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Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction

Kayacan, Erdal; Coupland, Simon; John, Robert; Khanesar, Mojtaba Ahmadieh

Authors

Erdal Kayacan

Simon Coupland

Robert John

Mojtaba Ahmadieh Khanesar



Abstract

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.

Publication Date Jul 9, 2017
Peer Reviewed Peer Reviewed
Book Title 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
APA6 Citation Kayacan, E., Coupland, S., John, R., & Khanesar, M. A. (2017). Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction. In 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)doi:10.1109/FUZZ-IEEE.2017.8015457
DOI https://doi.org/10.1109/FUZZ-IEEE.2017.8015457
Keywords Elliptic membership function, type-2 fuzzy logic theory, uncertainty, fuzzy sets, Gaussian, triangular, time series
prediction
Publisher URL http://ieeexplore.ieee.org/abstract/document/8015457/
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information doi:10.1109/FUZZ-IEEE.2017.8015457

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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