# Leveraging Industry 4.0 for Sustainable Manufacturing: A Quantitative Analysis Using FI-RST
## 2 Methods
### FI-RST Model
#### 2.2.1 FI-RST Model: Application and Conditions
Conditions for FI-RST Model Application  
The FI-RST model was applied under the following conditions:  
Data Availability: sustainability data from 36 firms in Fujian Province were available, including their technology adoption levels and sustainability metrics (e.g., energy savings and waste reduction). Technology Adoption: the firms varied in their adoption of Industry 4.0 technologies, including Manufacturing Execution Systems (MES), Industrial Internet of Things (IIoT), and Additive Manufacturing (AM). The model was applied to examine how the adoption levels of these technologies affected sustainability outcomes. Heterogeneous Impacts: the technologies had non-uniform effects across different firms and sustainability dimensions. The fuzzy logic aspect of the FI-RST model was critical in handling this heterogeneity by allowing for partial membership in different sustainability performance categories. Example of Model Application  
For instance, the Industrial Internet of Things (IIoT) was found to have a high impact on both environmental and economic dimensions. The fuzzy integral aggregated its impact on energy savings and waste reduction, while the rough set theory identified IIoT as a core attribute for firms with high sustainability scores. The Choquet fuzzy integral is applied to handle fuzzy measures and integrate the sustainability scores across different dimensions (economic, environmental, and social). The Choquet integral is defined as follows:  
\[(c)\int hdg=\sum_{i=1}^{n}(h(x_{i})-h(x_{i-1}))g(H_{i})\]  
where \((h(x_{i})\) represents the evaluation of each criterion, and \(g(H_{i})\) represents the fuzzy measure for each subset of criteria. In the context of rough set theory, the model evaluates the upper and lower approximations of the data. For an information system \(IS=(U,A,V,f)\), where \(U\) is the universe of objects, and AAA is the set of attributes, we define the lower approximation as  
\[R(X)=\{x\in U|[x]_{R}\subseteq X\}\]  
and the upper approximation as  
\[R(X)=\{x\in U|[x]_{R}\cap X\
eq\varnothing\}\]  
These formulas provide the mathematical basis for understanding how different Industry 4.0 technologies can influence sustainability through fuzzy evaluations and data approximations. In this study, the FI-RST model was deliberately designed in a way to analyze the triple bottom line of sustainability--that is, economic, environmental, and social impacts resulting or caused by each technology. This methodology is composed of several main transition points: the outset, which is establishing a comprehensive evaluation system that consists of traditional sustainability performance measures, followed by a fuzzy integration to treat imprecision in the previously described dataset, and finally, the rough set theory, the methodology for identifying the different impacts and significances of various Industry 4.0 technologies for the sake of the humanity. This mode of operation involves strong data, gives a valuable multi-upran approach that can cope with a complicated proceeding, and enables us to interpretably assess the sustainability of the production processes. This figure illustrates the step-by-step implementation of the FI-RST model, starting from data collection to final classification and sustainability scoring. Additionally, a new diagram has been added to demonstrate the relationships between the selected technologies and sustainability dimensions.