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Constrained Interval Type-2 Fuzzy Sets

Dalterio, Pasquale; Garibaldi, Jonathan M.; John, Robert; Pourabdollah, Amir

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Authors

Pasquale Dalterio

Robert John

Amir Pourabdollah



Abstract

In many contexts, type-2 fuzzy sets are obtained from a type-1 fuzzy set to which we wish to add uncertainty. However, in the current type-2 representation there is no restriction on the shape of the footprint of uncertainty and the embedded sets that can be considered acceptable. This leads, usually, to the loss of the semantic relationship between the type-2 fuzzy set and the concept it models. As a consequence, the interpretability of some of the embedded sets and the explainability of the uncertainty measures obtained from them can decrease. To overcome these issues, constrained type-2 fuzzy sets have been proposed. However, no formal definitions for some of their key components (e.g. acceptable embedded sets) and constrained operations have been given. The goal of this paper is to provide some theoretical underpinning for the definition of constrained type-2 sets, their inferencing and defuzzification method. To conclude, the constrained inference framework is presented, applied to two real world cases and briefly compared to the standard interval type-2 inference and defuzzification method.

Citation

Dalterio, P., Garibaldi, J. M., John, R., & Pourabdollah, A. (2021). Constrained Interval Type-2 Fuzzy Sets. IEEE Transactions on Fuzzy Systems, 29(5), 1212-1225. https://doi.org/10.1109/tfuzz.2020.2970911

Journal Article Type Article
Acceptance Date Jan 30, 2020
Online Publication Date Jan 31, 2020
Publication Date 2021-05
Deposit Date Mar 26, 2020
Publicly Available Date Mar 29, 2024
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 5
Pages 1212-1225
DOI https://doi.org/10.1109/tfuzz.2020.2970911
Keywords Type-2 fuzzy logic , Embedded sets , Constrained type-2 fuzzy sets
Public URL https://nottingham-repository.worktribe.com/output/4204760
Publisher URL https://ieeexplore.ieee.org/document/8977348

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