Kybernetika 54 no. 1, 175-201, 2018

Comparative analysis of noise robustness of type 2 fuzzy logic controllers

Emanuel Ontiveros-Robles, Patricia Melin and Oscar CastilloDOI: 10.14736/kyb-2018-1-0175


Nowadays Fuzzy logic in control applications is a well-recognized alternative, and this is thanks to its inherent advantages as its robustness. However, the Type-2 Fuzzy Logic approach, allows managing uncertainty in the model. Type-2 Fuzzy Logic has recently shown to provide significant improvement in image processing applications, however it is also important to analyze its impact in controller performance. This paper is presenting a comparison in the robustness of Interval Type-2 and Generalized Type-2 Fuzzy Logic Controllers, in order to generate criteria to decide which type of controller is better in specific applications. The plants considered in the experimentation are two benchmark control plants and we report the Integral Squared Error (ISE), Integral Absolute Error (IAE) and Integral Time-weighted Absolute Error (ITAE) performance metrics, and also another important metric reported is the execution time. Based on the experimental results, Fuzzy Logic Controller selection criteria are proposed according to the performance and execution time requirements.


interval Type-2 fuzzy logic, type-reduction, Type-2 fuzzy control, Type-2 fuzzy edge detection


68T01, 93C42


  1. M. E. Abdelaal, H. M. Emara and A. Bahgat: Interval type 2 fuzzy sliding mode control with application to inverted pendulum on a cart. In: 2013 IEEE International Conference on Industrial Technology (ICIT), pp. 100-105.   DOI:10.1109/icit.2013.6505655
  2. L. Amador-Angulo and O. Castillo: Optimization of the Type-1 and Type-2 fuzzy controller design for the water tank using the Bee Colony Optimization. In: 2014 IEEE Conference on Norbert Wiener in the 21st Century (21CW), 2014, pp. 1-8.   DOI:10.1109/norbert.2014.6893876
  3. C. Caraveo, F. Valdez and O. Castillo: Optimization of fuzzy controller design using a new bee colony algorithm with fuzzy dynamic parameter adaptation. Appl. Soft Comput. 43 (2016), 131-142.   DOI:10.1016/j.asoc.2016.02.033
  4. O. Castillo, L. Amador-Angulo, J. R. Castro and M. Garcia-Valdez: A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf. Sci. 354 (2016), 257-274.   DOI:10.1016/j.ins.2016.03.026
  5. U. Farooq, J. Gu and J. Luo: On the interval type-2 fuzzy logic control of ball and plate system. In: 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 2250-2256.   DOI:10.1109/robio.2013.6739804
  6. M. A. C. Fernandes: Fuzzy controller applied to electric vehicles with continuously variable transmission. Neurocomputing 214 (2016), 684-691.   DOI:10.1016/j.neucom.2016.06.051
  7. H. Hagras: Type-2 FLCs: A new generation of fuzzy controllers. IEEE Comput. Intell. Mag. 2 (2007), 1, 30-43.   DOI:10.1109/mci.2007.357192
  8. M. A. Hannan, Z. A. Ghani, A. Mohamed and M. N. Uddin: Real-time testing of a fuzzy-logic-controller-based grid-connected photovoltaic inverter system. IEEE Trans. Ind. Appl. 41 (2015), 6, 4775-4784.   DOI:10.1109/tia.2015.2455025
  9. H. M. Hasanien and M. Matar: A fuzzy logic controller for autonomous operation of a voltage source converter-based distributed generation system. IEEE Trans. Smart Grid 6 (2015), 1, 158-165.   DOI:10.1109/tsg.2014.2338398
  10. S. A. Hoseini and B. Labibi: Robust fuzzy controller design with bounded control effort for nonlinear systems with parametric uncertainties. In: 2009 International Conference on Networking, Sensing and Control, 2009, pp. 118-123.   DOI:10.1109/icnsc.2009.4919257
  11. S. Hassan, A. Khosravi, J. Jaafar and M. A. Khanesar: A systematic design of interval type-2 fuzzy logic system using extreme learning machine for electricity load demand forecasting. Energy Build. 127 (2016), 95-104.   CrossRef
