# Review of Recent Type-2 Fuzzy Controller Applications

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. T2 FLS

#### 2.1. General T2 FLS

#### 2.2. IT2 FLS

#### 2.2.1. Karnik–Mendel Method

- (1)
- Arrange ${y}_{r}^{i}$ in ascending order.
- (2)
- ${y}_{r}$ is calculated as:$${y}_{r}=\frac{{{\displaystyle \sum}}_{i=1}^{M}{f}_{r}^{i}{y}_{r}^{i}}{{{\displaystyle \sum}}_{i=1}^{M}{f}_{r}^{i}}$$
- (3)
- Find $S$, such that ${y}_{r}^{S}\le {y\prime}_{r}\le {y}_{r}^{S+1}$.
- (4)
- Find ${y\prime}_{r}=\frac{{{\displaystyle \sum}}_{i=1}^{M}{f}_{r}^{i}{y}_{r}^{i}}{{{\displaystyle \sum}}_{i=1}^{M}{f}_{r}^{i}}$ with ${f}_{r}^{i}=\underset{\_}{{f}^{i}}$ for $i\le S$ and ${f}_{r}^{i}=\overline{{f}^{i}}$ for $i>S$; now, let ${y\u2033}_{r}={y}_{r}.$
- (5)
- If ${y\u2033}_{r}\ne {y\prime}_{r}$, go to Step 6. If ${y\u2033}_{r}={y\prime}_{r},$ set ${y}_{r}={y\u2033}_{r},\text{and stop}.$
- (6)
- Let ${y\prime}_{r}$ = ${y\u2033}_{r}$, and go to Step 3.

#### 2.2.2. Wu–Mendel Method

#### 2.2.3. Biglarbegian–Melek–Mendel Method

#### 2.2.4. Nie–Tan Method

#### 2.2.5. Other IT2 Algorithms

## 3. Review of IT2 FLCs

#### 3.1. Robotic Control

#### 3.2. Controller Systems Using IT2 FLC and Neural Networks

#### 3.3. Internet Bandwidth Control

#### 3.4. Industrial System Controllers

#### 3.5. Power Management and Electrical Control

#### 3.6. Aircraft Control

#### 3.7. General Control Problems

_{∞}performance if the actuator fails. Combining T2 FLC and neural networks can be used in developing controllers with learning capabilities while they handle uncertainties [94].

