## 5 Conclusions  
This study developed a multi-dimensional index system of LCCC based on the theory of carrying capacity, evaluated the LCCC of Liaoning Province using the normal cloud model and entropy methods, and examined its interaction using coupling and coordination degrees. To address issues such as incomplete indicators, mixed qualitative and quantitative descriptions, and uncertainty in the process of LCCC evaluation, a multi-dimensional LCCC evaluation method based on the normal cloud model was proposed in this study. It included four primary indicators (geological conditions, resources and environment, economic scale, and urban construction) and 19 secondary indicators to evaluate LCCC. The results showed that the determinacy of the different evaluation levels Ex, En and He can be obtained according to the numerical characteristics obtained from the normal cloud model through the generator algorithm, so as to determine the carrying capacity level of the land. Since this model was able to consider LCCC in terms of both quantitative results and the reliability of the results, it promotes the scientific application of uncertainty theory in the field of comprehensive land evaluation as well as carrying capacity.  
In addition, the practical results of applying the normal cloud model to LCCC evaluation showed that prefecture-level cities in Liaoning Province had significantly different LCCCs. Greater capacity was seen in cities with mature economies and comparatively adequate infrastructure. As a result, Liaoning Province's spatial distribution of total land carrying capacity remained unbalanced, exhibiting \"low in the west and high in the east\" characteristics overall. In Liaoning Province's prefecture-level cities, there was minor variation in the coupling and coordination degrees of the LCCC system, with overall consistency. However, the coordination degree also exhibited the \"low in the west and high in the east\" spatial distribution characteristics.  
Conceptualization, H.Y.; investigation, H.Y. and X.Z.; methodology, H.Y. and X.Z.; software, X.Z. and Y.X.; data curation, W.Y. and Y.X.; validation, H.Y.; writing--original draft preparation, H.Y.; writing--review and editing, Y.G. and W.S.; project administration, W.Y.; visualization, X.Z., W.Y. and Y.X.; resources, Y.G.; supervision, Y.G. and W.S.; funding acquisition, Y.G., W.S. and D.S. All authors have read and agreed to the published version of the manuscript.  
This research study was supported by the National Natural Science Foundation of China (grant no. 41771178, 42030409), the Fundamental Research Funds for the Central Universities (grant no. N2111003), the Basic Scientific Research Project (Key Project) of the Education Department of Liaoning Province (grant no. IJKZ0964), the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (grant no. 2019 QZKK1004), and the Innovative Talents Support Program of Liaoning Province (grant no. LR2017017).  
Not applicable.  
**Data Availability Statement**: Except for the quotation noted, the data are from the authors' own measurements and calculations.  
**Conflicts of Interest**: The authors declare no conflict of interest.