Type-2 Fuzzy Elliptic Membership Functions for Modeling Uncertainty

TY - JOUR

T1 - Type-2 Fuzzy Elliptic Membership Functions for Modeling Uncertainty

AU - Kayacan, Erdal

AU - Sarabakha, Andriy

AU - Coupland, Simon

AU - John, Robert

AU - Ahmadieh Khanesar, Mojbata

PY - 2018/4

Y1 - 2018/4

N2 - Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance with existing type-2 fuzzy MFs. Furthermore, fuzzy arithmetic operations are also investigated, and our finding is that the elliptic MF has similar features to the Gaussian and triangular MFs in addition and multiplication operations. Moreover, we have tested the prediction capability of elliptic MFs using interval type-2 fuzzy logic systems on oil price prediction problem for a data set from 2nd Jan 1985 till 25th April 2016. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem of a quadrotor. We believe that the results of this study will open the doors to elliptic MFs’ wider use of real-world identification and control applications as the proposed MF is easy to interpret in addition to its unique features.

AB - Whereas type-1 and type-2 membership functions (MFs) are the core of any fuzzy logic system, there are no performance criteria available to evaluate the goodness or correctness of the fuzzy MFs. In this paper, we make extensive analysis in terms of the capability of type-2 elliptic fuzzy MFs in modeling uncertainty. Having decoupled parameters for its support and width, elliptic MFs are unique amongst existing type-2 fuzzy MFs. In this investigation, the uncertainty distribution along the elliptic MF support is studied, and a detailed analysis is given to compare and contrast its performance with existing type-2 fuzzy MFs. Furthermore, fuzzy arithmetic operations are also investigated, and our finding is that the elliptic MF has similar features to the Gaussian and triangular MFs in addition and multiplication operations. Moreover, we have tested the prediction capability of elliptic MFs using interval type-2 fuzzy logic systems on oil price prediction problem for a data set from 2nd Jan 1985 till 25th April 2016. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic MFs have comparable prediction results when compared to Gaussian and triangular MFs. Finally, in order to test the performance of fuzzy logic controller with elliptic interval type-2 MFs, extensive real-time experiments are conducted for the 3D trajectory tracking problem of a quadrotor. We believe that the results of this study will open the doors to elliptic MFs’ wider use of real-world identification and control applications as the proposed MF is easy to interpret in addition to its unique features.

KW - Addition

KW - Elliptic membership function

KW - Fuzzy arithmetics

KW - Fuzzy sets

KW - Gaussian

KW - Multiplication

KW - Triangular

KW - Type-2 fuzzy logic theory

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85042282189&partnerID=8YFLogxK

U2 - 10.1016/j.engappai.2018.02.004

DO - 10.1016/j.engappai.2018.02.004

M3 - Journal article

SN - 0952-1976

VL - 70

SP - 170

EP - 183

JO - Engineering Applications of Artificial Intelligence

JF - Engineering Applications of Artificial Intelligence

ER -