Fuzzy Model of Human s Performance for Guarding a Territory in an Air Combat

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1 Fuzzy Model of Human Performance for Guarding a Territory in an Air Combat ABSTRACT R. Ghaemi i *, S.K.Y. Nikraveh ii, M.B. Menhaj iii and S. Akbari iv Received 1 October 9; received in revied 5 May 1; acceted Setember 1 Thi aer rooe a new method for a three dimenional fuzzy model of ilot' erformance for guarding a territory with a hort-ditance between two aircraft in an air combat tak with a gun. A third-order nonlinear oint ma vehicle model i conidered for an aircraft' flight dynamic. The ired value of the velocity, the flight ath and the heading angle are obtained from ome derived equation and rule bae develoed in thi aer. The hyical control arameter are comuted through a mean quare error cheme. To model ilot' erformance and generate a comlicated offenive maneuver in an air combat, we need to imitate ilot' deciion making erformance. The rooed model how romiing erformance in all cenario in which two aircraft can hold in an air combat. Thi model emloy a time otimal combination of claic uruit when needed. Thi make our model very owerful. We conider two cae for modeling, the firt one i the model of the ilot with contant ecific energy and the other i with time varying ecific energy. Finally, thi aer rooe a new 3-Dimentional flight imulator. KEYWORDS Fuzzy modeling, Guarding a territory, Pilot' erformance, Maneuvering Offender, Puruit Evaion Game, flight imulator. 1. INTRODUCTION In the at, ilot have to obtain all neceary data and information only through their ene. Technology imrovement caue to change the figure of the air combat. Nowaday, electronic and control ytem decreae role of ilot in an air combat tak. The firt method emloyed to model an air combat wa otimal control trategy. For examle, [1] emloyed concet of differential game theory for develoing an otimal uruit-evaion roblem between two aircraft. Another alication of differential game theory to uruitevaion roblem i an air combat between two aircraft for a long-range miile duel reorted in []. An otimal guidance law wa derived in [3] for a vehicle uruing a maneuvering evader with the aumtion that a comlete knowledge of the evader' motion i available to the uruer. Reference [4] rooed a non-fuzzy baed aroach that introduce a way to roduce an otimal flight ath reference in one-to-one air combat in which a multitage influence diagram model the ilot equential maneuvering deciion. The model rovided by the differential game theory in an air combat modeling i not reliable enough to rereent the erformance of the ilot. Intelligent baed technique have alo been ued to imitate the roblem of ilot erformance in an air combat. For examle, a ilot aitance ytem ued in aociated ytem offer data and information to ilot [5]. An air combat between many aircraft ha alo been dicued in [6]. In [7], a guidance law wa develoed againt very high-eed target. A fuzzy guidance law ha been rooed for midcoure hae baed on human deciion-making. A fuzzy guidance law for -D modeling offenive maneuver i conidered for an air combat and a two- i * Correonding Author, R. Ghaemi i with the Deartment of Electrical Engineering, Damavand Ilamic Azad Univerity, Damavand, Iran ( reghaemi@gmail.com. ii S.K.Y. Nikraveh i with the Deartment of Electrical Engineering, Amirkabir Univerity of Technology, Tehran, Iran ( knikravh@aut.ac.ir. iii M. B. Menhaj i with the Deartment of Electrical Engineering, Amirkabir Univerity of Technology, Tehran, Iran ( mmenhaj@aut.ac.ir. iv S. Akbari i with the Deartment of Electrical Engineering, Kahan Univerity, Kahan, Iran ( .akbari@ku.ac.ir. Amirkabir / MISC / Vol. 43 / No.1 / Sring 11 17