#### 3.8. Membership Functions Used in T2 FLC Applications

## 4. Conclusions

## Conflicts of Interest

## Abbreviations

FLS | fuzzy logic systems |

FLC | fuzzy logic controller |

T2 | Type-2 |

IT2 | Type-2 |

T1 | Type-1 |

KM | Karnik–Mendel |

EKM | Enhanced Karnik–Mendel |

WM | Wu–Mendel |

BMM | Biglarbegian–Melek–Mendel |

NT | Nie–Tan |

## References

- Zadeh, L.A. Fuzzy Sets. Inf. Control
**1965**, 8, 338–353. [Google Scholar] [CrossRef] - Mamdani, E.H.; Baaklini, N. Prescriptive method for deriving control policy in a fuzzy-logic controller. Electron. Lett.
**1975**, 11, 625–626. [Google Scholar] [CrossRef] - Zamani, M.; Nejati, H.; Jahromi, A.T.; Partovi, A.R.; Nobari, S.H.; Shirazi, G.N. Toolbox for Interval Type-2 Fuzzy Logic Systems. In Proceedings of the Joint Conference on Information Sciences, Shenzhen, China, 15–20 December 2008.
- Liang, Q.; Mendel, J.M. Interval Type-2 Fuzzy Logic Systems: Theory and Design. IEEE Trans. Fuzzy Syst.
**2000**, 8, 535–550. [Google Scholar] [CrossRef] - Hisdal, E. The IF THEN ELSE statement and interval-valued fuzzy sets of higher type. Int. J. Man-Mach. Stud.
**1981**, 15, 385–455. [Google Scholar] [CrossRef] - Mendel, J.M.; John, R.I.; Liu, F. Interval Type-2 Fuzzy logic Systems Made Simple. IEEE Trans. Fuzzy Syst.
**2006**, 14, 808–821. [Google Scholar] [CrossRef] - Biglarbegian, M.; Melek, W.; Mendel, J.M. On the robustness of Type-1 and Interval Type-2 fuzzy logic systems in modeling. Inf. Sci.
**2011**, 181, 1325–1347. [Google Scholar] [CrossRef] - Chopra, S.; Mitra, R.; Kumar, V. Fuzzy Controller: Choosing an Appropriate and Smallest Rule Set. Int. J. Comput. Cogn.
**2005**, 3, 73–79. [Google Scholar] - Mendel, J.M. General Type-2 fuzzy logic systems made simple: A tutorial. IEEE Trans. Fuzzy Syst.
**2014**, 22, 1162–1182. [Google Scholar] [CrossRef] - Karnik, N.N.; Mendel, J.M.; Liang, Q. Type-2 Fuzzy Logic Systems. IEEE Trans. Fuzzy Syst.
**1999**, 7, 643–658. [Google Scholar] [CrossRef] - Schrieber, M.D.; Biglarbegian, M. Hardware implementation and performance comparison of interval Type-2 fuzzy logic controllers for real-time applications. Appl. Soft Comput.
**2015**, 32, 175–188. [Google Scholar] [CrossRef] - Torshizi, A.D.; Zarandi, M.H.F.; Zakeri, H. On type-reduction of Type-2 fuzzy sets: A review. Appl. Soft Comput.
**2015**, 27, 614–627. [Google Scholar] [CrossRef] - Karnik, N.N.; Mendel, J.M. Centroid of a Type-2 fuzzy set. Inf. Sci.
**2001**, 132, 195–220. [Google Scholar] [CrossRef] - Mendel, J.M. Rule-Based Fuzzy Logic Systems: Introduction and New Directions; Prentice-Hall: Upper Saddle River, NJ, USA, 2001. [Google Scholar]
- Greenfield, S.; Chiclana, F. Accuracy and complexity evaluation of defuzzification strategies for the discretised interval Type-2 fuzzy set. Int. J. Approx. Reason.
**2013**, 54, 1013–1033. [Google Scholar] [CrossRef] - Wu, D.; Nie, M. Comparison and Practical Implementation of Type-Reduction Algorithms for Type-2 Fuzzy Sets and Systems. In Proceedings of the IEEE International Conference on Fuzzy Systems, Taipei, Taiwan, 27–30 June 2011.
- Liu, F.; Mendel, J. Aggregation Using the Fuzzy Weighted Average as Computed by the Karnik-Mendel Algorithms. IEEE Trans. Fuzzy Syst.
**2008**, 16, 1–12. [Google Scholar] - Dodurka, M.F.; Kumbasar, T.; Sakalli, A.; Yesil, E. Boundary Function based Karnik-Mendel type Reduction Method for Interval Type-2 Fuzzy PID Controllers. In Proceedings of the IEEE International Conference on Fuzzy Systems, Beijing, China, 6–11 July 2014.
- Wu, D.; Mendel, J.M. Enhanced Karnik-Mendel Algorithms. IEEE Trans. Fuzzy Syst.
