**6. Conclusions**

An ER rule-based health assessment model for a complex system is proposed, where the transformation matrix is considered. In addition, case study of the bus of control system and the engine is investigated to demonstrate the validity and practicality of the proposed method.

There are mainly two contributions of this paper. First, the transformation matrix is employed to solve the disaccord problem between the input indicator reference grades and assessment result grades, which keeps the consistency and completeness of the possession of the input information transformation. Second, the calculation methods of indicator weight and reliability are conducted, where the qualitative knowledge and quantitative information are fully used. Then, the optimization method of the model is conducted, and a complete health assessment model is constructed.

According to the proposed model, the future research work can be summarized into the following two points:

(1) In engineering practice, the forms of health status threshold can be various, and the forms are not only numerical, but can also be in interval form or normal distribution form. Therefore, how to solve the disaccord problem between the indicators reference grades and assessment result grades under the different forms of threshold should be addressed.

(2) The integration model between deep learning and ER rule can be established based on the good uncertainty processing ability and interpretability of ER rule.

**Author Contributions:** Z.L. and Z.Z. contributed equally to this work. Conceptualization, Z.L. and Z.Z.; methodology, Z.L. and J.W.; software, X.Z.; validation, Z.L., Z.Z. and J.W.; formal analysis, Z.Z. and J.W.; investigation, W.H.; data curation, Z.L.; writing—original draft preparation, Z.L.; writing—review and editing, Z.L. and W.H.; visualization, Z.L.; supervision, W.H. and X.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the Shaanxi Outstanding Youth Science Foundation under Grant 2020JC-34, in part by the Postdoctoral Science Foundation of China under Grant No. 2020M683736, in part by the Natural Science Foundation of Heilongjiang Province of China under Grant No. LH2021F038.

**Institutional Review Board Statement:** Not appliable.

**Informed Consent Statement:** Not appliable.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