2 hae uruit law wa reented a fuzzy "if then " rule in [8]. A three-dimenional fuzzy guidance law for generating a comlex offenive maneuver againt a maneuverable evader i reented in [9]. Reference [1] reented a new method for ilot erformance modeling uing both, the claic and the fuzzy method. Thee model can be ued in a real time manner and it erformance i quite the ame a the ilot' erformance. An intelligent method baed on fuzzy comutation i reented in [11] and the cature rate of the reented model i higher than that of the one given in [5]. [1] emloyed -dimentional fuzzy differential game theory to model ilot erformance in guarding a territory. A method baed on fuzzy differential game theory wa develoed in [13] for modeling the ilot' erformance in guarding a moveable object. The model rooed in [1, 13] erform quite differently from the ilot erformance. [18] reented a concurrent fuzzy-neural network aroach combining unuervied and uervied learning technique to develo the Tactical Air Combat Deciion Suort Sytem. [19] develoed an evaluation aroach baed on the technique for order Performance by imilarity to ideal olution to hel the air force academy chooe otimal initial training aircraft in a fuzzy environment. [] modeled the air combat effectivene aement roblem a a multi-criteria deciion making roblem. An imroved Fuzzy C-mean algorithm i alied to claify the multi-target in the air combat, and divi them into everal colonie averagely in [1]. In thi aer, we rooe a new 3-D fuzzy baed method to model ilot' erformance for guarding a territory in a hort ditance air combat with a gun. A et of fuzzy "if then" rule and ome claic equation can model ilot deciion in an air combat tak. The ired value of the velocity, the flight ath and heading angle are obtained from ome rule bae and equation. The hyical control arameter are comuted through a mean quare error cheme. The comuter imulation rovide an encouraging validation of the rooed model. Mimicing ilot' maneuvering in an air combat i one of the advantage of the reented model. The remaining of the aer i organized a follow: Section reent the roblem tatement. Section 3 dicue the aircraft model. Section 4 reent the linguitic model of ilot' erformance. Section 5 reent the fuzzy model of the guarding ilot. Section 6 reent Real-time imulation rogram. Simulation reult are hown in ection 7 and finally Section 8 conclu the aer.. THE PROBLEM STATEMENT Here, we conider the ituation given in figure 1. Two aircraft (P and E are engaged in a combat tak in which the P aircraft trie to guard the territory and the other one i in the offenive mode. The P aircraft ha an energy advantage and further two aircraft can maneuver in the three dimenional ace. The flight dynamic of both aircraft are governed by the third-order nonlinear oint ma equation fully dicued in ection 3. Being more realitic, we conider here the two aircraft both have thrut, velocity and turn radiu limitation. The roblem i to find a model of ilot' erformance that ut the E aircraft in it rear hemihere and then trie to ut target in it effective gun enveloe before the E aircraft can arrive to the ecified territory. The effective gun enveloe hall lie between a minimum and maximum range. The maximum range i becaue of the bullet velocity, the rate fire and bullet aerodynamic. The minimum range i to avoid colliion with the target or the target debri. The rooed model mut act in a manner in which the P aircraft doe not loe any energy in energy contant mode. In addition to reaching a uitable oition for hooting, the P aircraft mut not let the E aircraft to enter the ecified territory. The ilot alway ue the contant energy mode. If the energy of the aircraft decreae in an air combat, the ilot may loe hi ituation advantage. The firt cae in which the contant energy mode conidered, we invetigate another cae with the almot energy contant mode. With thi aumtion, we gue that the cature time decreae. Fig. 1: air combat geometry Let the oition of the P aircraft be ( y z x, the oition of the E aircraft be ( e ye ze oition of the territory be at (,, x and the x y z and the T T T following i lited. Flight ath angle( : the angle between velocity vector and horizontal lane, Heading angle( χ : the angle between rojection of the velocity vector in X-Y lane with X-axi, LOS (Line of ight: direct line between aircraft, Vertical ditance: ditance between P and Q oint, Horizontal ditance: ditance between E and Q oint, Lead angle ( ψ : angle between rojection of the velocity vector of uruer ( V in X-Y lane and LOS, P 18 Amirkabir / MISC / Vol. 43 / No.1 / Sring11

