Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T05:59:34.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Vertical take-off and landing hybrid unmanned aerial vehicles: An overview

Published online by Cambridge University Press:  14 April 2022

M. Rehan Open the ORCID record for M. Rehan [Opens in a new window] ,
F. Akram ,
A. Shahzad ,
T.A. Shams  and
Q. Ali
M. Rehan*
Affiliation:
College of Aeronautical Engineering, National University of Sciences & Technology, Islamabad, Pakistan
F. Akram
Affiliation:
College of Aeronautical Engineering, National University of Sciences & Technology, Islamabad, Pakistan
A. Shahzad
Affiliation:
College of Aeronautical Engineering, National University of Sciences & Technology, Islamabad, Pakistan
T.A. Shams
Affiliation:
College of Aeronautical Engineering, National University of Sciences & Technology, Islamabad, Pakistan
Q. Ali
Affiliation:
College of Aeronautical Engineering, National University of Sciences & Technology, Islamabad, Pakistan
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This article presents the research status and development trends of Vertical Take-off and Landing hybrid Unmanned Aerial Vehicles. In this research, a special emphasis is laid on the design philosophies, analysis techniques, dynamic modeling, and control laws of hybrid VTOL UAVs. It studies and compares various design configurations of hybrid VTOL UAVs, based on key design features such as aerodynamic performance, flight stability, structural strength, propulsive power, avionics systems, flight controls, autonomy, ease of fabrication and flight transition mechanisms. The benefits and shortcomings of each design configuration are expressed in detail. A selection problem is formulated in a fuzzy environment and the Multi-Attribute Decision-Making technique is employed. Ongoing research projects in the field are discussed and a novel design of tail sitter hybrid VTOL UAV is presented by the authors. This work serves as a useful guide for the prospective explorers of this challenging field of research.

Keywords

Unmanned Aerial VehiclesVertical Take-off and LandingMulti-Attribute Decision Making
Type
Survey Paper
Information
The Aeronautical Journal , Volume 126 , Issue 1306 , December 2022 , pp. 2017 - 2057
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Yanguo, S. and Huanjin, W. Design of flight control system for a small unmanned tilt rotor aircraft, Chinese J. Aeronaut., 2009, 22, pp 250–256.Google Scholar
(2020, 28 December). AgustaWestland Project Zero (defunct). Available: https://evtol.news/agustawestland-project-zero/ Google Scholar
Papachristos, C., Alexis, K. and Tzes, A. “Design and experimental attitude control of an unmanned tilt-rotor aerial vehicle,” in 2011 15th International Conference on Advanced Robotics (ICAR), 2011, pp 465-470.Google Scholar
(2020, 30 December). Unmanned Aerial Vehicles (UAVs). Flying where others can’t. Available: https://www.4frontrobotics.com/uavs Google Scholar
(2020, 30 December). Bell Eagle Eye Tiltrotor UAV. Available: https://www.navaltechnology.com/projects/belleagleeyeuavcNavBarChannelContentCentralNervousSystem Google Scholar
Ozdemir, U., Aktas, Y.O., Demirbag, K., Erdem, A., Kalaycioglu, G.D., Ozkol, I., and Inalhan, G. Design of a commercial hybrid VTOL UAV system, 2013 International Conference on Unmanned Aircraft Systems (ICUAS), 2013, pp 214–220.Google Scholar
Ozdemir, U., Aktas, Y.O., Vuruskan, A., Dereli, Y., Tarhan, A.F., Demirbag, K., Erdem, A., Kalaycioglu, G.D., Ozkol, I., and Inalhan, G. Design of a commercial hybrid VTOL UAV system, J. Intell. Robot. Syst., 74, pp 371–393, 2014.Google Scholar
