Application of the Fuzzy AHP -VIKOR Hybrid Model in the Selection of an Unmanned Aircraft for the Needs of Tactical Units of the Armed Forces

Unmanned aerial vehicles represent an indispensable segment in the range of weapons of both military and police units. The expansion in development of unmanned aerial vehicles for both commercial and military purposes has created a need for constant improvement of drones and anti-drone means. A wide range of possibilities opens up a wide range of uses for them. The paper presents the choice of an unmanned aerial vehicle as an important combat system for the needs of tactical units of the army and police. The complexity of the problem is conditioned by various tactical - technical and economic characteristics of unmanned aerial vehicles, it has conditioned the use of different methods of multicriteria decision making. A hybrid model of multicriteria decision making fuzzy AHP - VIKOR was used to select the unmanned aerial vehicle for the needs of tactical units. Criteria of importance for the selection of an unmanned aerial vehicle for the needs of tactical units have been defined on the basis of which the most optimal solution (unmanned aerial vehicle) has been selected. The criteria are defined on the basis of tactical-technical and economic characteristics of unmanned aerial vehicles. The calculation of the weight coefficients of the defined criteria was performed using the fuzzy AHP method, while the selection of the drone (the most favorable alternative) based on the defined criteria was performed using the VIKOR method. The obtained result represents the starting point for further research and implementation of unmanned aerial vehicles in tactical units of the army and police.


Introduction
HE tendency to create modern, better equipped and more efficient military and police forces in all countries of the world is growing as well as the need for the use of drones as one of the most important combat systems. Unmanned aerial vehicles with a wide range of use in different conditions and different operating environment are the means of increasing the efficiency of military and police units.
The term UAV has a broad meaning, it means a system with a motor that is remotely controlled by the operator or it is a system that has a certain level of autonomy (control is done using communication software, and often uses artificial intelligence and different types of sensors), which can be used once or repeatedly and can carry deadly or non-lethal cargo and transmit data in real time. It is a synthesis of the means and devices necessary to manage it. They differ in purpose, construction characteristics (shape, dimensions, weight, payload, maximum flight altitude, maximum range, flight time, speed, etc.) of the environment in which they are used, the energy source with which they are driven. Depending on the purpose, they can be used in different environment such as land, water, air and space, and a wide range of possibilities has created a condition for application in defense and security (for the needs of the army and police -original purpose). agriculture, construction, traffic, trade, communication, science, medicine, research, architecture, video and photography, geology, forestry, mining, oceanography, environmental management, sports, mapping, etc. The term drone is more general than the term unmanned aerial vehicle, because all unmanned aerial vehicles can be called drones, while a drone does not necessarily have to be an unmanned aerial vehicle. A comparative analysis of unmanned aerial vehicles was performed in this paper.
A wide range of possibilities of unmanned aerial vehicles provides the possibility of using unmanned aerial vehicles for: shooting, photography, monitoring, tracking [1], reconnaissance [2], detection, attack on certain means and facilities, combat with other drones, transporting different cargo [3], protection of humankind and facilities, etc. These functions provide the possibility of using UAVs in various military and police units [4]. A detailed classification of drones was performed by Hasanalian and Abdelkefi in the paper [5], Yaacoub, Noura, Salman and Chehab in paper [6]. Petrovski and Radovanović in paper [7] defined the term drone as well as the detailed classification of drones shown in Fig.1. [7]. T There are objective needs for the implementation of UAVs, the implementation which would provide an adequate support to the military and police units in conducting various operations. The final selection of the most optimal solution and their implementation in the tactical units of the army and police would significantly improve three key capabilities: the ability to command, the ability to use information space, and the ability to use forces effectively.
It is possible to find a large number of UAVs on the market today, with different features and different purposes (application in agriculture, medicine, transport, architecture, meteorology, photography, army, police, etc.) [8]. A large number of police and military units in the world have a certain model of UAV in their armament. The military and police requirements for the characteristics of UAVs for use in different types of operations are very uneven. Based on the above, the goal was set to choose the most favorable alternative (UAV) which, according to its characteristics in largely meets the needs of army and police tactical units. The results of the research can be used in further implementation of UAVs for the needs of tactical units of the army and police.