3 AOT ( ψ 3 : angle between the velocity vector of evader ( V E and LOS, Off angle ( ψ 1 : angle between V P and LOS, Ditance: the difference ditance between two aircraft at time t k andt k 1, Lead angle: the difference lead angle of the P aircraft at time intant t k andt k 1, X-ditance aigned by ( x xe difference ditance along the x-axi, Y- ditance reented by ( y ye i difference ditance along the y-axi, Z-ditance aigned by z z i ( e difference ditance along the z-axi. V i the aireed, T the thrut, D the vehicle drag, L the lift, m the vehicle ma, g the acceleration due to gravity, the flight a angle, χ the heading angle, ϕ the bank angle, E S the ecific energy, Ee the energy tate and H rereent the height of the aircraft. The V velocity ratio aigned by P in which V V P and E VE are velocity of P and E aircraft. Ditance ratio i a ( x xe + ( y ye + ( z z e. ρ i the atmohere ( x x + ( y y + ( z z e T e T e T denity, S i the reference area of wing, C d i the drag coefficient, C l i the lift coefficient, D i the drag and L denote the lift. the ired value of flight ath angle and χ i the ired heading angle. W i a weighting arameter that i defined in ection ( AIRCRAFT MODEL The oint ma equation of motion for an aircraft for a flat non-rotating earth, thrut along the ath and a quiecent atmohere are given by the following equation [7]. T D V = g in m L in φ χ = mv co g L co φ = ( co V mg x = V co co χ y = V co in χ z = V in The aerodynamic drag and lift are calculated a: (1 1 D = ρ V SC d ( 1 L = ρ V SC L (3 The motion equation of the evader are in the ame form a thoe of the uruer given in (1. The total "energy tate" i um of the kinetic energy and the otential energy. The energy tate i calculated a: 1 Ee = mgh + mv (4 Eliminating the weight of aircraft from the energy tate calculation caue the "ecific energy" defined in (5. V E = H + (5 g Where, H and V tand for the otential and the kinetic energy, reectively. 4. LINGUISTIC MODELS In thi ection, we reent uitable linguitic model for both P and E aircraft. To do o, we are required to comly with the aumtion made in ection (, exert deciion a well a the ilot' maneuvering kill [14-17]. After ome invetigation the linguitic model are rooed a follow. The P aircraft attemt to do the out of lane maneuver to ut the target in it effective gun enveloe before the E aircraft arrive at the ecified territory. In thi air combat, the guarder mut avoid lo of energy. The E aircraft offend to the territory by diving toward it. In an air combat, ilot uually determine the flight ath angle a well a the heading angle. The linguitic model of the guarder i ummarized below. A. The flight ath angle In thi cae, the ilot ue lead uruit in the flight ath angle when the ditance between two aircraft i big, but near the target, the P aircraft hold it noe directly on the target. B. The heading angle Through ome invetigation, we reach to the concluion that the heading angle become different when the two aircraft are head on cae or head to tail cae with the following rule: If AOT i more than 9 and le than 7, the aircraft i in head to tail cae. Otherwie, it i in head on cae. In the head on cae, the ilot emloy the lag uruit when the x-ditance i big or the y-ditance i mall. A the y-ditance increae and the x-ditance decreae the lag angle decreae. In the head to tail cae, the ilot emloy lead uruit and decreae the lead angle when they are cloe to the Amirkabir / MISC / Vol. 43 / No.1 / Sring 11 19