  12. E. Kamal, A. Aitouche and O. Kuzmych: Robust fuzzy controller for photovoltaic maximum power point tracking. In: 21st Mediterranean Conference on Control and Automation 2013, pp. 1304-1309.   DOI:10.1109/med.2013.6608888
  13. N. N. Karnik and J. M. Mendel: Centroid of a type-2 fuzzy set. Inf. Sci. 132 (2001), 1-4, 195-220.   DOI:10.1016/s0020-0255(01)00069-x
  14. N. N. Karnik, J. M. Mendel and Q. Liang: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7 (1999), 6, 643-658.   DOI:10.1109/91.811231
  15. Q. Liang and J. M. Mendel: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8 (2000), 5-6, 535-550.   DOI:10.1109/91.873577
  16. J. Liu, W. Zhang, X. Chu and Y. Liu: Fuzzy logic controller for energy savings in a smart LED lighting system considering lighting comfort and daylight. Int. J. Electr. Power Energy Syst. 82 (2016), 1-10.   CrossRef
  17. J. Liu, W. Zhang, X. Chu and Y. Liu: Fuzzy logic controller for energy savings in a smart LED lighting system considering lighting comfort and daylight. Energy Build. 127 (2016), 95-104.   DOI:10.1016/j.enbuild.2016.05.066
  18. M. J. Mahmoodabadi and H. Jahanshahi: Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems. Eng. Sci. Technol. Int. J. 19 (2016), 2, 1084-1098.   DOI:10.1016/j.jestch.2016.01.010
  19. E. H. Mamdani: Application of fuzzy algorithms for control of simple dynamic plant. Proc. Inst. Electr. Eng. 121 (1974), 12, 1585-1588.   DOI:10.1049/piee.1974.0328
  20. M. S. Masmoudi, N. Krichen, M. Masmoudi and N. Derbel: Fuzzy logic controllers design for omnidirectional mobile robot navigation. Appl. Soft Comput. 45 (201), 901-919.   DOI:10.1016/j.asoc.2016.08.057
  21. M. S. Masmoudi, N. Krichen, M. Masmoudi and N. Derbel: Fuzzy logic controllers design for omnidirectional mobile robot navigation. Appl. Soft Comput. 49 (2016), 901-919.   DOI:10.1016/j.asoc.2016.08.057
  22. P. Melin, C. I. Gonzalez, J. R. Castro, O. Mendoza and O. Castillo: Edge-Detection Method for Image Processing Based on Generalized Type-2 Fuzzy Logic. IEEE Trans. Fuzzy Syst. 22 (2014), 6, 1515-1525.   DOI:10.1109/tfuzz.2013.2297159
  23. J. M. Mendel and R. I. B. John: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10 (2002), 2, 117-127.   DOI:10.1109/91.995115
  24. J. M. Mendel, F. Liu and D. Zhai: Alpha-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications. IEEE Trans. Fuzzy Syst. 17 (2009), 5, 1189-1207.   DOI:10.1109/tfuzz.2009.2024411
  25. A. R. Ofoli and A. Rubaai: Real-Time Implementation of a Fuzzy Logic Controller for Switch-Mode Power-Stage DC - DC Converters. IEEE Trans. Ind. Appl. 42 (2006), 6, 1367-1374.   DOI:10.1109/tia.2006.882669
  26. K. Premkumar and B. V. Manikandan: Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor. Eng. Sci. Technol. Int. J. 19 (2016), 2, 818-840.   DOI:10.1016/j.jestch.2015.11.004
  27. M. A. Sanchez, O. Castillo and J. R. Castro: Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems. Expert Syst. Appl. 42 (2015), 14, 5904-5914.   DOI:10.1016/j.eswa.2015.03.024
  28. M. Singh, P. Kumar and I. Kar: Implementation of vehicle to grid infrastructure using fuzzy logic controller. IEEE Trans. Smart Grid 3 (2012), 1, 565-577.   DOI:10.1109/tsg.2011.2172697
  29. D. A. R. Wati: Maximum power point tracking of photovoltaic systems using simple interval type-2 fuzzy logic controller based on hill climbing algorithm. In: 2016 International Seminar on Intelligent Technology and Its Applications (ISITIA), pp. 687-692.   DOI:10.1109/isitia.2016.7828743
  30. D. Wu: On the fundamental differences between interval Type-2 and Type-1 fuzzy logic controllers. IEEE Trans. Fuzzy Syst. 20 (2012), 5, 832-848.   DOI:10.1109/tfuzz.2012.2186818
  31. L. A. Zadeh: Fuzzy logic $=$ computing with words. IEEE Trans. Fuzzy Syst. 4 (1996), 2, 103-111.   DOI:10.1109/91.493904