Distributed　optimization　methods　have　been　vastly　investigated　and　approved　by　the　researchers　due　to　their　major　advantages　including　high　accuracy,　secured　performance　and　low　time-consuming　structure　compared　to　the　centralized　frameworks.　This　paper　aims　to　provide　a　novel　method　based　on　fuzzy　primal-dual　method　of　multipliers　(PDMM)　to　manage　the　optimal　energy　scheduling　problem　in　the　smart　grids.　The　proposed　method　illustrates　some　unrivaled　points　of　interest　which　are　more　preferable　than　the　conventional　alternating　direction　method　of　multipliers　(ADMM)　in　terms　of　preciseness　and　convergence　speed.　The　proposed　smart　grid　is　constructed　of　different　components　such　as　generators,　wind　park　and　storage　devices　as　two　of　the　most　profitable　and　applicable　energy　sources　in　the　power　grids.　In　order　to　model　the　uncertainty　effects,　a　stochastic　method　based　on　fuzzy　cloud　theory　is　developed　to　capture　the　high-dimension　uncertainty　in　a　more　realistic　way.　The　units　are　scheduled　to　exchange　energy　in　the　smart　grid　in　a　fully　distributed　manner　when　meeting　the　active/reactive　generation　and　demand　balance.　Such　an　energy　exchanging　process　continues　until　a　proper　solution　would　be　found　through　which　all　the　agents　in　the　system　are　satiated.　The　simulation　results　on　the　IEEE　24-bus　test　system　indicate　that　the　proposed　stochastic　distributed　energy　management　framework　yields　an　error　of　less　than　0.018%　compared　to　the　centralized　approach.