4 target. According to the acquired data from [14-17] and ilot a well, the change of the flight ath angle and the heading angle do not hare the ame value of imortance. The relative imortance of the angle in an air combat i dicued below. C. The relative imortance of the angle Conider in which the E aircraft tart to dive toward the territory. If either the ditance i big and the horizontal ditance i mall or the heading angle of the E aircraft i big, then the flight ath angle become imortant. On the contrary, the heading angle become more imortant, if both of the vertical ditance i mall and the horizontal ditance i big, Furthermore, we evaluate the imortance of the both angle the ame, if either of the following two cae i atified 1 dangerou overhoot may be occurred, the ditance i mall, then the degree of imortance of both angle become the ame. 5. THE FUZZY MODEL OF THE GUARDER For igning uitable rule bae of fuzzy guidance block, we mut ue linguitic model of ilot erformance and exerimental data a well. The linguitic model i eential for igning a et of roer table to etablih a et of related memberhi function. We deliver exerimental data to ilot and evaluate it erformance in an air combat tak. A amle of thee table i given below. TABLE 1 PILOT S NUMERICAL DATA Inut X-ditance 5 Data Y- ditance 5 Z-ditance 1 Lead angle 5 outut Data χ 6 45 According to the information mentioned in ection (4 and numerical data, thi ection rooe a fuzzy model a deicted in figure (. Fig. : 3-D fuzzy model of the guarder erformance A oberved in figure (, the rooed model of the ilot ha three ditinct block: Inut generator, Fuzzy guidance law (FGL, and the otimal converter. Each block i dicued below. A. The inut generator Thi block i for generating the inut of the FGL block. The formula ued in thi block are given below. xe x LOS = ye y ze z Off Angle = ( x ( ( 1 e x x + ye y y ze z z co ( x + y z(( xe x ( ye y ( ze z ( y co ( in 1 e y χ xe x χ Lead Angle = tan ( xe xco χ + ( ye yinχ (6 B. The fuzzy guidance law Thi block i for generating maneuver of guiding aircraft. Thi block inclu four ub-block: for the calculation of the heading angle, for the calculation of the flight ath angle, for the calculation of the weighting arameter and alo the velocity rediction. The rooed ub-block are hown in figure (3. In the following ection, the term et v, b,, ze,, la, nb and n are tand for very mall, oitive big, mall, zero, oitive, large, negative big, and negative value reectively. Fig. 3: Fuzzy guidance law block The next ubection deliver comlete detail about figure 3. In the following rule bae, the memberhi function are arbitrarily choen a triangular and traezoidal hae. The memberhi function arameter have been derived through both the information acquired from ilot and reference [14-17]. In the following rule bae, the fuzzification method i ingleton, the defuzzification method i defined a centroid, the imlication method i reented a min, and the aggregation method max. Amirkabir / MISC / Vol. 43 / No.1 / Sring11

5 C. The flight ath angle block Thi block i for calculation of the flight ath angle in an air combat. According to the linguitic model given in ection (4, the effective inut of thi block are the vertical and the horizontal ditance, the lead angle and the ratio of the ditance between two aircraft to the ditance of the E aircraft from the ecified territory. Thi angle ha a lead angle that mut be aigned by the ilot. The flight ath angle without the lead angle can be calculated a conidering the definition of the ection. vertical ditance = tan 1 ( + (9 horizontal ditance i the ired flight ath angle of the P aircraft and i the actual flight ath angle of the P aircraft. The ired flight ath angle with the lead angle i determined a: vertical ditance+ M = tan 1 ( + (1 horizontal ditance The arameter M indicate the amount of lead angle required for a high cature rate. It i calculated from a et of rule bae develoed in thi aer and the inut to thee rule bae are the ditance between two aircraft, the