SPFI: Shape-Preserving Choquet Fuzzy Integral for Non-Normal Fuzzy Set-Valued Evidence

Havens, Timothy C.; Pinar, Anthony J.; Anderson, Derek T.; Wagner, Christian

Abstract

© 2018 IEEE. Information or data aggregation is an important part of nearly all analysis problems as summarizing inputs from multiple sources is a ubiquitous goal. In this paper we propose a method for non-linear aggregation of data inputs that take the form of non-normal fuzzy sets. The proposed shape-preserving fuzzy integral (SPFI) is designed to overcome a well-known weakness of the previously-proposed sub-normal fuzzy integral (SuFI). The weakness of SuFI is that the output is constrained to have maximum membership equal to the minimum of the maximum memberships of the inputs; hence, if one input has a small height, then the output is constrained to that height. The proposed SPFI does not suffer from this weakness and, furthermore, preserves in the output the shape of the input sets. That is, the output looks like the inputs. The SPFI method is based on the well-known Choquet fuzzy integral with respect to a capacity measure, i.e., fuzzy measure. We demonstrate SPFI on synthetic and real-world data, comparing it to the SuFI and non-direct fuzzy integral (NDFI).

Citation

Havens, T. C., Pinar, A. J., Anderson, D. T., & Wagner, C. (2018). SPFI: Shape-Preserving Choquet Fuzzy Integral for Non-Normal Fuzzy Set-Valued Evidence. In 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (1-6). https://doi.org/10.1109/Fuzz-Ieee.2018.8491555

• Conference Name: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• Conference Location: Rio de Janeiro
• Start Date: Jul 8, 2018
• End Date: Jul 13, 2018
• Acceptance Date: May 8, 2018
• Online Publication Date: Oct 15, 2018
• Publication Date: 2018-07
• Deposit Date: Aug 9, 2018
• Publicly Available Date: Aug 9, 2018
• Volume: 2018-July
• Pages: 1-6
• Book Title: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
• ISBN: 978-1-5090-6021-4
• DOI: https://doi.org/10.1109/Fuzz-Ieee.2018.8491555
• Keywords: Fuzzy Integral; Choquet Integral; Capacity Measure; Fuzzy Measure; Aggregation; Fusion
• Public URL: https://nottingham-repository.worktribe.com/output/972085
• Publisher URL: https://ieeexplore.ieee.org/document/8491555
• Additional Information: © 2018 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.