Vuruskan, A., Yuksek, B., Ozdemir, U., Yukselen, A. and Inalhan, G. Dynamic modeling of a fixed-wing VTOL UAV, 2014 International Conference on Unmanned Aircraft Systems (ICUAS), 2014, pp 483–491.Google Scholar
Yuksek, B., Vuruskan, A., Ozdemir, U., Yukselen, M. and Inalhan, G. Transition flight modeling of a fixed-wing VTOL UAV, J. Intell. Robot. Syst., 2016, 84, pp 83–105.Google Scholar
(2020, 31 December). Introducing FireFLY6 PRO welcome to the revolution. Available: https://www.birdseyeview.aero/pages/firefly6-pro Google Scholar
(2020, 30 December). IAI Panther Tilt-Rotor Unmanned Aerial Vehicle (UAV). Available: https://www.militaryfactory.com/aircraft/detail.asp?aircraft_id=1093 Google Scholar
(2020, 30 December). Tilt rotor technology developments. Available: https://barnardmicrosystems.com/UAV/milestones/tilt_rotor.html Google Scholar
(2021, 29 December). Kestrel. No Runway. No Problem. Available: https://www.autelrobotics.com/kestrel Google Scholar
(2020, 29 December). Boeing Phantom Swift Selected for DARPA X-Plane Competition. Available: https://boeing.mediaroom.com/Boeing-Phantom-Swift-Selected-for-DARPA-X-Plane-Competition Google Scholar
(2020, 30 December). Quantum Systems. The high payload eVTOL PPK drone. Available: https://www.quantum-systems.com/project/tron-f90/ Google Scholar
(2020, 29 December). Phantom Swift: Putting Rapid Into Rapid Prototyping. Available: https://www.boeing.com/features/2013/09/bds-phantom-swift-09-11-13.page Google Scholar
Fang, X., Lin, Q., Wang, Y. and Zheng, L. Control strategy design for the transitional mode of tiltrotor UAV, IEEE 10th International Conference on Industrial Informatics, 2012, pp 248–253.Google Scholar
Kendoul, F., Fantoni, I. and Lozano, R. Modeling and control of a small autonomous aircraft having two tilting rotors, IEEE Trans. Robot., 2006, 22, pp 1297–1302.Google Scholar
Chowdhury, A.B., Kulhare, A. and Raina, G. Back-stepping control strategy for stabilization of a tilt-rotor uav, in 2012 24th Chinese Control and Decision Conference (CCDC), 2012, pp 3475–3480.Google Scholar
Kleinhesselink, K. “Stability and control modeling of tiltrotor aircraft,” 2007.Google Scholar
Chowdhury, A.B., Kulhare, A. and Raina, G. A generalized control method for a Tilt-rotor UAV stabilization, 2012 IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems (CYBER), 2012, pp 309–314.Google Scholar
Ta, D.A., Fantoni, I. and Lozano, R. Modeling and control of a tilt tri-rotor airplane, 2012 American control conference (ACC), 2012, pp 131–136.Google Scholar
Papachristos, C. and Tzes, A. Modeling and control simulation of an unmanned tilt tri-rotor aerial vehicle, 2012 IEEE International Conference on Industrial Technology, 2012, pp 840–845.Google Scholar
Armutcuoglu, O., Kavsaoglu, M.S. and Tekinalp, O. Tilt duct vertical takeoff and landing uninhabited aerial vehicle concept design study, J. Aircr., 2004, 41, pp 215–223.Google Scholar
Okan, A., Tekinalp, O. and Kavsaoglu, M. Flight control of a tilt-duct UAV, 1st UAV Conference, 2002, p 3466.Google Scholar
Tekinalp, O., Unlu, T. and Yavrucuk, I. Simulation and flight control of a tilt duct uav, AIAA Modeling and Simulation Technologies Conference, 2009, p 6138.Google Scholar
Flores, G. and Lozano, R. Transition flight control of the quad-tilting rotor convertible MAV, 2013 International Conference on Unmanned Aircraft Systems (ICUAS), 2013, pp 789–794.CrossRefGoogle Scholar
Flores-Colunga, G.R. and Lozano-Leal, R. A nonlinear control law for hover to level flight for the quad tilt-rotor uav, IFAC Proc. Vol.,, 2014, 47, pp 11055–11059.Google Scholar
Abras, J. and Narducci, R. Analysis of CFD modeling techniques over the MV-22 tiltrotor, in American Helicopter Society 66th Annual Forum, 2010, pp 11–13.Google Scholar
Abdollahi, C. Aerodynamic analysis and simulation of a twin-tail tilt-duct unmanned aerial vehicle, 2010.Google Scholar