**2009**, 17, 923–934. [Google Scholar] - Melgarejo, M.A.; Duran, L.K. A Hardware Architecture Proposal for the Enhanced Karnik Mendel Algorithm Based on Sequential Arithmetic Operators. In Proceedings of the IEEE International Conference on Fuzzy Systems, Barcelona, Spain, 18–23 July 2010.
- Mendel, J.M. Type-2 Fuzzy Sets and Systems: An Overview. IEEE Comput. Intell.
**2007**, 2, 20–29. [Google Scholar] [CrossRef] - Wu, H.; Mendel, J.M. Uncertainity bounds and their use in the design of interval Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst.
**2002**, 10, 622–639. [Google Scholar] - Biglarbegian, M.; Melek, W.; Mendel, J.M. On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems. IEEE Trans. Syst. Man Cybern.
**2010**, 40, 798–818. [Google Scholar] [CrossRef] [PubMed] - Biglarbegian, M. On the design of robust intelligent controllers with application to mobile robot tracking. In Proceedings of the American Control Conference, Montreal, QC, Canada, 27–29 June 2012.
- Nie, M.; Tan, W.W. Toward an efficient type-reduction method for interval Type-2 fuzzy logic systems. In Proceedings of the IEEE International Conference on Fuzzy Systems, Hong Kong, China, 1–6 June 2008.
- Mendel, J.M.; Liu, X. Simplified Interval Type-2 Fuzzy Logic Systems. IEEE Trans. Fuzzy Syst.
**2013**, 21, 1056–1069. [Google Scholar] [CrossRef] - Coupland, S.; John, R. Geometric Type-1 and Type-2 Fuzzy Logic Systems. IEEE Trans. Fuzzy Syst.
**2007**, 15, 3–15. [Google Scholar] [CrossRef] - Wu, D. Approaches for Reducing the Computational Cost of Interval Type-2 Fuzzy Logic Systems: Overview and Comparisons. IEEE Trans. Fuzzy Syst.
**2013**, 21, 80–99. [Google Scholar] [CrossRef] - Khosravi, A.; Nahavandi, S. Effects of type reduction algorithms on forecasting accuracy of IT2FLS models. Appl. Soft Comput.
**2014**, 17, 32–38. [Google Scholar] [CrossRef] - Greenfield, S.; Chiclana, F.; Coupland, S.; John, R. The collapsing method of defuzzification for discretised interval Type-2 fuzzy sets. Inf. Sci.
**2009**, 179, 2055–2069. [Google Scholar] [CrossRef] - Du, X.; Ying, H. Derivation and Analysis of the Analytical Structures of the Interval Type-2 Fuzzy-PI and PD Controllers. IEEE Trans. Fuzzy Syst.
**2010**, 18, 802–814. [Google Scholar] - Tao, C.W.; Taur, J.S.; Chang, C.-W.; Chang, Y.-H. Simplified Type-2 fuzzy sliding controller for wing rock system. Fuzzy Sets Syst.
**2012**, 207, 111–129. [Google Scholar] [CrossRef] - Li, C.; Yi, J.; Zhao, D. A Novel Type-Reduction Method for Interval Type-2 Fuzzy Logic Systems. In Proceedings of the Fifth International Conference on Fuzzy Systems and Knowledge Discovery, Jinan, China, 18–20 October 2008.
- Torshizi, A.D.; Zarandi, M.H.F. Hierarchical collapsing method for direct defuzzification of general Type-2 fuzzy sets. Inf. Sci.
**2014**, 277, 842–861. [Google Scholar] [CrossRef] - Melgarejo, M. A Fast Recursive Method to Compute the Generalized Centroid of an Interval Type-2 Fuzzy Set. In Proceedings of the Annual Meeting of the North American Fuzzy Information Processing Society, San Diego, CA, USA, 24–27 June 2007.
- Hassan, S.; Khanesar, M.A.; Kayacan, E.; Jaafar, J.; Khosravi, A. Optimal design of adaptive Type-2 neuro-fuzzy systems: A review. Appl. Soft Comput.