Literature analysis
The paper analyzes military drones for the needs of tactical units of the army and police. According to the literature that was available to the authors, there are a number of works by foreign authors who used the method of multi-criteria decision-making to select drones for different needs showing the selection of the optimal unmanned aerial vehicle for precision agriculture using the AHP method and the The complexity of drone selection has necessitated the application of a hybrid model of multi-criteria decision making. Due to the specifics of the problem, the research has defined a hybrid model composed of two methods: fuzzy AHP (Analytical Hierarchical Process) and VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) methods.
The paper presents a model that selects the most optimal solution (UAV) in relation to the given criteria. The aim of this paper is to enable the selection of the most optimal solution through the application of multi-criteria decisionmaking methods in order to implement it in the tactical units of the army and police.

Research methods
The hybrid model, used to solve the problem of choosing an unmanned aerial vehicle for the needs of tactical units of the army and police, was defined by a combination of fuzzy AHP and VIKOR methods of multi-criteria decision-making. This part of the paper describes the methods used in the paper. The fuzzy AHP method was used to determine the weighting coefficients for the given criteria, while the VIKOR method was used to select the most optimal solution (unmanned aerial vehicles). The data used in the research were obtained on the basis of available literature and content analysis. Fig.2 shows the phases through which this model was realized.
Analytical hierarchical process is a method based on decomposition of a complex problem into a hierarchy, with the goal at the top, criteria, sub-criteria and alternatives at the levels and sublevels of the hierarchy [14]. For comparisons in pairs, which is the basis of the AHP method, the Saaty scale is usually used, Table 1. The comparison in pairs leads to the initial decision matrices. The Saaty scale is most commonly used to determine the weighting coefficients of the criteria [31], but can also be used to rank alternatives. Very often when taking values from the Saaty scale in the pairwise comparison process, decision makers hesitate between the values they will assign to a particular comparison. In other words, it happens that they are not sure of the comparison they are making. Due to the above, various modifications of the Saaty scale are often made. One of them is the application of fuzzy numbers [32].
There are different approaches in the fuzzification of the Saaty scale, and in principle they can be divided into two groups: sharp (hard) and soft fuzzification. The fuzzification can be done with different types of fuzzy numbers, and is most often done using a triangular fuzzy number, Fig.3. Figure 3. Triangular fuzzy number T [27] The "sharp" fuzzification means that for a fuzzy number a   1 2 3 , , T t t t  confidence interval is predetermined, i.e., it is predefined that the value of the fuzzy number will not be greater than 3 t , not less than 1 t [15]. Based on a predefined fuzzy Saaty scale, a comparison is made in pairs. In soft fuzzification, the confidence interval of the values in the Saaty scale is not predetermined, but is defined during the decision-making process, based on additional parameters.
The definition of the weight coefficients of the criteria in this paper was performed by applying the phased Saaty scale presented in the papers [16,17,33,34,35].
The starting elements of this fuzzification are [34]:  Table 2. An example of the appearance of a fuzzy number with different degrees of confidence is given in Fig.4. For example, the value of low dominance from the Saaty scale and degrees of confidence were taken =1, =0.7 and =0.3.  1  2  1  2  1 2   1 2 3  2  2  2   3  2  3  2  2 3 , , , 1 /9 , 9 , , , 1/ 9,9 2 , , , 1/9,9 where the value of t 2 represents the value of the linguistic expression from the classical Saaty scale, which in the fuzzy number has a maximum affiliation t 2 =1. Fuzzy number Accordingly, the initial decision matrix has the following form [15]: ; ; n n n n n n n n n n n n n n where is  ji =  ij . Reaching the final results implies further application of the standard steps of the AHP method. At the end of the application, the fuzzy number is converted to a real number. Numerous methods are used for this procedure [31].
