To　solve　many-objective　flow-shop　scheduling　problems　(FSP),　a　genetic　algorithm　based　on　the　relative　entropy　of　fuzzy　sets　(REFS_GA)　is　proposed.　A　mathematical　model　of　the　many-objective　FSP　is　built,　which　involves　four　scheduling　criterions　of　FSP.　In　REFS_GA,　the　Pareto　front　is　mapped　to　fuzzy　set,　and　the　relational　entropy　coefficient　of　fuzzy　sets　is　used　to　measure　the　similarity　between　the　fuzzy　sets　of　Pareto　solutions　and　ideal　solution.　The　coefficient　is　used　as　the　fitness　of　genetic　algorithm　(GA)　and　to　guide　algorithm　evolution.　The　performance　of　REFS_GA　is　evaluated　through　compared　with　GA　based　on　g-dominance　(gGA),　random　weight　GA　(rwGA)　and　the　third　version　of　non-dominated　sorting　genetic　algorithm　(NSGA-III).　Experiments　are　carried　out　with　eight　DTLZ　benchmark　functions,　six　MaF　benchmark　functions　with　4,　7　or　10　objectives,　respectively,　nine　scheduling　problems　with　four　objectives　and　a　real-world　many-objective　FSP.　Experimental　results　show　that　REFS_GA　can　solve　may-objective　benchmark　functions　and　many-objective　FSP.　The　optimisation　solution　and　performance　indicators　of　REFS_GA　are　better　than　gGA,　rwGA　and　NSGA-III.　It　can　be　concluded　that　REFS_GA　is　an　effective　method　to　solve　many-objective　optimisation　problems.　The　main　contributions　of　the　work　are　that　a　four-objective　model　of　FSP　is　built　and　a　priori　approach　based　on　fuzzy　set　is　proposed　to　solve　many-objective　FSP.　©　2019　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.