Park, S., Bae, J., Kim, Y. and Kim, S. Fault tolerant flight control system for the tilt-rotor UAV, J. Franklin Inst., 2013, 350, pp 2535–2559.Google Scholar
Holsten, J., Ostermann, T. and Moormann, D. Design and wind tunnel tests of a tiltwing UAV, CEAS Aeronaut. J., 2011, 2, pp 69–79.Google Scholar
Ostermann, T., Holsten, J., Dobrev, Y. and Moormann, D. Control concept of a tiltwing uav during low speed manoeuvring, Proceeding of the 28th International Congress of the Aeronautical Sciences: ICAS Brisbane, Australia, 2012.Google Scholar
Holsten, J., Ostermann, T., Dobrev, Y. and Moormann, D. Model validation of a tiltwing UAV in transition phase applying windtunnel investigations, Congress of the International Council of the Aeronautical Sciences, 2012, pp 1–10.Google Scholar
Dickeson, J.J., Mix, D.R., Koenig, J.S., Linda, K.M., Cifdaloz, O., Wells, V.L., and Rodriguez, A.A. H∞ hover-to-cruise conversion for a tilt-wing rotorcraft, Proceedings of the 44th IEEE Conference on Decision and Control, 2005, pp 6486–6491.Google Scholar
Fredericks, W.J., Moore, M.D. and Busan, R.C. Benefits of hybrid-electric propulsion to achieve 4x cruise efficiency for a VTOL UAV, 2013 International Powered Lift Conference, 2013, p 4324.Google Scholar
(2021, 08 January). Ten-Engine Electric Plane Completes Successful Flight Test. Available: https://www.nasa.gov/langley/ten-engine-electric-plane-completes-successful-flight-test Google Scholar
(2021, 08 January). AT-10 VTOL Hybrid Tactical UAS. Available: http://acuityaero.com/pages/AT-10.htm Google Scholar
(2021, 08 January). Successful Trial Integration of DHL Parcelcopter into Logistics Chain. Available: https://www.https://www.dhl.com/en/press/releases/releases_2016/all/parcel_ecommerce/successful_trial_integration_dhl_parcelcopter_chain.html Google Scholar
(2021, 08 January). DHL Parcelcopter 3.0 - Autonomous flight in the Alps. Available: https://www.dpdhl.com/en/media-relations/media-center/tv-footage/dhl-parcelcopter-v3-flight-full-hd.html Google Scholar
Muraoka, K., Okada, N. and Kubo, D. Quad tilt wing vtol uav: Aerodynamic characteristics and prototype flight, AIAA Infotech@ Aerospace Conference and AIAA Unmanned… Unlimited Conference, 2009, p 1834.Google Scholar
(2021, 08 January). Flight tests at Taiki Aerospace Research Field to evaluate the flight controller for Quad Tilt Wing (QTW) VTOL UAV. Available: https://www.aero.jaxa.jp/eng/research/frontier/vtol/qtw/news140331.html Google Scholar
Çetinsoy, E., Sirimoğlu, E.F.E., Öner, K.T., Hancer, C., Ünel, M., Akşit, M.F., Kandemir, İ., and Gülez, K. Design and development of a tilt-wing UAV, Turk. J. Electr. Eng. Comput. Sci., 2011, 19, pp 733–741.Google Scholar
Öner, K.T., Çetinsoy, E., Ünel, M., Akşit, M.F., Kandemir, I. and Gülez, K. Dynamic model and control of a new quadrotor unmanned aerial vehicle with tilt-wing mechanism, 2008.Google Scholar
Öner, K.T., Çetinsoy, E., Sirimoğlu, E., Hancer, C., Ayken, T. and Ünel, M. LQR and SMC stabilization of a new unmanned aerial vehicle, 2009.Google Scholar
Kinder, D. and Whitcraft, G. Design and development of a tilt-wing aircraft, 2000 AIAA Student Conference, 2000.Google Scholar
Mix, D. and Seitz, D. Dynamics of control system design for a tilt-wing vehicle, 2000 AIAA Student Conference, 2000.Google Scholar
Öner, K.T., Çetinsoy, E., Sirimoğlu, E.F.E., Hançer, C., Ünel, M., Akşit, M.F., Gülez, K., and Kandemir, İ. Mathematical modeling and vertical flight control of a tilt-wing UAV, Turk. J. Electr. Eng. Comput. Sci., 2012, 20, pp 149–157.Google Scholar
Cetinsoy, E., Dikyar, S., Hançer, C., Oner, K.T., Sirimoglu, E., Ünel, M., and Aksit, M.F. Design and construction of a novel quad tilt-wing UAV, Mechatronics, 2012, 22, pp 723–745.Google Scholar
Heredia, G., Duran, A. and Ollero, A. Modeling and simulation of the HADA reconfigurable UAV, J. Intell. Robot. Syst., 2012, 65, pp 115–122.Google Scholar
(2021, 12 January). Rheinmetall Airborne Systems Tactical Hybrid UAS. Available: https://www.uasvision.com/2012/09/03/rheinmetall-airborne-systems-tactical-hybrid-uas/ Google Scholar
(2021, 12 January). The Airbus Group’s Quadcruiser concept is validated in flight tests. Available: https://www.suasnews.com/2014/12/the-airbus-groups-quadcruiser-concept-is-validated-in-flight-tests/ Google Scholar
(2021, 12 January). PROJEKT QUADCRUISER. Available: http://www.sfl-gmbh.de/en/blog/projekte/projekt-quadcruiser/ Google Scholar
(2021, 12 January). Out of the Black: SLT VTOL UAV. Available: https://diydrones.com/profiles/blogs/out-of-the-black-slt-vtol-uav Google Scholar
(2021, 12 January). Arcturus Jump 15 UAV. Available: https://arcturus-uav.com/product/jump-15 Google Scholar
(2021, 12 January). Latitude Engineering HQ-40 (Hybrid Quadcopter) VTOL Unmanned Aerial Vehicle (UAV). Available: https://www.militaryfactory.com/aircraft/detail.asp?aircraft_id=1106 Google Scholar
(2021, 12 January). FOXTECH Great Shark 330 VTOL. Available: https://www.foxtechfpv.com/foxtech-great-shark-330-vtol.html Google Scholar
(2021, 22 February). HADA-Helicopter Adaptive Aircraft. Available: https://www.embention.com/project/hada-helicopter-adaptive-aircraft/ Google Scholar
(2021, 13 January). HADA-Helicopter Adaptive Aircraft. Available: https://www.embention.com/project/hada-helicopter-adaptive-aircraft/ Google Scholar
(2021, 13 January). Rheinmetall Airborne Systems. Available: https://www.rheinmetall-defence.com/en/rheinmetall_defence/public_relations/news/archiv/2017/aktuellesdetailansicht_7_1857.php Google Scholar
Low, J.E., Win, L.T.S., Shaiful, D.S.B., Tan, C.H., Soh, G.S. and Foong, S. Design and dynamic analysis of a transformable hovering rotorcraft (thor), 2017 IEEE International Conference on Robotics and Automation (ICRA), 2017, pp 6389–6396.Google Scholar
Jenkins, D.R., Landis, T. and Miller, J. American X-Vehicles: An Inventory X-1 to X-50 Centennial of Flight Edition, 2003.Google Scholar
Tayman, S.K. Stop-rotor rotary wing aircraft, ed: Google Patents, 2011.Google Scholar
Vargas-Clara, A. and Redkar, S. Dynamics and control of a stop rotor unmanned aerial vehicle, Int. J. Electr. Comput. Eng. (2088-8708), 2012, 2, pp 597–608.Google Scholar
Clara, A. and Redkar, S. Dynamics of a vertical takeoff and landing (vtol) unmanned aerial vehicle (uav), Int. J. Eng. Res. Innovation, 2011, 3, pp 52–58.Google Scholar
Cord, T. Skytote advanced cargo delivery system, AIAA International Air and Space Symposium and Exposition: The Next 100 Years, 2003, p 2753.Google Scholar
Jung, Y. and Shim, D.H. Development and application of controller for transition flight of tail-sitter UAV, J. Intell. Robot. Syst., 2012, 65, pp 137–152.Google Scholar
(2021, 15 January). FLEXROTOR. Available: https://aerovel.com/flexrotor/ Google Scholar
(2021, 15 January). V-BAT Industry-Leading VTOL Unmanned Aerial System. Available: https://martinuav.com/ Google Scholar
(2021, 15 January). Thirty two hour flight record for Aerovel Flexrotor VTOL. Available: https://www.suasnews.com/2017/10/thirty-two-hour-flight-record-aerovel-flexrotor-vtol/ Google Scholar
(2021, 15 January). Martin UAV V-BAT. Available: https://martinuav.com/v-bat/ Google Scholar
Manouchehri, A., Hajkarami, H. and Ahmadi, M.S. Hovering control of a ducted fan VTOL Unmanned Aerial Vehicle (UAV) based on PID control,n 2011 International Conference on Electrical and Control Engineering, 2011, pp 5962–5965.Google Scholar