Some of the well-known terms for defuzzification are [35,38,39]: where  represents an index of optimism, which can be described as the belief/attitude of DO in risk in decision making. Most often, the optimism index is 0, 0.5 or 1, which corresponds to the pessimistic, average or optimistic view of the decision maker [40].
Description VIKOR method VIKOR (Multi-Criteria-Compromise Ranking) is a method of multi-criteria decision-making whose use is very common. It was developed by Serafim Opricović in 1986 [41]. It is suitable for solving various decision-making problems. It is especially emphasized for situations where criteria of a quantitative nature prevail.
The VIKOR method starts from the "boundary" forms of Lp -metrics, where the choice of the solution that is closest to the ideal is made. The presented metric represents the distance between the ideal point F* and the point F(x) in the space of criterion functions [40]. Minimizing this metric determines a compromise solution. As a measure of the distance from the ideal point, the following is used: The VIKOR method has been applied in a large number of papers in its original form [35,42,43,44,45] but also in fuzzy [46,47,48,49,50] and rough [51,52,53,54] environment.
When applying the VIKOR method, the following terms are used: n -number of criteria m -number of alternatives for multicriteria ranking ij f -the values of the i-th criterion function for the j-th alternative, w j -weight of the j-th criterion function, -the weight of the strategy, meeting most of the criteria, i -ordinal number of the alternative, i = 1, ..., m., j -ordinal number of criteria, j = 1, ..., n, -Q i -measure for multicriteria ranking and -and alternatives For each alternative, there are Q i values, after which the alternative with the lowest value is selected. The measure for multicriteria ranking of the i-th action (Q i ) is calculated according to the expression [55]: where is: By calculating the QS i , QR i , and Q i sizes for each alternative, it is possible to form three independent rankings. Size QS i , is a measure of deviation that shows the requirement for maximum group benefit (first ranking list) Size QR i is a measure of deviation that shows the requirement to minimize the maximum distance of an alternative from the "ideal" alternative (second ranking list). Q i size represents the establishment of a compromise ranking list that combines QS i and QR i sizes (third ranking list). By choosing a smaller or larger value for v (the weight of strategies to meet most criteria), the decision maker can favor the influence of QS i size or QR i size in the compromise ranking list. For example, higher values for v (v> 0.5) indicate that the decision maker gives greater relative importance to the strategy of meeting most of the criteria. Modeling the preferential dependence of criteria usually includes the weights of individual criteria. If weight values are specified 1 2 , ,..., n w w w , multicriteria ranking by VIKOR method is realized using the measure Si and R i . In the previous terms, the labels used have the following meanings: Alternative a i is better than alternative a k according to jtom criterion, if: In multi-criteria ranking by the VIKOR method, alternative ai is better than alternative a k (in total, according to all criteria), if: Q i < Q k . A compromise ranking list for the value v = 0.5 is taken as an acceptable ranking list according to the VIKOR method.
The f an alternative is in the first position on such a compromising ranking list, it still does not mean that this alternative is considered the best. In order for an alternative to be adopted as the best, it must be the first on the compromise ranking list and meet two conditions: condition U1 and condition U2 [34].

Condition U1
The first alternative on the compromise ranking list for the value v = 0.5, must have a "sufficient advantage" over the action from the next position. The "advantage" is calculated as the difference of the measure Q i for the value v = 0.5. Alternative a 'has a "sufficient advantage" over the next a "from the ranking list, if fulfilled: where is: DQ -"sufficient advantage" threshold m -number of alternatives, 0.25 -size of the "sufficient advantage" threshold which limits the threshold for cases with a small number of alternatives Condition U2 The first alternative on the compromise ranking list for the value v = 0.5, must have a "sufficiently stable" first position with a change in weight v. The first alternative on the compromise ranking list has a "sufficiently stable" position, if it meets at least one of the following conditions: -has the first position on the ranking list according to QS, -has the first position on the ranking list according to QR, -has the first position on the ranking list according to Q for v =0,25 and v = 0,75. If the first action from the compromise ranking list does not meet one or both conditions (U1 and U2), it is considered that it is not "sufficiently" better than the action from the second position and possibly some more actions. In such cases, a set of compromise solutions is formed, which consists of the first, second and possibly some other actions (third, fourth ...). If the first action does not meet the condition U2 only, then only the first and second actions are included in the set of compromise solutions. However, if the first action does not meet condition U1 (or both conditions, both U1 and U2), then the set of compromise solutions contains actions from the compromise ranking list to the action that meets condition U1, i.e., to the one over which the first action has a "sufficient advantage" via DQ.
