Permutation　flow　shop　scheduling　problems　(PFSPs)　with　many　objectives　are　highly　important　scheduling　problems　in　operations　research.　They　have　attracted　substantial　attention　from　enterprise　operators　and　researchers　in　recent　years.　In　this　article,　a　membership　function　is　used　to　connect　the　function　values　of　many-objective　optimization　problems　with　a　fuzzy　membership　degree.　An　approach　for　mapping　function　values　to　fuzzy　sets　is　presented.　Thus,　the　fuzzy　relative　entropy　(FRE)　can　be　employed　in　many-objective　PFSPs.　A　many-objective　PFSP　model　with　four　objectives,　namely,　the　makespan,　total　tardiness,　inventory　holding　cost,　and　energy　consumption　cost,　is　established.　The　optimal　foraging　algorithm　(OFA)　with　FRE　(OFA/FRE)　is　proposed　for　solving　many-objective　PFSPs.　FRE　is　used　as　the　fitness　strategy　of　OFA.　OFA/FRE　is　evaluated　in　three　classification　experiments　and　compared　with　five　algorithms　on　the　Walking-Fish-Group　test　suite,　PFSP　benchmark　instances,　and　a　practical　PFSP　for　machine　tool　components.　The　results　demonstrate　that　OFA/FRE　is　a　promising　tool　for　many-objective　PFSP.　The　FRE　can　be　used　in　scheduling　problems　and　in　many-objective　optimization　problems.