# Real-Time Safety Decision-Making Method for Multirotor Flight Strategies Based on TOPSIS Model
## 2 Motivation and Main Methodology
### Construction of Real-Time Attribute Decision-Making Model of Multirotor Based on TOPSIS
#### 2.4.1 Construction of the Attribute-Strategy Matrix and Weight Matrix  
Firstly, an attribute-strategy matrix needs to be constructed, where the rows of the matrix are the candidate manipulation strategy sets \(\mathbf{A}=\{a_{1},a_{2},\cdots,a_{s}\}\), and the columns of the matrix are attribute sets \(\mathbf{B}=\left\{b_{1},b_{2},\cdots,b_{g}\right\}\). That is,  
\[\mathbf{AB}= \begin{pmatrix}r_{11}&\cdots&r_{1g}\\ \vdots&\ddots&\vdots\\ r_{s1}&\cdots&r_{sg}\end{pmatrix} . \tag{1}\]  
In the attribute weight matrix \(\mathbf{W}\) and the attribute-strategy matrix \(\mathbf{AB}\) with the same scale, every element in the matrix \(\omega_{ij}\) represents the first \(j\) attribute to the first \(i\); the influence degree of each strategy is given by multirotor control experts in actual management. The weight of different strategies on an attribute represents the satisfaction degree of different candidate manipulation strategies on each attribute, namely \(r_{ij}\) in the attribute-strategy matrix \(\mathbf{AB}\). To determine the weight scientifically and reasonably, the grade evaluation method and vague set are introduced. The evaluation includes the membership of certainty and uncertainty, which belongs to a type of fuzzy information. The vague set is the information that expresses support, opposition, and unknown simultaneously in the form of interval numbers. Experts with rich professional knowledge and relevant experience are invited to publish rating evaluations on the performance of different flight strategies on a certain attribute, which can be generally divided into 5, 7, 9, and 11 grades from low to high. The method adopts 11-grade language variables to more accurately reflect the distinction. Set \(\alpha\) is the domain of discourse, and \(\lambda\) is an element in this domain \(\alpha\). The last vague set of \(\mathbf{B}\) is a pair of membership functions, \(t_{B}\) and \(f_{B}\), in which \(t_{B}\): \(\alpha\rightarrow[0,1]\) and  
Figure 2: Random forest model framework diagram. \(f_{B}\): \(\alpha\rightarrow[0,1]\) satisfy \(0\leq t_{B}(\lambda)+f_{B}(\lambda)\leq 1\), in which \(t_{B}\) is called the vague set \(B\) true membership function, which supports the lower bound of the membership degree of the evidence \(\lambda\in B\). \(f_{B}\) is called the vague set \(B\) the false membership function, which refers to opposition. \(\lambda\in B\) is the lower bound of the membership degree of evidence. \(\pi_{B}(\lambda)=1-t_{B}(\lambda)-f_{B}(\lambda)\) points to \(\lambda\) relative to \(B\) hesitancy, \(\pi_{B}(\lambda)\); the larger the value, it means \(\lambda\) right \(B\) the higher the unknown level. Set \(\lambda\in\alpha\) is called closed interval, and \([t_{B}(\lambda),1-f_{B}(\lambda)]\) is a vague set. \(B\) at point \(\lambda\) is a vague set. The corresponding relationship between the language variables of the 11-grade evaluation and vague values is shown in Table 1.  
The expert's evaluation of candidate strategies and attributes is transformed into a vague value representation, in which the closer the vague value is to [1, 1], the higher the degree of satisfaction of the strategy for this attribute. Therefore, [1, 1] is regarded as the ideal value, and the closeness of each matrix element to the ideal value is compared. If the element under an attribute is closer to the ideal value, the attribute weight is higher; on the contrary, if the element under an attribute is further from the ideal value, the attribute weight will be lower. According to the above principle, the projection and distance of the vague set are used to reflect the similarity of two objects, and the evaluation value of \(r_{ij}\) can be defined as:  
\[W\big{(}r_{ij},r_{0j}\big{)}=\frac{D\big{(}r_{ij},r_{0j}\big{)}}{D\big{(}r_{ij },r_{0j}\big{)}+J\big{(}r_{ij},r_{0j}\big{)}}. \tag{2}\]  
Set the ideal attribute value \(r_{0j}\) expressed by the vague value [1,1].