**2016**, 44, 134–143. [Google Scholar] [CrossRef] - Hagras, H.A. A Hierarchical Type-2 Fuzzy Logic Control Architecture for Autonomous Mobile Robots. IEEE Trans. Fuzzy Syst.
**2004**, 12, 524–539. [Google Scholar] [CrossRef] - Biglarbegian, M.; Melek, W.; Mendel, J.M. Design of Novel Interval Type-2 Fuzzy Controllers for Modular and Reconfigurable Robots: Theory and Experiments. IEEE Trans. Ind. Electron.
**2011**, 58, 1371–1384. [Google Scholar] [CrossRef] - Liu, Z.; Zhang, Y.; Wang, Y. A Type-2 Fuzzy Switching Control System for Biped Robots. IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.)
**2007**, 37, 1202–1213. [Google Scholar] [CrossRef] - Juang, C.-F.; Hsu, C.-H. Reinforcement Ant Optimized Fuzzy Controller for Mobile-Robot Wall-Following Control. IEEE Trans. Ind. Electron.
**2009**, 56, 3931–3940. [Google Scholar] [CrossRef] - Kumbasar, T.; Hagras, H. Big Bang—Big Crunch optimization based interval Type-2 fuzzy PID cascade controller design strategy. Inf. Sci.
**2014**, 282, 277–295. [Google Scholar] [CrossRef] - Khanesar, M.A.; Kayacan, E. Feedback error learning control of magnetic satellites using Type-2 fuzzy neural networks with elliptic membership functions. IEEE Trans. Cybern.
**2015**, 45, 858–868. [Google Scholar] [CrossRef] [PubMed] - Chaoui, H.; Gueaieb, W. Type-2 Fuzzy Logic Control of a Flexible-Joint Manipulator. J. Intell. Robot. Syst.
**2008**, 51, 159–186. [Google Scholar] [CrossRef] - Chen, C.-S. Supervisory adaptive tracking control of robot manipulators using interval Type-2 TSK fuzzy logic system. IET Control Theory Appl.
**2011**, 5, 1796–1807. [Google Scholar] [CrossRef] - Allawi, Z.T.; Abdalla, T.Y. A PSO-Optimized Type-2 Fuzzy Logic Controller for Navigation of Multiple Mobile Robots. In Proceedings of the IEEE International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, 2–5 September 2014.
- Selvi, V.; Umarani, R. Comparative Analysis of Ant Colony and Particle Swarm Optimization Techniques. Int. J. Comput. Appl.
**2010**, 5, 1–6. [Google Scholar] [CrossRef] - Astudillo, L.; Castillo, O.; Melin, P.; Alanis, A.; Soria, J.; Aguilar, L.T. Intelligent Control of an Autonomous Mobile Robot using Type-2 Fuzzy Logic. Eng. Lett.
**2006**, 13, 88–93. [Google Scholar] - Valdez, F.; Melin, P.; Castillo, O. Fuzzy Control of Parameters to Dynamically Adapt the PSO and GA Algorithms. In Proceedings of the IEEE International Conference on Fuzzy Systems, Barcelona, Spain, 18–23 July 2010.
- Martinez, R.; Rodriguez, A.; Castillo, O.; Aguilar, L.T. Type-2 Fuzzy Logic Controllers Optimization using Genetic Algorithms and Particle Swarm Optimization. In Proceedings of the IEEE International Conference on Granular Computing, San Jose, CA, USA, 14–16 August 2010.
- Martinez-Soto, R.; Castillo, O.; Aguilar, L.T. Type-1 and Type-2 fuzzy logic controller design using a Hybrid PSO-GA optimization method. Inf. Sci.
**2014**, 285, 35–49. [Google Scholar] [CrossRef] - Castillo, O.; Neyoy, H.; Soria, J.; Melin, P.; Valdez, F. A new approach for dynamic fuzzy logic parameter tuning in Ant Colony Optimization and its application in fuzzy control of mobile robot. Appl. Soft Comput.
**2015**, 28, 150–159. [Google Scholar] [CrossRef] - Mohammadi, S.M.; Gharaveisi, A.A.; Machinchi, M. An Evolutionary Tuning Technique for Type-2 Fuzzy Logic Controller in a Non-linear System Under Uncertainty. In Proceedings of the Electrical Engineering (ICEE), Isfahan, Iran, 11–13 May 2010.
- Cortes-Rios, J.C.; Gomez-Ramirez, E.; Ortiz-de-la-Vega, H.A.; Castillo, O.; Melin, P. Optimal design of interval type 2 fuzzy controllers based on a simple tuning algorithm. Appl. Soft Comput.
