The　belief-rule-based　system　(BRBS)　is　one　of　the　most　visible　and　fastest　growing　branches　of　decision　support　systems.　As　the　knowledge　base　in　the　BRBS,　the　belief-rule-base　(BRB)　is　required　to　be　equipped　with　the　optimal　parameters　and　structure,　which　means　the　optimal　value　and　number　of　parameters,　respectively.　Several　optimization　methods　were　therefore　proposed　in　the　past　decade.　However,　these　methods　presented　different　limitations,　such　as　the　use　of　the　incomplete　parameter　optimization　model,　lack　of　structure　optimization,　and　so　on.　Moreover,　it　is　impracticable　to　determine　the　optimal　parameters　and　structure　of　a　BRB　using　the　training　error　because　of　over-fitting.　The　present　work　is　focused　on　the　joint　optimization　on　parameter　and　structure　for　the　BRB.　Firstly,　a　simple　example　is　utilized　to　illustrate　and　analyze　the　generalization　capability　of　the　BRBS　under　different　numbers　of　rules,　which　unveils　the　underlying　information　that　the　BRBS　with　a　small　training　error　may　not　have　superior　approximation　performances.　Furthermore,　by　using　the　Hoeffding　inequality　theorem　in　probability　theory,　it　is　a　constructive　proof　that　the　generalization　error　could　be　a　better　choice　of　criterion　and　measurement　to　determine　the　optimal　parameters　and　structure　of　a　BRB.　Based　on　the　above　results,　a　heuristic　strategy　to　optimize　the　structure　of　the　BRB　is　proposed,　which　is　followed　by　a　parameter　optimization　method　using　the　differential　evolution　(DE)　algorithm.　Finally,　a　joint　optimization　method　is　introduced　to　optimize　the　parameters　and　structure　of　the　BRB　simultaneously.　In　order　to　verify　the　generality　and　effectiveness　of　the　proposed　method,　two　practical　case　studies,　namely　oil　pipeline　leak　detection　and　bridge　risk　assessment,　are　examined　to　demonstrate　how　the　proposed　method　can　be　implemented　in　the　BRB　under　disjunctive　and　conjunctive　assumptions　along　with　their　performance　comparative　analysis.　(C)　2017　Elsevier　B.V.　All　rights　reserved: