A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems

D'Alterio, Pasquale; Garibaldi, Jonathan M.; John, Robert I.; Wagner, Christian

Abstract

Constrained interval type-2 (CIT2) fuzzy sets have been introduced to preserve interpretability when moving from type-1 to interval type-2 (IT2) membership functions. Although they can be used to produce type-2 fuzzy systems with enhanced explainability, so far, the latter comes at the expense of high computational cost. Specifically, the exhaustive type-reduction method for CIT2 Mamdani systems has been shown to be too slow to be used in practical applications and even the current approximation procedure is much slower than modern type-reduction algorithms used for IT2 fuzzy sets. In this article, a novel type-reduction procedure for CIT2 sets is presented, based on the concept of switch indices. The algorithm is applied on a real-world classification problem and compared to other type-reduction approaches used in IT2 and CIT2 systems. In the case studies presented, the new algorithm is significantly faster than the exhaustive and sampling CIT2 approaches while keeping the high level of interpretability of the type-reduction operation that characterizes CIT2 fuzzy sets.

Citation

D'Alterio, P., Garibaldi, J. M., John, R. I., & Wagner, C. (2021). A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems. IEEE Transactions on Fuzzy Systems, 29(11), 3323-3333. https://doi.org/10.1109/TFUZZ.2020.3018379

• Journal Article Type: Article
• Acceptance Date: Aug 5, 2020
• Online Publication Date: Sep 20, 2020
• Publication Date: 2021-11
• Deposit Date: Sep 11, 2020
• Publicly Available Date: Sep 11, 2020
• 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: 29
• Issue: 11
• Article Number: 9172115
• Pages: 3323-3333
• DOI: https://doi.org/10.1109/TFUZZ.2020.3018379
• Keywords: Explainable AI; explainable fuzzy systems; explainable type-2 fuzzy systems; constrained type-2 fuzzy sets; switch indices
• Public URL: https://nottingham-repository.worktribe.com/output/4896423
• Publisher URL: https://ieeexplore.ieee.org/document/9172115
• Additional Information: © 2020 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.; ; P. D'Alterio, J. M. Garibaldi, R. John and C. Wagner, "A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems," in IEEE Transactions on Fuzzy Systems, doi: 10.1109/TFUZZ.2020.3018379.