**2014**, 23, 270–285. [Google Scholar] [CrossRef] - Mohammadi, S.M.; Gharaveisi, A.; Mashinchi, M.; Vaezi-Nejad, S. Development of a novel reinforcement learning automata method for optimum design of proportional integral deviation controller for nonlinear systems. In Proceedings of the World Congress On Engineering, London, UK, 2–4 July 2008.
- Hassan, M.Y.; Kothapalli, G. Interval Type-2 fuzzy position control of electro-hydraulic actuated robotic excavator. Int. J. Min. Sci. Technol.
**2012**, 22, 437–445. [Google Scholar] [CrossRef] - Linda, O.; Manic, M. Uncertainty-Robust Design of Interval Type-2 Fuzzy Logic Controller for Delta Parallel Robot. IEEE Trans. Ind. Inf.
**2011**, 7, 661–670. [Google Scholar] [CrossRef] - Ganjefar, S.; Solgi, Y. A Lyapunov stable Type-2 fuzzy wavelet network controller design for a bilateral teleoperation system. Inf. Sci.
**2015**, 311, 1–17. [Google Scholar] [CrossRef] - Jammeh, E.A.; Fleury, M.; Wagner, C.; Hagras, H.; Ghanbari, M. Interval Type-2 Fuzzy Logic Congestion Control for Video Streaming Across IP Networks. IEEE Trans. Fuzzy Syst.
**2009**, 17, 1123–1149. [Google Scholar] [CrossRef] - Jammeh, E.; Mkwawa, I.; Sun, L.; Ifeachor, E. Type-2 fuzzy logic control of PQoS driven adaptive VoIP scheme. Electron. Lett.
**2010**, 46, 137–138. [Google Scholar] [CrossRef] - Jammeh, E.A.; Fleury, M.; Ghanbari, M. Fuzzy logic congestion control for broadband wireless IPTV. Electron. Lett.
**2008**, 44, 1365–1366. [Google Scholar] [CrossRef] - Kabranov, O.; Yang, T.; Makrakis, D. Fuzzy Control pf Pricing for Bandwidth Demand in Obtainable Forwarding Service for Differentiated Services Architecture. In Proceedings of the IEEE Global Telecommunications Conference, Taipei, Taiwan, 17–21 November 2002.
- Own, C.-M. Predictable Type-2 fuzzy mobile units for energy balancing in wireless sensor networks. Inf. Sci.
**2013**, 241, 70–84. [Google Scholar] [CrossRef] - Méndez, G.M.; Leduc-Lezama, L.; Colás, R.; Murillo-Perez, G.; Ramirez-Cuellar, J.; López, J.J. Modelling and control of coiling entry temperature using interval Type-2 fuzzy logic systems. Ironmak. Steelmak.
**2010**, 37, 126–134. [Google Scholar] [CrossRef] - Méndez, G.M.; Castillo, O.; Colás, R.; Moreno, H. Finishing mill strip gage setup and control by internal Type-1 non-singleton Type-2 fuzzy logic systems. Appl. Soft Comput.
**2014**, 24, 900–911. [Google Scholar] [CrossRef] - Lin, F.-J.; Shieh, P.-H.; Hung, Y.-C. An intelligent control for linear ultrasonic motor using interval Type-2 fuzzy neural network. IET Electr. Power Appl.
**2008**, 2, 32–41. [Google Scholar] [CrossRef] - Barkat, S.; Tlemçani, A.; Nouri, H. Noninteracting Adaptive Control of PMSM Using Interval Type-2 Fuzzy Logic Systems. IEEE Trans. Fuzzy Syst.
**2011**, 19, 925–936. [Google Scholar] [CrossRef] - Chen, C.-S.; Lin, W.-C. Self-adaptive interval Type-2 neural fuzzy network control for PMLSM drives. Expert Syst. Appl.
**2011**, 38, 14679–14689. [Google Scholar] [CrossRef] - Naik, N.V.; Singh, S.P. Improved Torque and Flux Performance of Type-2 Fuzzy-based Direct Torque Control Induction Motor Using Space Vector Pulse-width Modulation. Electr. Power Compon. Syst.
**2014**, 42, 658–669. [Google Scholar] [CrossRef] - Ramesh, T.; Panda, A.K.; Kumar, S.S. Type-1 and Type-2 Fuzzy Logic and Sliding-Mode Based Speed Control of Direct Torque and Flux Control Induction Motor Drives—A Comparative Study. Int. J. Emerg. Electr. Power Syst.
