapore　Pte　Ltd.