vertical ditance and ditance ratio. A amle of the rule i hown below. if(ditance i zeand(vertical_ditance i not zethen(m i The cending rule bae contain 1 rule. D. The heading angle Thi block i for calculation of the ired heading angle of the P aircraft in an air combat tak. The inut of thi block are the x-ditance, the y-ditance, the vertical ditance and the ditance between two aircraft. The ilot emloy the lead angle. The ired heading angle without conideration of the lead angle can be derived a: 1 X_ ditance χ = tan ( (11 Y_ ditance According to the linguitic model given in the ection (4, in the head on cae, the P aircraft ue lag uruit. The ired heading angle can be calculated a: 1 Y ditan ce χ = tan ( (1 X_ dixtance+ N A rule bae calculate the arameter N. The inut of thi rule bae are the ditance and the horizontal ditance. In the head to tail cae, the P aircraft ue the lead uruit. In thi cae the ired heading angle can be calculated a: 1 Y_ ditance+ N χ = tan ( (13 X_ ditance Amirkabir / MISC / Vol. 43 / No.1 / Sring 11 The arameter N i alo obtained from a et of rule whoe inut are the x-ditance, the z-ditance and the y- ditance. A amle of the rule i hown below. if(ditance i zeand(horizontal_ditance i not zethen(n i The heading angle rule bae contain 1 rule. E. The weighting arameter According to the linguitic model dicued in ection (4, the inut to thi block are the horizontal and the vertical ditance, the velocity ratio, the lead angle, the change of the lead angle, the flight ath angle of the P aircraft and the change of the lead angle. A amle of the rule i hown below. If(horizontal_ditance i not or(gama i not or(velocity_ratio i not lathen(w i teta W i teta in the above rule, mean that χ i imortant in thi ituation. The climb weighting arameter rule bae conit of 17 rule. F. Velocity rediction Thi block i for the velocity rediction in which the ecific energy i contant. According to the contancy of energy in the P aircraft, we firt take the derivative of ( and then ue the equation (1 to obtain (14. V = gin (14 T = D According to thi equation the maximum value of the thrut and the drag are equal. Here, we mut conider a velocity limitation a follow. If the velocity given in (14 i maller thanv Min, we mut ue the following equation. V = (15 G. The otimal converter block If the ecific energy i contant then thi block i for converting the ired value of the tate variable to correonding the hyical inut of the aircraft dynamic uch a the thrut, the lift and the bank angle. Thee variable hould atify the following relationhi. Min{ W ( ( k ( χ( k + 1 χ }.t. L LMax, 9 ϕ 9 (16 The condition L Lmax tate that the P aircraft will not loe any energy, L i the required lift and L Max rereent the valid maximum lift that can be obtained a: ρsv LMax = ( TMax.5 CDSρV K L= ( mv χin + ( mv + mgco (17 1

6 where K i a contant value. In the varying ecific energy, we can inut the derived the ecific energy in equation (16. If the ecific energy i almot contant then the reviou equation and the rediction block i not valid and the velocity, the thrut, the lift and the bank angle are determined a follow. M in{ W 1 ( E ( k + 1 E ( k + W ( χ ( k + 1 χ + ( ( k + 1 } π π t.. < T T max, L L max, ϕ (18 T D V( k+ 1 = V( k + TS ( + gin ( k (19 m where W 1,W are the energy contancy arameter and the weighting arameter, reectively. The LMax can be determined from V-n Diagram a mentioned in [14]. By uing the equation (1 through (5, we can rewrite the equation (18 a: V ( k + 1 V ( k Min( W1( z ( k + 1 z ( k + g TLSin ϕ + W ( χ( k χ + mvco gt LCoϕ ( ( k ( Co( k V mg π π t.. < T Tmax, L Lmax, ϕ ( 6. REAL-TIME SIMULATION PROGRAM In order to viually rereent the imulation roce in real-time, we develoed a comuter rogram under Window oerating ytem uing C++ language. Thi rogram ha two major mo. The firt mode i real-time imulation of the flight, which uer can change inut value uing the rovided GUI control and ee the effect intantly. The