Elliptic Membership Functions and the Modeling Uncertainty in Type-2 Fuzzy Logic Systems As Applied to Time Series Prediction

TY - GEN

T1 - Elliptic Membership Functions and the Modeling Uncertainty in Type-2 Fuzzy Logic Systems As Applied to Time Series Prediction

AU - Kayacan, Erdal

AU - Coupland, Simon

AU - John, Robert

AU - Ahmadieh Khanesar, Mojbata

PY - 2017/8/23

Y1 - 2017/8/23

N2 - In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, - 'Elliptic membership function'. After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution along its support, and we compare its uncertainty modeling capability with the existing membership functions. We also show how the elliptic membership functions perform in fuzzy arithmetic. In addition to its extra advantages over the existing type-2 fuzzy membership functions such as having decoupled parameters for its support and width, this novel membership function has some similar features to the Gaussian and triangular membership functions in addition and multiplication operations. Finally, we have tested the prediction capability of elliptic membership functions using interval type-2 fuzzy logic systems on US Dollar/Euro exchange rate prediction problem. 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 membership functions have comparable prediction results when compared to Gaussian and triangular membership functions.

AB - In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, - 'Elliptic membership function'. After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution along its support, and we compare its uncertainty modeling capability with the existing membership functions. We also show how the elliptic membership functions perform in fuzzy arithmetic. In addition to its extra advantages over the existing type-2 fuzzy membership functions such as having decoupled parameters for its support and width, this novel membership function has some similar features to the Gaussian and triangular membership functions in addition and multiplication operations. Finally, we have tested the prediction capability of elliptic membership functions using interval type-2 fuzzy logic systems on US Dollar/Euro exchange rate prediction problem. 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 membership functions have comparable prediction results when compared to Gaussian and triangular membership functions.

KW - Elliptic membership function

KW - Fuzzy sets

KW - Gaussian

KW - Time series prediction

KW - Triangular

KW - Type-2 fuzzy logic theory

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85030151259&partnerID=8YFLogxK

U2 - 10.1109/FUZZ-IEEE.2017.8015457

DO - 10.1109/FUZZ-IEEE.2017.8015457

M3 - Article in proceedings

SN - 978-1-5090-6034-4

SP - 1

EP - 7

BT - 2017 IEEE International Conference on Fuzzy Systems, FUZZ 2017

PB - IEEE

T2 - IEEE International Conference on Fuzzy Systems 2017

Y2 - 9 July 2017 through 12 July 2017

ER -