The results of the VIKOR method are: -Ranking of lists according to QS i , QR i and Q i measures, -A set of compromise solutions (in case the conditions U1 and / or U2 are not met). -These results represent the basis for deciding and adopting the final solution (multi-criteria optimal solution).

Defining criteria, alternatives and calculation of weighting coefficients of criteria
In the first phase of the application of the hybrid model of multi-criteria decision-making, the definition of criteria that influence the selection of the most optimal solution (UAV) was performed, for the needs of defense and security systems, i.e., for the needs of military and police tactical units. When defining the criteria for the selection of UAV, it is necessary to include all relevant characteristics of the system to be optimized, which is further important for defining the weight coefficients of the criteria. The criteria are defined on the basis of a study of the available literature and the views of experts. The following six criteria were identified on the basis of which the UAV comparison was performed. We emphasize that the experts stated that there is no need to establish subcriteria, which is why all criteria present the same hierarchical level in the analysis.
Maximum speed (C1) is a criterion that is of the beneficial type (higher values are more desirable). Maximum speed directly affects the efficiency of the system, increasing the maximum speed increases the efficiency of UAV. Higher maximum speed directly affects the increase of maneuvering and tactical capabilities of UAV, which also directly increases their efficiency. Higher speed provides the possibility of a faster response to a new situation. The stated criterion is of a numerical character and is expressed in the distance traveled in a unit of time (km/h) and represents one of the most important criteria when choosing a drone.
Flight autonomy (C2) represents the total time that an aircraft can spend in flight, without recharging energy. The criterion is of the beneficial type. Greater flight autonomy increases the efficiency of the combat system and enables a longer time to complete the task, which is extremely important when the requirements are such that it is not possible to interrupt the task due to the replacement or replenishment of energy sources. The level of autonomy can vary from fully autonomous operation to full control by the remote operator. The difference in the concept of autonomy is the difference between automatic and autonomous systems. [56]. Flight autonomy is a criterion of a numerical character, expressed in a unit of time (h).
Maximum range (C3) represents the maximum distance to which the UAV can travel. The higher the maximum range, the higher the efficiency of UAVs, because it realizes the possibility of realizing long-range combat tasks. The higher maximum range allows the use of drones at different distances and allows the use of drones in the depths of enemy territory, which is more important for military than for police units. Like the previous criteria, this criterion is of the beneficial type, and is expressed in kilometers (km). A higher maximum range also increases the operator's protection from enemy action.
Maximum flight altitude (C4) is the maximum altitude at which the drone can be used. Higher maximum flight altitude opens greater opportunities for the use of UAV/drones and increases the efficiency of the combat system. The criterion expresses the requirement for maximization, and is expressed in meters (m).
The price of one system (aircraft plus accompanying ground and reconnaissance equipment) (C5) represents the total price to be paid for one UAV with accompanying equipment. The criterion is of economic character and "cost" type. The price of the system is expressed in US dollars (USD ($)). This criterion can also be expressed in another monetary currency. This criterion is important for choosing the most favorable solution due to the high price of tactical drones and the need for a large number of drones to equip tactical units of the army and police. The stated criterion is directly influenced by the economic power of the state. The financial stability of the state is inversely proportional to the importance of this criterion.
Maximum payload weight (payload) (C6) is an additional equipment (additional payload) that is placed on the UAV, based on which type, purpose and class of affiliation is characterized. For the needs of tactical units of the army and police, it is necessary for drones equipped with various types of cameras, sensors, weapons and other useful equipment. The stated criterion is of the "benefit" type, and is expressed in kilograms (kg) [2].