**2013**, 14, 385–400. [Google Scholar] [CrossRef] - Yu, W.-S.; Chen, H.-S. Interval Type-2 fuzzy adaptive tracking control design for PMDC motor with the sector dead-zones. Inf. Sci.
**2014**, 288, 108–134. [Google Scholar] [CrossRef] - Maldonado, Y.; Castillo, O. Genetic Design of an Interval Type-2 Fuzzy Controller for Velocity Regulation in a DC motor. Int. J. Adv. Robot. Syst.
**2012**, 9. [Google Scholar] [CrossRef] - Maldonado, Y.; Castillo, O.; Melin, P. A multi-objective optimization of Type-2 fuzzy control speed in FPGAs. Appl. Soft Comput.
**2014**, 24, 1164–1174. [Google Scholar] [CrossRef] - Wang, T.; Tong, S. Direct inverse control of cable-driven parallel system based on Type-2 fuzzy systems. Inf. Sci.
**2015**, 310, 1–15. [Google Scholar] [CrossRef] - Martínez, J.S.; John, R.I.; Hissel, D.; Péra, M.-C. A survey-based Type-2 fuzzy logic system for energy management in hybrid electrical vehicles. Inf. Sci.
**2012**, 190, 192–207. [Google Scholar] [CrossRef] - Martínez, J.S.; Mulot, J.; Harel, F.; Hissel, D.; Péra, M.-C.; John, R.I.; Amiet, M. Experimental validation of a Type-2 fuzzy logic controller for energy management in hybrid electrical vehicles. Eng. Appl. Artif. Intell.
**2013**, 26, 1772–1779. [Google Scholar] [CrossRef] - Nechadi, E.; Harmas, M.N.; Hamzaoui, A.; Essounbouli, N. Type-2 fuzzy based adaptive synergetic power system control. Electr. Power Syst. Res.
**2012**, 88, 9–15. [Google Scholar] [CrossRef] - Tripathy, M.; Mishra, S. Interval Type-2-based thyristor controlled series capacitor to improve power system stability. IET Gener. Transm. Distrib.
**2011**, 5, 209–222. [Google Scholar] [CrossRef] - Panda, M.K.; Pillai, G.; Kumar, V. An interval Type-2 fuzzy logic controller for TCSC to improve the damping of power system oscillations. Front. Energy
**2013**, 7, 307–316. [Google Scholar] [CrossRef] - Panda, M.K.; Pillai, G.N.; Kumar, V. Design of an Interval Type-2 Fuzzy Logic Controller for Automatic Voltage Regulator System. Electr. Power Compon. Syst.
**2012**, 40, 219–235. [Google Scholar] [CrossRef] - Sudha, K.R.; Santhi, R.V. Robust decentralized load frequency control of interconnected power system with Generation Rate Constraint using Type-2 fuzzy approach. Int. J. Electr. Power Energy Syst.
**2011**, 33, 699–707. [Google Scholar] [CrossRef] - Lu, J.-J.; Huang, H.-H.; Chou, H.-P. Evaluation of an FPGA-based fuzzy logic control of feed-water for ABWR under automatic power regulating. Prog. Nucl. Energy
**2015**, 79, 22–31. [Google Scholar] [CrossRef] - Kumar, M.; Panda, M.K.; Kundu, S.; Kumar, V. Designing of an Interval Type-2 Fuzzy Logic Controller for Magnetic Levitation System with Reduced Rule base. In Proceedings of the Computing Communication & Networking Technologies (ICCCNT), Coimbatore, India, 26–28 July 2012.
- Altin, N. Interval Type-2 Fuzzy Logic Controller Based Maximum Power Point Tracking in Photovoltaic Systems. Adv. Electr. Comput. Eng.
**2013**, 13, 65–70. [Google Scholar] [CrossRef] - Altin, N. Single Phase Grid Interactive PV System With MPPT Capability Based on Type-2 Fuzzy Logic Systems. In Proceedings of the International Conference on Renewable Energy Research and Applications, Nagasaki, Japan, 11–14 November 2012.
- Yang, T.-C.; Juang, J.-G. Application of Adaptive Type-2 Fuzzy CMAC to Automatic Landing System. In Proceedings of the International Symposium on Computational Intelligence and Design, Hangzhou, China, 29–31 October 2010.
