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Comparison of modified Karnik-Mendel algorithm-based interval type-2 ANFIS and type-1 ANFIS

Muhammet Öztürk (Faculty of Aviation and Astronautics, Department of Astronautical Engineering, Necmettin Erbakan University , Konya, Turkey and Faculty of Aeronautics and Astronautics, Istanbul Technical University , Istanbul, Turkey)
İbrahim Özkol (Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Istanbul Technical University , Istanbul, Turkey)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Article publication date: 13 September 2021

Issue publication date: 30 November 2021




This study aims to propose, as the first time, the interval type-2 adaptive network-fuzzy inference system (ANFIS) structure, which is given better results compared to previously presented in the open literature. So, the ANFIS can be used effectively for training of interval type-2 fuzzy logic system (IT2FLS) parameters.


Karnik–Mendel algorithm (KMA) is modified to use in interval type-2 ANFIS. The modified Karnik–Mendel algorithm (M-KMA) is implemented to change the uncertain ANFIS parameters into known ones. In this way, the interval type-2 ANFIS removes uncertainties of IT2FLS. Therefore, the interval type-2 ANFIS is reduced to a simple one, i.e. less mathematical operation required. Only consequent parameters are trained, and the consequent parameters are chosen in the form of crisp.


By applying the mentioned procedure, it can be shown that interval type-2 ANFIS has generally better results compared to type-1 ANFIS. However, it was noticed that the worst results obtained in the case of interval type-2 ANFIS are equal to the best result obtained in the case of type-1 ANFIS. Therefore, users in this field can use this approach in solving nonlinear problems.

Practical implications

The interval type-2 ANFIS can be used as controller for highly nonlinear systems such as air vehicles.


As stated in the open literature, it is ineffective to use ANFIS for IT2FLS. In this study, the KMA is modified for IT2FLS, and it is seen that the ANFIS can be used effectively for IT2FLS.



Öztürk, M. and Özkol, İ. (2021), "Comparison of modified Karnik-Mendel algorithm-based interval type-2 ANFIS and type-1 ANFIS", Aircraft Engineering and Aerospace Technology, Vol. 93 No. 10, pp. 1526-1532.



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