Effectively Communicating Information and Uncertainty from Fuzzy Sets, Why and How

Zhao, Yu; Wagner, Christian; Ryan, Brendan; Pekaslan, Direnc; Kreinovich, Vladik

Abstract

Fuzzy Sets (FSs) are widely used in real-world applications due to their ability to model the inherent uncertainty in human perceptions and knowledge. While valuable, the complexity of FSs often poses challenges in interpretation and communication for stakeholders and decision-makers. Defuzzification methods are commonly used to reduce FSs to single values, but this simplification often results in the loss of inherent uncertainty-a critical component of FSs. As an alternative, Interval-Valued Defuzzification (IVD) reduces FSs to intervals, offering sufficient degrees of freedom to retain uncertainty information through the intervals' widths. Although substantial literature addresses IVD, most work focuses on convex, normal FSs, such as Fuzzy Numbers (FNs) with limited exploration of appropriate IVD approaches for non-convex FSs, which are prevalent in data-driven contexts. In this paper, we review established IVD methods and propose desirable properties for IVD of non-convex FSs. Leveraging discontinuous intervals, we introduce a new IVD method that more effectively represents the non-convex features of FSs, minimizing information loss. We explain how the latter is critical for modeling real-world scenarios, such as group opinions or preferences, where FSs capture discordant or divided perspectives. Through synthetic examples, we demonstrate that the proposed method better satisfies these desired properties compared to existing methods. Finally, we discuss limitations, potential extensions, and future directions.

Citation

Zhao, Y., Wagner, C., Ryan, B., Pekaslan, D., & Kreinovich, V. (2025, July). Effectively Communicating Information and Uncertainty from Fuzzy Sets, Why and How. Presented at 2025 IEEE International Conference on Fuzzy Systems, Reims, France

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 2025 IEEE International Conference on Fuzzy Systems
• Start Date: Jul 6, 2025
• End Date: Jul 9, 2025
• Acceptance Date: Apr 3, 2025
• Online Publication Date: Jul 7, 2025
• Publication Date: Jul 7, 2025
• Deposit Date: May 1, 2025
• Publicly Available Date: Jul 7, 2025
• Peer Reviewed: Peer Reviewed
• Keywords: Interval-Valued Defuzzification; Interval; Non- convex; Discontinuous interval; Alpha-cut
• Public URL: https://nottingham-repository.worktribe.com/output/48370313
• Related Public URLs: https://fuzzieee2025.conf.lip6.fr/