- Yang, F.; Yuan, R.; Yi, J.; Fan, G.; Tan, X. Direct adaptive Type-2 fuzzy neural network control for a generic hypersonic flight vehicle. Soft Comput.
**2013**, 17, 2053–2064. [Google Scholar] [CrossRef] - Chen, X.; Li, D.; Xu, Z.; Bai, Y. Gain adaptive sliding mode controller based on interval type-II fuzzy neural network designed for attitude control for micro aircraft vehicle. Int. J. Intell. Comput. Cybern.
**2008**, 7, 209–226. [Google Scholar] [CrossRef] - Chen, X.; Li, D.; Xu, Z.; Bai, Y. Robust control of quadrotor MAV using self-organizing interval type-II fuzzy neural networks (SOIT-IIFNNs) controller. Int. J. Intell. Comput. Cybern.
**2011**, 4, 397–412. [Google Scholar] [CrossRef] - Lin, T.-C.; Liu, H.-L.; Kuo, M.-J. Direct adaptive interval Type-2 fuzzy control of multivariable nonlinear systems. Eng. Appl. Artif. Intell.
**2009**, 22, 420–430. [Google Scholar] [CrossRef] - Hwang, J.-H.; Kwak, H.-J.; Park, G.-T. Adaptive interval Type-2 fuzzy sliding mode control for unknown chaotic system. Nonlinear Dyn.
**2011**, 63, 491–502. [Google Scholar] [CrossRef] - El-Bardini, M.; El-Nagar, A.M. Interval Type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system. ISA Trans.
**2014**, 53, 732–743. [Google Scholar] [CrossRef] [PubMed] - Lin, T.-C. Observer-based robust adaptive interval Type-2 fuzzy tracking control of multivariable nonlinear systems. Eng. Appl. Artif. Intell.
**2010**, 23, 386–399. [Google Scholar] [CrossRef] - Li, H.; Sun, X.; Shi, P.; Lam, H.-K. Control design of interval Type-2 fuzzy systems with actuator fault: Sampled-data control approach. Inf. Sci.
**2015**, 302, 1–13. [Google Scholar] [CrossRef] - Khanesar, M.A.; Kayacam, E. Fuzzy Neural Networks for Real Time Control Applications: Concepts, Modeling and Algorithms for Fast Learning; Elsevier: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Wu, D. Interval Type-2 Fuzzy PI Controllers: Why They are More Robust. In Proceedings of the International Conference on Granular Computing, Silicon Valley, CA, USA, 14–16 August 2010.
- Castillo, O.; Melin, P. A review on interval Type-2 fuzzy logic applications in intelligent control. Inf. Sci.
**2014**, 279, 615–631. [Google Scholar] [CrossRef] - Shill, P.C.; Amin, M.F.; Akhand, M.A.H.; Murase, K. Optimization of Interval Type-2 Fuzzy Logic Controller Using Quantum Genetic Algorithms. In Proceedings of the IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Brisbane, Australia, 10–15 June 2012.
- Wagner, C.; Hagras, H. zSlices based General Type-2 FLC for the Control of Autonomous Mobile Robots in Real World Environments. In Proceedings of the IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 20–24 August 2009.

**Figure 1.**Structure of a GT2 FLS, with permission from [9].

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**MDPI and ACS Style**

Tai, K.; El-Sayed, A.-R.; Biglarbegian, M.; Gonzalez, C.I.; Castillo, O.; Mahmud, S.
Review of Recent Type-2 Fuzzy Controller Applications. *Algorithms* **2016**, *9*, 39.
https://doi.org/10.3390/a9020039

**AMA Style**

Tai K, El-Sayed A-R, Biglarbegian M, Gonzalez CI, Castillo O, Mahmud S.
Review of Recent Type-2 Fuzzy Controller Applications. *Algorithms*. 2016; 9(2):39.
https://doi.org/10.3390/a9020039

**Chicago/Turabian Style**

Tai, Kevin, Abdul-Rahman El-Sayed, Mohammad Biglarbegian, Claudia I. Gonzalez, Oscar Castillo, and Shohel Mahmud.
2016. "Review of Recent Type-2 Fuzzy Controller Applications" *Algorithms* 9, no. 2: 39.
https://doi.org/10.3390/a9020039