A Decision-Making Method for Landing Routes of Aircraft on the Carrier

The landing safety of aircraft is of great significance for the normal operation of an aircraft carrier. This paper presents an optimal method for landing routes of aircraft. Owing to the fuzziness of environmental information and human judgment, a decision-making method is introduced to reduce the workload of landing console operators (LCO). Specifically, a route option method for aircraft landing is proposed based on Fuzzy Multi-attribute Group Decision Making (FMAGDM). Firstly, the route option problem is described. Then the essential elements of route option are described. A group decision-making method is proposed, and the most reasonable landing route in current environment is obtained considering the knowledge composition and the weight of each decision maker. Finally, simulations under different environments are conducted. The results indicate that the decision-making method is able to adapt to the environment changes, and determine the most reasonable route for each validation case.


Introduction
Landing aircraft on an aircraft carrier is a task laden with inherent risks [1]. There exist numerous uncertainties during the fight before the aircraft landing, e.g. the flight condition and the maritime environment [2], [3]. As a result, it increases the uncertainty of landing. The landing console operator (LCO) is in charge of determination of landing route [4], [5]. He/she makes decisions for the guidance of aircraft within a short time according to his knowledge and the information displayed on the instruments [6]. However, reasonable judgment is usually not able to be made quickly and accurately due to the fuzziness of the information. Artificial intelligence (AI) is suitable for dealing with fuzziness problem and is introduced to the route decision-making system of aircraft in order to reduce the workload of LCO.
Unlike the path planning problem [7], [8], the route modes for landing of carrier aircraft are fixed. The landing route is chosen for aircraft before they reach the aircraft carrier. It is the first step in the landing guidance support system. This issue is obviously essential to the automatic landing system and thus worthwhile to study in depth.
The aircraft usually adopt different routes to land depending on its performance, the traffic conditions, a variety of weather conditions and visibility [9].Some biases or even errors may occur if we only rely on the judgments of human. Therefore, a decision-making system for route option is essential to reduce the workload of staffs and improve the safety level of landing.
The main contribution of this paper is to point out the necessity and importance of researching the route option problem for aircraft landing, and have a comprehensive description of the problem. The establishment of mathematical model and the proposed method provide a valuable reference for assistant decision of the pilot and LCO. This group decision-making method is crucial to realize the intelligent decision-making.

Problem description
The air control system sends return command to an aircraft in flight. Specifically, Tactical Air Navigation (TACAN) provides the position and distance information. The airborne early warning (AEW) provides the overall air traffic situation. The sea weather is measured by the observatory set up on the aircraft carrier, and the weather measurements are transmitted to a pilot. The route option problem is further depicted in Fig. 1  The dotted arrow denotes the receiver will only view the information as a reference to make a judgment. The pilot and the LCO are both decision makers when solving the route option problem. However, the LCO is chosen as the major decision maker in order to better master the air traffic situation and enhance the safety level of landing.

Analysis of essential elements
There are several essential elements in a route option problem. They will be discussed in this section.

The alternative routes
There are four modes of landing route according to the differences in atmospheric environment, performance of an aircraft and the air traffic situation. ݈ ଵ : The weather, visibility, performance of an aircraft and air traffic situation are all good when landing is permitted.The pilot lands the aircraft by vision under such conditions. ݈ ଶ :The weather and visibility are at a medium level and the performance of the aircraft and air traffic are in good conditions.A landing mode with higher safety standard will be adopted when clouds become heavy. It becomes dangerous to land the aircraft by vision.
݈ ଷ : The weather and visibility are bad, the performance of the aircraft and air traffic are in good conditions.It is also unsafe to land the aircraft by vision in such conditions. ݈ ସ : The performance of aircraft is poor or the air traffic is in a bad condition.No proper conditions exist for aircraft landing on the carrier. In this case, the pilot has to get in touch with the land base for emergency landing.

