## 6 Conclusions  
Predicting the missing values of FR is necessary in requirements modeling of product customized design. In this study, a multi-layer framework for prediction is introduced with the KNN's strengths in continuous variable prediction and SVM's advantages in categorical variables prediction. A case study on elevator customized design validates the effectiveness and feasibility of the proposed approach. To conclude, the proposed approach reveals the following advantages:  
(1) A layered KNN-SVM approach is proposed to predict the missing values of FR efficiently. It focuses on a potential problem arising in requirements modeling, therefore, helps provide the complete function requirements to managers to design products that fulfill individual customer requirements.  
(2) The proposed layered KNN-SVM approach, considering continuous and categorical variables synchronously, outperforms other five single and five composite methods in terms of RMSE, Ang, Len, and FSN. Specifically, KNN-SVM results in average reduction in RMSE of 46%, 39%, 30%, and 21% against KNN-SVD, KNN, KNN-Bay, and KNN-Tree, respectively. The computation time of KNN-SVM is always less than two seconds, which is acceptable in practical applications.  
(3) The proposed layered KNN-SVM approach also performs better in cold- and warm-start scenarios than other methods. With the number of FRs increasing in the cold-start scenario, KNN-SVM can provide valuable and effective predicted results to managers. In the warm-start scenario, which is the common scenario in practical application, managers can obtain the accurate predicted results using KNN-SVM even in the high missing rate cases.  
(4) The case analysis and practical application on real-world customized elevator validate the reasonability and reliability of the proposed layered KNN-SVM approach. The predicted results of categorical variables in FR (such as requirements of hoisting system and cab) are almost the same as the ground truth. The predicted results of continuous variables in FR (such as speed and requirements of building information) can provide valuable results to managers. With the help of the proposed approach, managers can obtain complete and correct requirements and improve the design efficiency in design process.  
In the future work, the proposed approach can be improved. For example, the predicted results of continuous variables in FR could be the numerical range, where the single value is less helpful to managers. KNN can be improved or integrated with other state-of-the-art algorithms to improve the performance in the missing continuous variables prediction. Furthermore, more validation is necessitated in other real-world customized products. The developed design tool for manufacturers can be improved for better human-computer interaction. Although this approach is applied in the domain of manufacturing, exploring and researching whether the proposed approach might be useful in filling in missing data in other domains are worthy and meaningful.  
Conceptualization, Y.G. and S.Z.; methodology, Y.G.; software, Y.G. and Z.W.; validation, L.Q.; formal analysis, Z.W.; resources, L.Z.; data curation, L.Z.; writing--original draft preparation, Y.G.; writing--review and editing, S.Z. and L.Q.; project administration, S.Z.; funding acquisition, S.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China, grant number 2018 YFB1700701, the National Natural Science Foundation of China, grant number 51875516, and Jiangsu Province Science and Technology Achievement Transforming Fund Project, China, grant number BA2018083.  
Not applicable.