Using the fuzzy AHP method shown in the previous section, the weight coefficients of the criteria were determined. The weighting coefficients were calculated for each expert separately, and the obtained values were aggregated into one. The obtained weighting coefficients of the criteria are given in Table 3.

Research results
Today, a large number of countries in the world produce UAVs of various sizes and purposes, but a small number of those that can be armed (UCAV -Unmanned Combat Aerial Vehicle). Combat drones generally belong to the class of medium drones that usually fly at altitudes of about 3000 to 9000 meters and can stay in the air for 20 to 60 hours. These aircraft are usually powered by a reciprocating or turboprop engine in a thrust configuration, with modern electro-optical systems containing TV, thermal and IR cameras, laser markers and rangefinders, satellite navigation, data links, and some drones have radars. They usually carry at least two to four lethal means to act on targets on land and sea (some can carry much more).
The most complex and modern unmanned aerial vehicles come from the USA. Israel is one of the leading countries when it comes to the development of these aircraft, and in recent years, the People's Republic of China has made a big breakthrough on the UCAV market. Today, Russia, Turkey, Iran, Pakistan and a few other countries are working intensively on the development of armed drones and their small-scale lethal weapons. American armed drones like the MQ-9 "Reaper" are expensive, and they can only be bought by the closest allies, politically eligible as well as rich countries. For the needs of tactical units of the army and police, it is necessary to create a model for the selection of the most optimal solution, depending on the defined criteria, in order to implement a certain drone in these units. The analysis defines seven alternatives, i.e., seven unmanned aerial vehicles that are analyzed for the purpose of procurement and implementation in the defense and security system. All seven alternatives come from different manufacturers and from different countries. Table 4 shows the initial decision matrix where the values of the criterion functions for each alternative are shown. Using the expression 11-16, the final values of the alternatives were obtained, which is shown in Table 5. The ranking of unmanned aerial vehicles was realized on the basis of the results shown in Table 5, and the ranking of alternatives is shown in Table 6. Based on the results from Table 6, it is concluded that the most optimal solution is alternative A 7 . In order for a certain alternative to be selected as the best, it is necessary to fulfill the conditions U1 and U2. Testing of condition U1 was performed, which was fulfilled because Q(A 4 ) -Q(A 7 ) = 0,151 -0,00= 0,151 > DQ= 0,0345.
Condition U2 is fulfilled because alternative A 7 has a "sufficiently stable first place" because it has the first position according to the ranking lists QR, QS and on the ranking list Q (v=0, 25) and Q (v=0,75).
Considering that the subjectivity of decision makers is always present to a certain extent, when defining input parameters for calculating weight coefficients of criteria, it is necessary to minimize errors. In practical terms, through the last step of the model, errors in defining weighting the coefficient of the criterion, regardless of the method by which these weighting coefficients are determined.

Sensitivity analysis
Sensitivity analysis is the last step that needs to be applied. Sensitivity analysis is an important segment of the validation of results. It has been featured in a number of papers [57,58,59,60,61,62,63,64]. Weak results of sensitivity analysis take the whole research process to the beginning [65]. There are different approaches to the sensitivity analysis of models; most often authors in their papers use sensitivity analysis by changing weight coefficients of the criteria [66]. This analysis implies evaluation of alternatives based on different weight coefficients of criteria, that is favoring one criterion in each scenario. In this research we defined seven scenarios, Table 7.  Rankings of alternatives obtained using different scenarios are shown in Table 8. Table 8. Rankings of alternatives obtained using different scenarios Alternative S-0 S-1 S-2 S-3 S-4 S-5 S-6 S-7 A1  6  5  6  7  7  3  6  6  A2  5  4  5  6  4  7  4  5  A3  7  7  7  5  6  4  7  7  A4  2  6  3  3  3  6  3  4  A5  4  2  4  1  2  1  2  1  A6  3  3  2  4  1  5  5  3  A7  1  1  1  2  5  2  1  2 Obtained rankings, shown in Table 9, imply that favoring certain criteria affects the differences in rankings; this further implies that the developed model is sensitive to the changes of weight coefficients. Rankings of alternatives by different scenarios are visible in the graph below, Fig.5. The worst-ranked alternatives (A3, A1) in a large number of scenarios kept their rankings, as well as the best-ranked ones (A1, A5). However, even though the correlation between rankings seems pretty obvious, a serious analysis demands quantitative indicators. In that sense, we checked rankings correlation using the Spearman's rank coefficient [58]: where: S -the value of the Spirman coefficient; Di -the difference in the rank of the given element in vector w and the rank of the correspondent element in the reference vector; nnumber of ranked elements. The values of the Spearman's coefficients range from -1 ("ideal negative correlation") up to 1 ("ideal positive correlation") [58].
