Multi-class　and　multi-attribute　are　two　important　features　of　classification　problems　and　have　different　effects　on　the　requirements　and　performance　of　the　classifier.　Decomposition　strategy　and　overlap　function　are　two　effective　ways　to　enhance　the　performance　of　classifiers,　because　the　former　decomposes　a　complex　multi-class　problem　into　multiple　simple　sub-problems;　the　latter　uses　various　functions　to　specify　the　conjunctive　relationship　of　input　variables　in　a　multi-attribute　problem.　Extended　belief　rule-based　system　(EBRBS)　is　an　advanced　rule-based　system　that　has　been　widely　used　in　classification　problems.　In　order　to　apply　decomposition　strategies　and　overlap　functions　to　enhance　the　performance　of　EBRBSs,　the　present　work　focuses　on　the　investigative　research　and　comparative　evaluation　of　the　commonly　used　one-versus-one　(OVO)　decomposition　strategy　and　five　common　overlap　functions　to　improve　the　performance　of　EBRBSs　on　multi-class　and　multi-attribute　problems.　More　specifically,　three　typical　kinds　of　EBRBSs,　namely　original　EBRBS　(O-EBRBS),　EBRBS　with　dynamic　rule　activation　(DRA-EBRBS),　and　a　latest　EBRBS　for　big　data　(Micro-EBRBS),　are　selected　to　conduct　extensive　experimental　studies　on　twenty　classification　problems.　To　best　of　our　knowledge,　this　present　work　is　the　first　time　to　provide　a　meaningful　and　useful　study　in　revealing　the　potential　capability　of　the　EBRBSs　with　decomposition　strategy　and　overlap　function　for　multi-class　and　multi-attribute　problems.　Experimental　results　demonstrate　that　the　square　product　overlap　function　and　the　OVO　strategy　can　enhance　the　performance　of　EBRBSs　over　others　for　twenty　classification　problems.