The　weighted　sum　of　binomial　proportions　and　the　interaction　effect　are　two　important　cases　of　the　linear　combination　of　binomial　proportions.　Existing　confidence　intervals　for　these　two　parameters　are　approximate.　We　apply　the　h　-function　method　to　a　given　approximate　interval　and　obtain　an　exact　interval.　The　process　is　repeated　multiple　times　until　the　final-improved　interval　(exact)　cannot　be　shortened.　In　particular,　for　the　weighted　sum　of　two　proportions,　we　derive　two　final-improved　intervals　based　on　the　(approximate)　adjusted　score　and　fiducial　intervals.　After　comparing　several　currently　used　intervals,　we　recommend　these　two　final-improved　intervals　for　practice.　For　the　weighted　sum　of　three　proportions　and　the　interaction　effect,　the　final-improved　interval　based　on　the　adjusted　score　interval　should　be　used.　Three　real　datasets　are　used　to　detail　how　the　approximate　intervals　are　improved.