Matsumoto, T., Kita, K., Suzuki, R., Oosedo, A., Go, K., Hoshino, Y., Konno, A., and Uchiyama, M. A hovering control strategy for a tail-sitter VTOL UAV that increases stability against large disturbance, 2010 IEEE international conference on robotics and automation, 2010, pp 54–59.Google Scholar
Bilodeau, P.-R. and Wong, F. Modeling and control of a hovering mini tail-sitter,. Int. J. Micro Air Veh., 2010, 2, pp 211–220.Google Scholar
Jeong, Y., Shim, D. and Ananthkrishnan, N. Transition Control of Near-Hover to Cruise Transition of a Tail Sitter UAV, AIAA Atmospheric Flight Mechanics Conference, 2010, p 7508.Google Scholar
Argyle, M.E., Beard, R.W. and Morris, S. The vertical bat tail-sitter: dynamic model and control architecture, 2013 American Control Conference, 2013, pp 806–811.Google Scholar
Frank, A., McGrew, J., Valenti, M., Levine, D. and How, J. Hover, transition, and level flight control design for a single-propeller indoor airplane, AIAA Guidance, Navigation and Control Conference and Exhibit, 2007, p 6318.Google Scholar
Stone, R.H. and Clarke, G. The T-wing: A VTOL UAV for Defense and Civilian Applications, in the proceedings UAV conference, Melbourne, 2001.Google Scholar
Stone, R.H., Anderson, P., Hutchison, C., Tsai, A., Gibbens, P. and Wong, K. Flight testing of the t-wing tail-sitter unmanned air vehicle, J. Aircr., 2008, 45, pp 673–685.Google Scholar
(2021, 15 January). Cardi VD200. Specifications. A photo. Available: https://avia-pro.net/blog/cardi-vd200-tehnicheskie-harakteristiki-foto Google Scholar
(2021, 15 January). Map larger, map faster, map anywhere. Available: https://wingtra.com/mapping-drone-wingtraone/ Google Scholar
Wong, K., Guerrero, J.A., Lara, D. and Lozano, R. Attitude stabilization in hover flight of a mini tail-sitter UAV with variable pitch propeller, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2007, pp 2642–2647.Google Scholar
Guerrero, J.A., Lozano, R., Romero, G., Lara-Alabazares, D. and Wong, K. Robust control design based on sliding mode control for hover flight of a mini tail-sitter unmanned aerial vehicle, 2009 35th Annual Conference of IEEE Industrial Electronics, 2009, pp 2342–2347.Google Scholar
Escareno, J., Salazar-Cruz, S. and Lozano, R. Attitude stabilization of a convertible mini birotor, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, 2006, pp 2202–2206.Google Scholar
Escareno, J., Salazar, S. and Lozano, R. Modelling and control of a convertible VTOL aircraft, Proceedings of the 45th IEEE Conference on Decision and Control, 2006, pp 69–74.Google Scholar
Sanchez, A., Escareno, J., Garcia, O. and Lozano, R. Autonomous hovering of a noncyclic tiltrotor UAV: Modeling, control and implementation, IFAC Proc. Vol., 2008, 41, pp 803–808.Google Scholar
Escareno, J., Sanchez, A., Garcia, O. and Lozano, R. Modeling and global control of the longitudinal dynamics of a coaxial convertible mini-UAV in hover mode, J. Intell. Robot. Syst., 2009, 54, pp 261–273.Google Scholar
VanderMey, J.T. A tilt rotor uav for long endurance operations in remote environments, Department of Aeronautics and Astronautics of Massachusetts Institute of Technology, USA, 2011.Google Scholar
Forshaw, J.L., Lappas, V.J. and Briggs, P. Transitional control architecture and methodology for a twin rotor tailsitter, J. Guid. Control Dyn., 2014, 37, pp 1289–1298.CrossRefGoogle Scholar
Knoebel, N.B. and McLain, T.W. Adaptive quaternion control of a miniature tailsitter UAV, 2008 American Control Conference, 2008, pp 2340–2345.Google Scholar
Kohno, S. and Uchiyama, K. Design of robust controller of fixed-wing UAV for transition flight, 2014 International Conference on Unmanned Aircraft Systems (ICUAS), 2014, pp 1111–1116.Google Scholar
Osborne, S.R. Transitions between hover and level flight for a tailsitter UAV, 2007.Google Scholar