In Table 9, one can see values of the Spearman's coefficients by comparing all scenarios to each other. In the first row of Table 9, when comparing scenario S-0 (values of weight coefficients obtained through research) to others we got values compared to the final ranking.   Table 9 and Fig.6, it is clear that the correlation of rankings by scenarios is very high. Certainly, the most important correlation of the ranks is between the S-0 scenario and others, where the value of the Spearman coefficient is usually above 0.600, which can be considered satisfactory. The lowest correlation of ranks is between scenarios S-4 and S-5 (-0.143), but it can be considered expected that there are lower correlations in situations where the weight coefficient of the criterion increases significantly, as is the case with criterion C5. Criterion C5 has the lowest weighting coefficient, significant favoring of this criterion leads to a negative value of correlation of ranks, and lower values of correlation with a given criterion. There are essentially no scenarios whose correlation tends to ideally uncorrelated ranks. This indicates that the fuzzy AHP -VIKOR model can lead to good solutions, even in cases where the weighting coefficients deviate from reality.

Conclusion
The development of unmanned aerial vehicles from the beginning of the XXI century, with their wide range of possibilities, opens the possibility of application in all spheres of society. Unmanned aerial vehicles are widely used in defense and security systems as well as for commercial purposes. The paper uses the fuzzy AHP-VIKOR model to select the most optimal solution (UAV) for the needs of equipping military and police units of the tactical level. In this way, a more detailed review of the presented problem was performed. The paper presents the phases of development and application of multicriteria decision making models. The criteria of importance for the selection of the model of unmanned aerial vehicle for the needs of tactical units of the army and police were defined and the calculation of the weight coefficients of the criteria was performed by the fuzzy AHP method. The selection of the most optimal compromise solution was realized by applying the VIKOR method of multi-criteria decision-making.
Alternative A7 stands out as the optimal solution from the analyzed characteristics of unmanned aerial vehicles in the previous part of the paper. The mentioned unmanned aerial vehicle represents the most modern and state-of-the-art scientific and technological solutions. The basic goal of such a high-tech tool is to prevent operational and tactical surprises. This alternative is equally effective in both military and police units.
The contribution of this paper is reflected in the selection of the most optimal unmanned aerial vehicle depending on the given criteria, whose implementation in tactical units of the army and police would significantly increase the efficiency of these units. We have also conducted sensitivity analysis of the model. The results obtained from the sensitivity analysis show that the output values (rankings of alternatives) change depending on the weight coefficients. On the other hand, changes in rankings while changing the weight coefficients of the criteria, demonstrated clearly the dominance of the firstranked alternatives. Everything listed above implies that the model provides the same or similar results, regardless of possible minor errors that can occur in the process of defining the weight coefficients of the criteria, as a consequence of subjectivity of experts, that is, the decision-makers. The presented model can be further improved by a more detailed analysis of the criteria depending on the needs of tactical units of the army and police, by defining the additional criteria relevant to the selection of drones, defining more alternatives to UAVs and applying other methods of multicriteria analysis needs of the defense and security system.

Acknowledgements
This paper was written as part of the scientific research project funded by the Military Academy of the University of Defence in Belgrade, number: VA-DH/1/21-23 "Uticaj savremenog okruženja na izvođenje borbenih dejstava u urbanim sredinama" ("Influence of contemporary environment on the conduct of combat activities in urban spaces").