From Interval-Valued Data to General Type-2 Fuzzy Sets

Wagner, Christian; Miller, Simon; Garibaldi, Jonathan M.; Anderson, Derek T.; Havens, Timothy C.

Abstract

In this paper, a new approach is presented to model interval-based data using fuzzy sets (FSs). Specifically, we show how both crisp and uncertain intervals (where there is uncertainty about the endpoints of intervals) collected from individual or multiple survey participants over single or repeated surveys can be modeled using type-1, interval type-2, or general type-2 FSs based on zSlices. The proposed approach is designed to minimize any loss of information when transferring the interval-based data into FS models, and to avoid, as much as possible, assumptions about the distribution of the data. Furthermore, our approach does not rely on data preprocessing or outlier removal, which can lead to the elimination of important information. Different types of uncertainty contained within the data, namely intra- and inter-source uncertainty, are identified and modeled using the different degrees of freedom of type-2 FSs, thus providing a clear representation and separation of these individual types of uncertainty present in the data. We provide full details of the proposed approach, as well as a series of detailed examples based on both real-world and synthetic data. We perform comparisons with analogue techniques to derive FSs from intervals, namely the interval approach and the enhanced interval approach, and highlight the practical applicability of the proposed approach.

Citation

Wagner, C., Miller, S., Garibaldi, J. M., Anderson, D. T., & Havens, T. C. (2015). From Interval-Valued Data to General Type-2 Fuzzy Sets. IEEE Transactions on Fuzzy Systems, 23(2), 248-269. https://doi.org/10.1109/tfuzz.2014.2310734

• Journal Article Type: Article
• Acceptance Date: Jan 27, 2014
• Online Publication Date: Mar 11, 2014
• Publication Date: 2015-04
• Deposit Date: Jun 23, 2015
• Publicly Available Date: Jun 23, 2015
• 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: 23
• Issue: 2
• Pages: 248-269
• DOI: https://doi.org/10.1109/tfuzz.2014.2310734
• Keywords: Survey data, zSlices, Uncertainty, Computing With Words, Type-2, Agreement, Interval Agreement Approach
• Public URL: https://nottingham-repository.worktribe.com/output/725364
• Publisher URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6762925&filter%3DAND%28p_IS_Number%3A7070767%29
• Additional Information: C. Wagner, S. Miller, J. Garibaldi, D.T. Anderson, T.C. Havens, From interval-valued data to general type-2 fuzzy sets, Fuzzy Systems, IEEE Transactions on, vol. 23, no. 2, pp. 248-269. ©2014 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: Jun 23, 2015