Monotonic classification is a special ordinal classification task that involves monotonicity constraints between features and the decision. Monotonic feature selection can reduce dimensionality while preserving the monotonicity constraints, ultimately improving the efficiency and performance of monotonic classifiers. However, existing feature selection algorithms cannot handle large-scale monotonic data sets due to their lack of consideration for monotonic constraints or their high computational complexities. To address these issues, building on our team's previous research, we define the monotonic related family method with lower time complexity to select informative features and obtain multi-reducts carrying complementary information from multi-view for raw feature space. Using bi-directional rank mutual information, we build two trees for each feature subset and fuse all trees using the corresponding decision support level (BFMDT). Compared with six representative algorithms for monotonic feature selection, BFMDT's average classification accuracy increased by 4.06% (FFREMT), 6.77% (FCMT), 5.61% (FPRS_up), 6.05% (FPRS_down), 5.86%(FPRS_global), 4.41% (Bagging), 7.65% (REMT) and 21.89% (FMKNN), the average execution time compared to tree-based algorithms decreased by 83.41% (FFREMT), 96.96% (FCMT), 75.64% (FPRS_up), 59.43% (FPRS_down), 84.65%(FPRS_global), 81.50% (Bagging) and 63.41% (REMT), while most of comparing algorithms were unable to complete computation on six high-dimensional datasets.