## 2 Construction of Assembly Multidimensional Evaluation Index
### Evaluation Index of Assembly Ontology Dimension
#### 2.2.1 Individual Indicators of Assembly Base Unit Parts  
The factors affecting the evaluation of the sequence of the individual base unit of an aviation reducer are mostly related to its ontological properties, mainly including the quality, size, symmetry, and fit relationship of the individual base unit. Because of the complex structure of aerospace gearbox assembly, not all the factors influencing the evaluation of the sequence of individual base units are necessarily considered in the actual assembly process. Additionally, the evaluation system of the sequence of individual base units can be selected according to the actual needs of the assembly sequence planning of an aerospace gearbox. The factors influencing the sequence evaluation of the individual base units of aeronautical reducer gear are described below. 1 Quality of individual base units  
In the assembly process of an aviation reducer, the larger the mass of an assembly unit individual, the more difficult it is for field craft personnel to carry out the assembly operation, resulting in the low operability of the assembly unit. For example, the mass of the main gearbox of a helicopter can only be moved to a tooling assembly station for the next assembly step by lifting it with a sling. This type of base unit, which requires additional auxiliary tools for assembly, will lead to an increase in the assembly cycle of the reducer and the assembly costs. In the assembly process of an aviation reducer, the smaller the mass of the assembly unit individual, the easier it can be freed from auxiliary tools and the easier it is for the craftsman to carry out direct assembly. Thus, according to fuzzy evaluation theory,the partial trapezoidal distribution fuzzy set function is selected to calculate the fuzzy evaluation value of the base unit quality [35]. The calculation method of the quality index of individual base units is shown in Equation (5), where the closer the value of \(q(x)\) to 1, the easier the base unit is to assemble. That is, the higher the evaluation value of the quality index of an individual base unit, the easier it is to assemble, and a base unit with a low evaluation value can be considered to be installed first. \[q(x)= \begin{cases}0&x>q_{\text{max}}\\ 1&x<q_{\text{min}}\\ \frac{q_{\text{max}}-x}{q_{\text{max}}-q_{\text{min}}}&q_{\text{min}}\leq x \leq q_{\text{max}}\end{cases}  \tag{5}\]  
\(x\) indicates the current quality of an individual base unit. \(q_{max}\) indicates the maximum mass of the base unit that can be lifted by a technician for smooth installation, and this is determined according to experience. \(q_{min}\) indicates the minimum mass of the foundation unit that can be lifted by a technician for smooth installation. \(2\) Individual size of the base unit  
The overall size of an aeronautical reducer is relatively large. Generally, the reducer box is fixed on the workstation first, and then components of different sizes are assembled sequentially. The site is effectively organized according to the actual number of craftsmen participating in the parallel assembly of multiple components. In the assembly process of an aviation reducer, the size of an individual assembly unit can be too large or too small to be suitable for assembly. According to fuzzy evaluation theory, the trapezoidal fuzzy set function is used to calculate the index value of the size of an individual base unit, as shown in Equation (6):  
\[w(x)= \begin{cases}0&x<d_{\text{min}},x\geq d_{\text{max}}\\ 1&d_{1}<x<d_{2}\\ \frac{x-d_{\text{min}}}{d_{\text{1}}-d_{\text{min}}}&d_{\text{min}}<x<d_{1}\\ \left|\frac{x-d_{\text{max}}}{d_{\text{max}}-d_{2}}\right|&d_{2}<x<d_{\text{ max}}\end{cases}  \tag{6}\]  
\(x\) denotes the current shape size of an individual base unit. \(d_{1}\) and \(d_{2}\) denote the intervals of the size of an individual base unit suitable for tight space assembly, and the fuzzy evaluation value \(w(x)\) in this interval is 1, i.e., suitable for the assembly process to be carried out.