econd mode i imulation of two airlane in fight, which get imulation reult from MATLAB and udate the cene, reectively. In both mo, we can ee the cene in 3D. Program conit of two main block, the rimary one handle GUI event and udate 3D cene, and the econdary one olve equation of motion. The relationhi between the two thread i hown in figure (4. Fig. 4: the view of the imulator rogramming A hown in the above diagram, the rogram ha 4 major module: GUI module: handle GUI event and uer interaction ODE Solver module: olve ytem of differential equation State module: define tate variable of the airlane and equation of motion 3D Grahic module: udate 3D cene Fig. 5 the view of the imulator 7. SIMULATION RESULTS In thi ection, we conider the erformance of the rooed model. The P and E aircraft arameter are given below [7]. 5 TMax = 1 N; k =.179; V = m ; 4 m = 1 kg, S = 6 m ; Ve = 1 m Cd =.169; ρ =.8, VMin = 6 m The ilot aroved the imulation reult of the fuzzy modeling. The imulation reult eaily arove the high caability of the rooed model for caturing the E aircraft in all cae before the E aircraft enter the guarding territory. We firt conider the cae in which the ecific energy i contant. The imulation reult how that the thrut and lift erformance are aroximately the bang-bang tye and our method erform near time otimal erformance. The guarding territory i located at (1,. The following cae are further invetigated. Amirkabir / MISC / Vol. 43 / No.1 / Sring11

7 1 Head to tail cae: in order to check how good our model erform, we conider the following cae. The P and E aircraft are initially located in (-5,, 5 and (,, 5, reectively with initial lead angle equal to. Figure (6 how the caability of the model in generating a near time otimal erformance combination of the vertical lead turn and the horizontal lag turn regularly done by ilot. Fig. 8: Thrut, Lift and bank angle variation of aircraft P during a maneuver in the firt imulation Fig. 6: the ath roduced by rooed model Head on cae: The P and E aircraft initially located in (5, 4, 5 and (,, 5, reectively and the initial lead angle i 18. Figure (7 lot the erformance of the rooed model in generating an otimal time combination of the claic maneuver. In thi cae, we eaily ee that the P aircraft initially ue out of lane lag turn and then emloy a claic maneuver to gain angular advantage. To ee how robut our method i againt noie, we conider the P and E aircraft initially located in (5, 5, 5 and (,, 5 reectively while the inut of the P aircraft are contaminated by noie. We conider the inut of the inut generator block are ignal. The ignal to noie ratio i 9%. Finally to how the rooed model behave in a bang-bang mode, at the firt imulation, we conider the P and E aircraft initially located in (-, 1, 5 and (,, 5 reectively in figure (8. Figure (9 how the thrut and the lift and the bank angle are the bang bang tye. Fig. 9: Thrut, Lift and bank angle variation of aircraft P during a maneuver in the econd imulation Then in the econd imulation, we conider the ituation in which the ecific energy i almot contant. At the third imulation, we conider the following cae. The P and E aircraft are initially located in (-1, 5, 5 and (,, 5 reectively with initial lead angle of and W 1 = 1. Figure (1 how the caability of the rooed model in generating a near time otimal erformance combination of the vertical lead turn and the horizontal lag turn regularly done by ilot. In thi cae, the Thrut, the Lift and the bank angle are hown in figure (11. Fig. 7: the ath roduced by rooed model in firt imulation Fig. 1: the ath roduced by rooed model with almot contant energy in the third imulation Amirkabir / MISC / Vol. 43 / No.1 / Sring 11 3

