# A Fuzzy Path Selection Strategy for Aircraft Landing on a Carrier
## 3 Landing Path Selection Method Based on FMAGDM
### Process of the Group Decision-Making  
The decision of a pilot or an LCO can be calculated separately according to the above mentioned procedure. In reality, a decision made by one of them may not be the optimal solution because different decision makers obtain different information and have difference in knowledge and preference. Therefore, to deal with the divergence and to make an optimal decision, the decision of both the pilot and the LCO should be integrated. The group decision-making problem will be discussed and addressed in this section.  
To solve this group decision-making problem, the pilot and the LCO are regarded as two contributing factors, and the problem is then translated into a decision-making problem by a single person [28]. The fuzzy decision matrix for group decision making is established below:  
\[\mathcal{O}=\left[\begin{array}{cccc}o_{11}&o_{12}&\ldots&o_{14}\\ o_{21}&o_{22}&\ldots&o_{24}\end{array}\right]. \tag{16}\]  
where \(o_{st}(s=1,2;t=1,2,3,4)\) is the closeness coefficient \(C(l_{j})\) calculated for each decision maker by Equation (15). The process of group decision making is depicted in detail in four steps:  
Step 1: The matrix \(\mathcal{O}\) is a normalized fuzzy decision matrix, so the normalization step can be skipped. We assume the weights of pilot and LCO as \(\lambda_{1}=[\lambda_{1}^{L},\lambda_{1}^{M},\lambda_{1}^{U}]\) and \(\lambda_{2}=[\lambda_{2}^{L},\lambda_{2}^{M},\lambda_{2}^{U}]\), respectively. The weighted normalized group fuzzy decision matrix can be calculated in the same way as in Section 3.2 and is expressed as \(V=\left(v_{kj}\right)_{2\times 4}(k=1,2;j=1,2,3,4)\). Note that the decison of the LCO should be granted greater weight due to the fact that the LCO is less subject to many kinds of distraction compared to a pilot. On the other hand, the opinion of the pilot should be also taken into account since he/she has a better feeling in weather and better knows the current aircraft performance.  
Step 2: Determine \(GP\) and \(GN\) (the fuzzy positive group ideal reference point (FPGIRP) and negative point (FNGIRP)). FPGIRP and FNGIRP can be denoted as \(GP=(gp_{1},gp_{2})\) and \(GN=(gn_{1},gn_{2})\) (\(gp_{k}=\max\limits_{1\leq j\leq 4}\{v_{kj}\}\) and \(gn_{k}=\min\limits_{1\leq j\leq 4}\{v_{kj}\}\)).  
Step 3: Calculate the fuzzy distance and the closeness coefficient.  
\[d(l_{j},GP)=\sum\limits_{k=1}^{2}d(v_{kj},gp_{k}) \tag{17}\]  
\[d(l_{j},GN)=\sum\limits_{k=1}^{2}d(v_{kj},gn_{k}) \tag{18}\]  
\[GC(l_{j})=\eta\frac{d(l_{j},GP)}{d(l_{j},GP)+d(l_{j},GN)}+(1-\eta)\frac{d(l_{ j},GN)}{d(l_{j},GP)+d(l_{j},GN)} \tag{19}\]  
where \(\eta(0<\eta<1)\) can also be adjusted to denote the different importance of FPGIRP and FNGIRP. Therefore, the principle of choosing \(\eta\) is similar to that of \(\mu\).  
Step 4: Obtain the mean value \(s(GC(l_{j}))\) using Equation (1), and the landing path corresponding to \(\max\limits_{1\leq j\leq 4}\{s(GC(l_{j}))\}\) is the optimal one in the current environment. The ranking of alterative paths can be calculated in the meantime. Note that the final decision has to be close to that of both decision makers.