The contributing factors:
The contributing factors for a route option problem are concludedas follows: Weather It is usually difficult to predict the weather around a large area accurately. Only the nearby weather condition can be mastered continuously.
The height of clouds The vision of a pilot will be affected when the clouds are low or cover a wide range of the sky. The heavy cloud may even lead to a bump of an aircraft during the flight.
Visibility The level of visibility plays an important role in affecting the visual observation and the judgment of a pilot.
Performance of aircraft The aircraft is usually in good performance during flight. However it may get damaged when accidents occur.
Air traffic situation The aircraft under consideration refers to the status of other aircraft which are near to the landing routes.

FMAGDM (Fuzzy multi-attribute group decision making) based method of route option
The FMAGDM method has a good description of the current environmental information and the weights of decision-makers [10], [11]. According to the developed fuzzy TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) approach [12], the triangular membership function is used to describe the performance ratings of contributing factors (short for PRCF for convenience in the rest of this paper). The PRCF is the knowledge base of the model which can be evaluated in advance. Similarly, the current environmental vector which is the input of the route option model can be also described by the triangular membership function. Subsequently a mathematical model is established to measure each alternative route. Based on this, the fuzzy judgment method for group decision-making is introduced to get the most reasonable one for the current environment.

Description of the PRCF and the current environmental vector
The PRCF or the current environmental vector needs to be described using fuzzy linguistic variables. The triangular membership function is introduced to define the value of each fuzzy linguistic variable. The properties of the triangular membership function are presented.
Definition 1: The mean value of a triangular membership function a=[ܽ ,ܽ ெ ,ܽ ] is defined as The mean valuecan be used to sort the triangular membership functions. In view of the triangular membership functions a and b, there exists a definition as follows: abif s(a)s(b) and a<bifs(a)<s(b).

Figure2. Definition of D -cut set
Definition 4:Assume a andb are twotriangular membership functionsand a b, the fuzzy distance between a and b is defined as follows.

Decision-making with the developed fuzzy TOPSIS approach
5 contributing factors determine the result of route option. They (weather, clouds height, visibility, performance of aircraft and air traffic situation) are written as݂ ଵ , ݂ ଶ , ݂ ଷ , ݂ ସ and ݂ ହ respectively. The performance ratings of contributing factors are shown in Table 1.
Thedescriptions mentioned above need to be unified with the same linguistic variables as shown in Table 2.
where matrix D is the knowledge base which has been mastered in advance. The matrix D can assist a pilot or LCO to make optimal decision. The detailed procedure of the method will be provided.
Step 1: Normalize of the fuzzy decision matrix Different contributing factors use different measurement units when collecting raw data. Therefore, normalization is needed to transform݁ into the interval of [0,1] in order to eliminate anomalies. In this paper, a linear transformation is adopted to get the normalized fuzzy decision matrix X: 11 12 13  14   21  22  23  24   51 52 54 Since the PRCF denote efficiency in route option, ‫ݔ‬ can be normalized using the largest value, i.e., efficiency, of this contributing factor:

Step 2: Integrate the current environment vector reported by a decision maker into the normalized fuzzy decision matrix
The environmental vector can also be described using linguisticvariable, as shown in Table 3. We denote the environmental evaluation of each contributing factor as߱ =[߱ ,߱ ெ ,߱ ], which compose the environmental vector (i=1,2,…,5, the value of ߱ can be chosenfrom Table 3). The normalized fuzzy decision matrix integrating the environmental vector is calculated: Step 3:Determine the positive and negative ideal solutions The positive ideal solution is obtained when each PRCF chooses its highest value from the fuzzy decision matrix D. On the contrary, the negative solution is obtained by choosing the lowest value for each performance rating.
The fuzzy positive ideal reference point (FPIRP) and negative point (FNIRP) are written as P and Nin the remainder of this paper for convenience. The FPIRP and FNIRP can be defined as 1 2 5 ( , ,..., ) P p p p and Step 4: Calculate the fuzzy distance between (j=1,2,3

,4)and P (or N)
According to Eq. (3), the fuzzy distance between݈ (j=1,2,3,4)and P (or N) are defined as follows: 5  Step 5:Obtain the closeness coefficient The larger the closeness coefficient is, the closer the alternative route is to the fuzzy ideal solution. Eq. (10) is adopted to calculate the closeness coefficient and distinguish the importance between FPIRP and FNIRP.
where ߤ(0<ߤ<1)is a weight for different distances from FPIRP and FNIRP, it is determined by the subjective attitude of a decision maker.

