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

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.

Citation

Kayacan, E., Coupland, S., John, R., & Khanesar, M. A. (2017, July). Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction. Presented at 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Naples, Italy

• Presentation Conference Type: Edited Proceedings
• Conference Name: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• Start Date: Jul 9, 2017
• End Date: Jul 12, 2017
• Acceptance Date: Mar 25, 2017
• Online Publication Date: Aug 24, 2017
• Publication Date: 2017
• Deposit Date: Aug 30, 2017
• Publicly Available Date: Aug 30, 2017
• Peer Reviewed: Peer Reviewed
• Pages: 1-7
• Series ISSN: 1558-4739
• Book Title: 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-6035-1
• 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
• Public URL: https://nottingham-repository.worktribe.com/output/871926
• Publisher URL: http://ieeexplore.ieee.org/abstract/document/8015457/
• Additional Information: doi:10.1109/FUZZ-IEEE.2017.8015457 ; ; © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
• Contract Date: Aug 30, 2017