Casau, P., Cabecinhas, D. and Silvestre, C. Autonomous transition flight for a vertical take-off and landing aircraft, 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, pp 3974–3979.Google Scholar
Casau, P., Cabecinhas, D. and Silvestre, C. Hybrid control strategy for the autonomous transition flight of a fixed-wing aircraft, IEEE Trans. Control Syst. Technol., 2012, 21, pp 2194–2211.Google Scholar
Stone, R.H. Control architecture for a tail-sitter unmanned air vehicle, 2004 5th Asian Control Conference (IEEE Cat. No. 04EX904), 2004, pp 736–744.Google Scholar
Hochstenbach, M., Notteboom, C., Theys, B. and De Schutter, J. Design and control of an unmanned aerial vehicle for autonomous parcel delivery with transition from vertical take-off to forward flight–vertikul, a quadcopter tailsitter, Int. J. Micro Air Veh., 2015, 7, pp 395–405.Google Scholar
(2021, 18 January). Quadshot RC aircraft combines quadricopter hovering with airplane flight. Available: https://newatlas.com/quadshot-hovers-and-flies/19449/ Google Scholar
(2021, 18 Janauary). What you need to know about Project Wing – Google’s drone delivery project. Available: https://home.bt.com/tech-gadgets/future-tech/project-wing-google-x-alphabet-11364225202942 Google Scholar
(2021, 18 January). Heliwing flies. Available: https://www.flightglobal.com/heliwing-flies/16421.article Google Scholar
(2021, 18 January). Meet ATMOS, the newest Dutch airplane maker. Available: https://startupjuncture.com/2013/12/03/delft-student-startup-atmos-makes-innovative-drones/ Google Scholar
(2021, 18 Jauary). X PlusOne: Your Ultimate Hover + Speed Aerial Camera Drone. Available: https://www.kickstarter.com/projects/137596013/x-plusone-your-ultimate-hover-speed-aerial-camera Google Scholar
J. d. G. Sander Hulsman, Dirk Dokter. (2013, MARCH 2013) High-tech startup with game-changing ideas. Leonardo Times.Google Scholar
Theys, B., De Vos, G. and De Schutter, J. A control approach for transitioning VTOL UAVs with continuously varying transition angle and controlled by differential thrust, 2016 international conference on unmanned aircraft systems (ICUAS), 2016, pp 118–125.Google Scholar
De Wagter, C., Remes, B., Ruisink, R., Van Tienen, F. and Van der Horst, E. Design and testing of a vertical take-off and landing UAV optimized for carrying a hydrogen fuel cell with a pressure tank, Unmanned Syst., 2020, 8, pp 279–285.Google Scholar
(2021, 22 February). Hybrid Project. Providing endurance VTOL platforms. Available: https://www.hybridproject.com/ Google Scholar
Mohanty, P.P., Mahapatra, S. and Mohanty, A. A novel multi-attribute decision making approach for selection of appropriate product conforming ergonomic considerations, Oper. Res. Perspect., 2018, 5, pp 82–93.Google Scholar
Rao, R.V. A logical approach to fuzzy MADM problems, Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods, 2007, pp 43–49.Google Scholar
Chang, Y.-H. and Yeh, C.-H. Evaluating airline competitiveness using multiattribute decision making, Omega, 2001, 29, pp 405–415.Google Scholar
Chen, S.-H. Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy sets Syst., 1985, 17, pp 113–129.Google Scholar
Chen, C.-T. Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets Syst., 2000, 114, pp 1–9.Google Scholar
Rao, R.V. Introduction to multiple attribute decision-making (MADM) methods, Decision Making in the Manufacturing Environment: Using Graph Theory and Fuzzy Multiple Attribute Decision Making Methods, 2007, pp 27–41.Google Scholar
Tomaszewska, K. Multi-attribute decision making method using in an acquisition of real estate, ed: Warszawa, 2010.Google Scholar
Yeh, C.H. A problem-based selection of multi-attribute decision-making methods,. Int. Trans. Oper. Res., 2002, 9, pp 169–181.Google Scholar