Group decision-making process
The main idea of solving the group decision problem is to regard the pilot and the LCO as two contributing factors, and view the group decision-making problem as a single person decision-making problem. The group fuzzy decision matrix is constructed as follows: where ܱ ௦௧ (s=1,2 ;t=1,2,3,4) is the closeness coefficientC(݈ ), which is calculated using Eq. (10). The group solution is depicted by the following steps: Step 1: The weights of pilot and LCO are assumed respectively. The weighted normalized group fuzzy decision matrix is written as V=ሺ‫ݒ‬ ሻ ଶൈସ (k=1,2 ;j=1,2,3,4).
Step 2: Write the fuzzy positive group ideal reference point (FPGIRP) and negative point (FNGIRP) as GP and GN respectively. The FPGIRP and FNGIRP can be formulated as Step 3: Calculate the fuzzy distance between ݈ (j=1,2,...,4)and the FPGIRP (or FNGIRP), and calculate the closeness coefficient.
where ߟ (0< ߟ <1) denotes the attitude of the group. It reflects the different importance of FPGIRP and FNGIRP.

Results and analyses of route option in different environments
Real cases are presented to illustrate the validity of the proposed method. Two different environmental conditions are used as test scenarios. On the basis of apriori knowledge, experience, current environment evaluations and weights of decision makers, the decisionmaking method is expected to choose the most reasonable route for the current environment. Further analysis of the simulation results implies that the proposed method has a bright future for real application in a practical project.

initialization and their fuzzy descriptions
The expressions of performance ratings and environment evaluations are shown in Table 4. In order to compare the results in different environments, 2 pairs of simulations are carried out independently. The environment settings and evaluations of decision makers are listed in Table 5 and Table 6.

Results and analyses
The proposed decision-making method is applied to determine the optimal route for different environment conditions. The results are given in Table 7 and Table 8. From Simulation i to Simulation ii, the environment condition set for each validation case is degrading gradually. With the changes of the environment setups, the decision-making method is able to adapt to the environment changes, and determine the most reasonable route for each validation case. The results indicate that the proposed method has the capability of dealing with the fuzziness in description successfully and can solve the troubles introduced by artificial decision-making. Above all, the proposed decision making approach is able to assist the pilot and the LCO to guide the aircraft to land safely and automatically. The proposed method can be used for air traffic control in an aircraft carrier. It can assist the LCO to make the landing route scheduling decision, and can provide the security information for the returning aircraft after having finished a combat or patrol mission.

Conclusion
In this paper, the route option problem of aircraft landing on an aircraft carrier is solved by proposing a new decision-making method. Firstly, the route option problem and theessential elements are described. Then using the improved fuzzy TOPSIS approach, fuzziness in description and judgment can be solved by introducing linguistic variables. Subsequently, a mathematical model, which can be later applied to measure the rationality of each alternative route for the current environment, is established. Finally, the group decision-making approach is introduced to take into account the judgments of both the LCO and the human pilot. Validation results for different environment setups indicate that the proposed decision-making method can adapt to the changes of environment and can make a quick and realistic decision.
The decision-making method proposed in this paper can reduce the workload of the pilot and the LCO by pointing out the optimal route option for the returning aircraft. The work of this paper provides a solution for landing route scheduling, which should be addressed at the first order to realize the automatic landing of carrier aircraft. Automatic flight controller design should be viewed as the future work under the framework of realizing automatic landing of aircraft.