## 3 Methodology  
### Conceptual Explanation of The Series of Integrative Methodologies  
The purpose of this section is to offer an overview of the whole analytical process, since it was combined with several procedures and methods. This study constructed a hybrid MCDM model. The decision-making trial and evaluation laboratory (DEMATEL) technique is used to build an influential network relation map (INRM); through the analytic network process (ANP), this DEMATEL-based ANP (DANP) was used to obtain influential weights (IWs). Finally, Vlse Kriterijuska Optimizacija Komoromisono Resenje (VIKOR, \"Optimization of Compression Resistance\"), combined with IWs to determine how to reduce gaps to achieve an ideal level, were used to assess the effectiveness of the enforcement of air pollution improvement by the Environmental Protection Bureau of Kaohsiung City Government (see Section 4.2. for a detailed description of this location and data collection). The hybrid MCDM model used in this study is the concept of \"gap\" [49]. This model believes that people will naturally pursue a level of aspiration, which is the concept of a perfect score. As a result, decision makers can clearly understand the gaps that need to be improved for each indicator and the need to achieve continuous improvement at the expected level. The second concept of the model explains how to systematically develop a strategy [50]. After realizing the problem, the decision maker must develop an improvement strategy to achieve the goal. Traditionally, the multivariate analysis model assumes that the factors are independent of each other, so the decision makers will be guided to look at each problem individually rather than looking at the relationship between all the indicators, so they can only address the obvious problems--improve, not solve the root cause of the problem. In the real world, the cause of the problem is not simple and often involves complex systems. In the system, each factor has more or less the influence of the target, and the analyst often deliberately ignores the inconspicuous relationship in order to simplify the analysis process. Therefore, this research model recognizes that all factors are causally related to each other and then finds the root cause of the problem and discusses how to improve to achieve the goal. In that vein, this study used a hybrid MCDM study model to perform analysis tools, composed of three technologies. The first is the decision-making trial and evaluation laboratory (DEMATEL), which uses an expert questionnaire to assess the relationship between each factor and expresses the interaction relationship through a pairwise comparison matrix to find the total impact relationship matrix [51; 52]. The second technique is the analytic network process (ANP), which is designed to loosen the independence assumptions of factors in the analytic hierarchy process (AHP) system to reflect real-world conditions [53; 54]. Then, the results of DEMATEL are combined with ANP (also known as DEMATEL-based ANP), and the influential weights (IWs) are derived from the calculation program. IWs are mainly used to express the relative importance of factors between the factors. The third technique is VIKOR. This study used modified VIKOR, which combines IWs with VIKOR. Its purpose is to shorten the gap between factors and expected level and find out where the problem lies, in order to refer back to the INRM drawn by DEMATEL. The INRM is used to identify the root cause of the problem and develop a systematic improvement strategy to prioritize the improvement strategy [55; 56]. The MCDM model has fully demonstrated its advantages in various research fields. Some scholars have optimized sustainable energy alternatives in the planning and development of renewable energy [57]. Some scholars assess and build sustainable housing affordability on various complex factors that affect the quality of family life [58]. Some scholars have provided continuous improvement strategies for the establishment of creative cities [59].