A Bidirectional Subsethood Based Fuzzy Measure for Aggregation of Interval-Valued Data

Kabir, Shaily; Wagner, Christian

Abstract

Recent advances in the literature have leveraged the fuzzy integral (FI), a powerful multi-source aggregation operator, where a fuzzy measure (FM) is used to capture the worth of all combinations of subsets of sources. While in most applications, the FM is defined either by experts or numerically derived through optimization, these approaches are only viable if additional information on the sources is available. When such information is unavailable, as is commonly the case when sources are unknown a priori (e.g., in crowdsourcing), prior work has proposed the extraction of valuable insight (captured within FMs) directly from the evidence or input data by analyzing properties such as specificity or agreement amongst sources. Here, existing agreement-based FMs use established measures of similarity such as Jaccard and Dice to estimate the source agreement. Recently, a new similarity measure based on bidirectional subsethood was put forward to compare evidence, minimizing limitations such as aliasing (where different inputs result in the same similarity output) present in traditional similarity measures. In this paper, we build on this new similarity measure to develop a new instance of the agreement-based FM for interval-valued data. The proposed FM is purposely designed to support aggregation, and unlike previous agreement FMs, it degrades gracefully to an average operator for cases where no overlap between sources exists. We validate that it respects all requirements of a FM and explore its impact when used in conjunction with the Choquet FI for data fusion as part of both synthetic and real-world datasets, showing empirically that it generates robust and qualitatively superior outputs for the cases considered.

Citation

Kabir, S., & Wagner, C. (2020, June). A Bidirectional Subsethood Based Fuzzy Measure for Aggregation of Interval-Valued Data. Presented at IPMU 2020 - Information Processing and Management of Uncertainty in Knowledge-Based Systems, Lisbon, Portugal

• Presentation Conference Type: Conference Paper (published)
• Conference Name: IPMU 2020 - Information Processing and Management of Uncertainty in Knowledge-Based Systems
• Start Date: Jun 15, 2020
• End Date: Jun 19, 2020
• Online Publication Date: Jun 5, 2020
• Publication Date: 2020
• Deposit Date: Nov 22, 2023
• Publisher: Springer
• Pages: 603-617
• Book Title: Information Processing and Management of Uncertainty in Knowledge-Based Systems
• ISBN: 978-3-030-50142-6
• DOI: https://doi.org/10.1007/978-3-030-50143-3_48
• Keywords: Data aggregation; Fuzzy measures; Fuzzy integrals; Subsethood; Similarity measure; Interval-valued data
• Public URL: https://keele-repository.worktribe.com/output/643441
• Publisher URL: https://link.springer.com/chapter/10.1007/978-3-030-50143-3_48
• Additional Information: First Online: 5 June 2020; Conference Acronym: IPMU; Conference Name: International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems; Conference City: Lisbon; Conference Country: Portugal; Conference Year: 2020; Conference Start Date: 15 June 2020; Conference End Date: 19 June 2020; Conference Number: 18; Conference ID: ipmu2020; Conference URL: https://ipmu2020.inesc-id.pt/; Type: Single-blind; Conference Management System: EasyChair; Number of Submissions Sent for Review: 213; Number of Full Papers Accepted: 146; Number of Short Papers Accepted: 27; Acceptance Rate of Full Papers: 69% - The value is computed by the equation "Number of Full Papers Accepted / Number of Submissions Sent for Review * 100" and then rounded to a whole number.; Average Number of Reviews per Paper: 3,2; Average Number of Papers per Reviewer: 4; External Reviewers Involved: Yes; Additional Info on Review Process: The IPMU 2020 was held virtually due to the coronavirus pandemic.; Free to read: This content has been made available to all.