8 Fig. 1: the view of the imulator Fig. 11: Bank angle, Thrut and Lift aircraft P during a maneuver with almot energy contant in the third imulation From figure (11, it i clear that the change in the bank angle, the thrut and the lift are not accetable. Thi how that the model with thi aumtion i not correct. Finally the rooed model alied in oftware imulator i hown in figure (1 where the red aircraft want to uruit the blue one. 8. CONCLUSION In thi aer, an intelligent model for modeling of the ilot erformance for guarding a territory i finally derived. Thi model i a combination of the claic model and the fuzzy modeling in which the fuzzy model allow u to model uncertainty and imreciion of the ilot knowledge; thi i uitable for guarding a territory and generating comlex maneuver in an air combat tak. The model emloy a near time otimal combination of the claic uruit. The ilot aroved that the fuzzy model can mimic the ilot' erformance in an air combat. Thi i the advantage of the rooed model. The comuter imulation rovided an encouraging validation of the rooed model in the contancy energy mode. The imulation reult howed that the rooed model i not erformable when the ecific energy i almot contant. The rooed imulator ha romiing erformance. 9. REFERENCE [1] Hammer J.M., Small R.L., An intelligent interface in an aociate ytem, In Roue W B (ed. Human / technology interaction in comlex ytem, vol.7, , [] Rodin E.Y., Geit D., Lirov Y., Flight and fire control knowledge rereentation, roceeding 8th IEEE CDC, 1989, [3] Lin C.L. and Chen Y.Y., Deign of fuzzy logic guidance law againt high eed target, Journal of guidance, control and dynamic, No.1, Vol.3,.17-5,. [4] Akbari S., Menhaj M.B., A fuzzy guidance law for modeling offenive air-to-air combat maneuver, IEEE conf, IFSA World congre and th NAFIPS international conference, , 1. [5] Akbari S., Qualitative model of ilot erformance in air to air combat tak: fuzzy et theory aroach., Phd diertation, Electrical Deartment, AUT, Iran,. [6] Virtanen K., Raivio T., Hamalainen R.P., Modeling ilot' equential maneuvering deciion by multitage influence diagram, Proceeding of AIAA guidance, control and dynamic conference, , 1. [7] Menon P.K. and Duck E.L., Time otimal uruit evaion with weaon enveloe contraint, journal of guidance, control and dynamic, vol. 15, No., 199, [8] Jamark B., A miile duel between two aircraft, journal of guidance, control and dynamic, vol.8, No.4, 1985, [9] Guelman M. and Shinar J., Otimal guidance law in the lane, Journal of Guidance, Control and Dynamic, vol.8, No.4, 1985, [1] K. H. Hia and J. G. Hieh, A firt aroach to fuzzy differential game roblem: guarding a territory, fuzzy et and ytem, vol. 55, 1993, [11] H. J. Chu, J. G. Hieh, K. H. and L. W. Chen, Fuzzy differential game of guarding a movable territory, Information Science, vol. 91, , [1] Ghaemi R, Nikraveh SKY, Menhaj MB, Akbari S, A near otimal fuzzy model of uruit-evaion in an air combat, WSEAS TRANSACTIONS ON MATHEMATICS, Iue 3, Volume 3, 4, [13] Ghaemi R, Nikraveh SKY, Menhaj MB, Akbari S, A 3-D fuzzy model of ilot erformance in the dogfight, WSEAS TRANSACTIONS ON MATHEMATICS, Iue 3, Volume 3, 4, [14] Anderon J.D., Introduction to flight, McGrow Hill, 3 rd edition, [15] Shaw R.L., Fighter combat: Tactic and Maneuvering, 1 t edition, United State Naval Int., [16] Raier, ACM, training: Angle Tactic, htt:// [17] Crenhaw D., How to live and die in the virtual ky, htt:// [18] Tran C., Abraham A. and Jain L., A Concurrent Fuzzy-Neural Network Aroach for Deciion Suort Sytem, IEEE International Conference on Fuzzy Sytem, , 3 [19] Wang T.C., Chang T.H., Alication of TOPSIS In Evaluating Initial Training Aircraft Under A Fuzzy Environment, Exert Sytem with Alication 33, , 7 [] Wang J., Fan K., Su Y., Liang S., and Wang W., Air Combat Effectivene Aement of Military Aircraft Uing a Fuzzy AHP and TOPSIS Methodology, IEEE 7 th intl. conf. on ytem imulation and cientific comuting, , 8. [1] Zhang K., Zhou D., Alication of Imroved FCM on Claification of Multi-Target Guided by AWACS, IEEE comuter Society, Fifth International Conference on Fuzzy Sytem and Knowledge Dicovery, , 8. 4 Amirkabir / MISC / Vol. 43 / No.1 / Sring11