For　the　multi-objective　flow　shop　scheduling　problem　in　the　supply　chain　environment,　this　paper　proposes　the　Fuzzy　Relevance　Entropy　method　(FREM)　to　solve　the　adaptive　value　assignment　problem　in　the　multi-objective　optimization　process　of　the　supply　chain　environment　by　combining　Fuzzy　Information　Entropy　Theory　(FIET)　and　Degree　of　Membership　Function　(DMF).　Firstly,　the　uncertainty　of　each　sub-objective　of　the　ideal　solution　and　Pareto　solution　of　the　objective　is　extracted　using　the　Degree　of　Membership　Function.　Secondly,　each　solution　is　mapped　into　an　affiliation　degree　fuzzy　set　and　the　information　contained　in　the　fuzzy　set　is　reprocessed　using　Fuzzy　Information　Entropy　Theory.　Finally,　the　amount　of　information　contained　in　the　ideal　solution　solved　by　the　Pareto　method　is　used　to　guide　the　evolution　of　the　Particle　Swarm　Optimization　(PSO)　algorithm,　thus　avoiding　the　traditional　multi-objective　optimization　process　of　assigning　weights　to　solve　the　fitness　link.　This　paper　combines　both　the　Fuzzy　Relevance　Entropy　method　and　the　Stochastic　Weight　method　with　Particle　Swarm　Optimization　(PSO)　and　Differential　Evolution　(DE)　algorithms　to　address　the　five-objective　flow　shop　scheduling　problem　in　the　supply　chain　environment.　Experimental　results　demonstrate　that　the　proposed　Fuzzy　Relevance　Entropy　method　effectively　solves　the　multi-objective　flow　shop　scheduling　problem　in　the　supply　chain　environment　and　achieves　better　optimization　results　compared　to　the　Stochastic　Weight　method.　©　The　Author(s)　2023.