Modelling　with　fuzzy　relations　in　approximate　reasoning　is　obstructed　sometimes　by　the　inconsistency　of　obtained　fuzzy　relational　equations.　This　paper　tackles　the　inconsistency　resolving　problem　for　a　finite　system　of　max–min　equations　by　modifying　only　the　right-hand　side　vector　as　slightly　as　possible　with　respect　to　the　sum　of　absolute　deviations.　It　is　demonstrated　that　this　problem　may　be　reformulated　equivalently　as　a　polynomial-sized　mixed　integer　linear　programming　problem.　Although　such　a　reformulation　results　in　a　problem　of　much　larger　size　than　its　original　compact　form,　it　may　be　solved　to　optimality　on　instances　of　moderate　size　or　even　large　size　by　an　off-the-shelf　solver　for　mixed　integer　linear　programming　and　in　some　sense　does　not　require　a　tailored　solving　method.　©　2024　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.