Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers

Havens, Timothy C.; Anderson, Derek T.; Wagner, Christian

Abstract

The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data.

Citation

Havens, T. C., Anderson, D. T., & Wagner, C. (2015). Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers. IEEE Transactions on Fuzzy Systems, 23(5), https://doi.org/10.1109/TFUZZ.2014.2382133

• Journal Article Type: Article
• Acceptance Date: Oct 31, 2014
• Online Publication Date: Dec 18, 2014
• Publication Date: Oct 1, 2015
• Deposit Date: Oct 24, 2016
• Publicly Available Date: Oct 24, 2016
• 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: 5
• DOI: https://doi.org/10.1109/TFUZZ.2014.2382133
• Keywords: Frequency modulation, Indexes, Density measurement, Additives, Educational institutions, Equations, Fuzzy sets
• Public URL: https://nottingham-repository.worktribe.com/output/981876
• Publisher URL: http://ieeexplore.ieee.org/document/6987326/
• Additional Information: (c) 2014 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; ; N.B. Acceptance date is estimated.
• Contract Date: Oct 24, 2016