Improved Uncertainty Capture for Nonsingleton Fuzzy Systems

Pourabdollah, Amir; Wagner, Christian; Aladi, Jabran Hussain; Garibaldi, Jonathan M.

Abstract

© 2016 IEEE. In nonsingleton fuzzy logic systems (NSFLSs), input uncertainties are modeled with input fuzzy sets in order to capture input uncertainty (e.g., sensor noise). The performance of NSFLSs in handling such uncertainties depends on both the appropriate modeling in the input fuzzy sets of the uncertainties present in the system's inputs and on how the input fuzzy sets (and their inherent model of uncertainty) interact with the antecedent and, thus, affect the inference within the remainder of the NSFLS. This paper proposes a novel development on the latter. Specifically, an alteration to the standard composition method of type-1 fuzzy relations is proposed and applied to build a new type of NSFLS. The proposed approach is based on employing the centroid of the intersection of input and antecedent sets as origin of the firing degree, rather than the traditional maximum of their intersection, thus making the NSFLS more sensitive to changes in the input's uncertainty characteristics. The traditional and novel approach to NSFLSs are experimentally compared for two well-known problems of Mackey-Glass and Lorenz chaotic time-series predictions, where the NSFLSs' inputs have been perturbed with different levels of Gaussian noise. Experiments are repeated for system training under noisy and noise-free conditions. Analyses of the results show that the new method outperforms the traditional approach. Moreover, it is shown that while formally more complex, in practice, the new method has no significant computational overhead compared with the standard approach.

Citation

Pourabdollah, A., Wagner, C., Aladi, J. H., & Garibaldi, J. M. (2016). Improved Uncertainty Capture for Nonsingleton Fuzzy Systems. IEEE Transactions on Fuzzy Systems, 24(6), 1513-1524. https://doi.org/10.1109/TFUZZ.2016.2540065

• Journal Article Type: Article
• Acceptance Date: Jan 6, 2016
• Online Publication Date: Mar 9, 2016
• Publication Date: 2016-12
• Deposit Date: Sep 5, 2017
• Publicly Available Date: Sep 5, 2017
• Journal: IEEE Transactions on Fuzzy Systems
• Print ISSN: 1063-6706
• Electronic ISSN: 1941-0034
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 6
• Pages: 1513-1524
• DOI: https://doi.org/10.1109/TFUZZ.2016.2540065
• Keywords: non-singleton, fuzzy logic systems, uncertainty,; time series prediction
• Public URL: https://nottingham-repository.worktribe.com/output/971708
• Publisher URL: http://ieeexplore.ieee.org/document/7429744/
• Additional Information: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works.
• Contract Date: Sep 5, 2017