Composite uncertainty measurements in relative weighted fuzzy rough sets for feature selection

Hongyuan Gou; Meng Chen; Benwei Chen; Hongyuan Gou; Meng Chen; Benwei Chen

doi:10.3934/math.20261049

AIMS Mathematics

2026, Volume 11, Issue 8: 26186-26223. doi: 10.3934/math.20261049

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Research article Topical Sections

Composite uncertainty measurements in relative weighted fuzzy rough sets for feature selection

1.
College of Computer Science, Chengdu University, Chengdu 610106, China
2.
Key Laboratory of Digital Innovation of Tianfu Culture, Sichuan Provincial Department of Culture and Tourism, Chengdu, China
3.
Department of Computer Sciences and Mathematics, North Sichuan Medical College, Nanchong 637000, China
4.
School of Mathematical Sciences, China West Normal University, Nanchong 637009, China

Received: 26 February 2026 Revised: 28 July 2026 Accepted: 11 August 2026 Published: 24 August 2026
MSC : 28D20, 28E10

Feature selection is strongly influenced by the appropriateness of distance modeling and the reliability of uncertainty evaluation. Existing fuzzy rough set-based approaches often suffer from insufficient sensitivity to data dispersion and limited ability to reflect class discrimination. To overcome these issues, this paper proposes a two-dimensional enhanced fuzzy rough set framework that refines distance measurement and uncertainty quantification. Feature variability is quantified via statistical dispersion. A relative distance scheme and a knowledge-granulation weighted fuzzy rough model are developed accordingly. Furthermore, the correlation information between samples and class centers is incorporated to enhance the discrimination capability of similarity evaluation. On this basis, three novel uncertainty measurements, namely relative fuzzy dependency degree (RFD), relative fuzzy composite entropy (RFCE), and relative fuzzy dependency-based composite entropy (RFDCE), are developed, together with their corresponding quantification principles and granulation-monotonicity properties. Corresponding feature selection algorithms are then designed. Experimental results demonstrate that the proposed methods achieve superior feature selection capability and classification accuracy compared with fuzzy rough set models and competing techniques.
- feature selection,
- weighted fuzzy rough model,
- relative distance,
- distance measurement,
- uncertainty measurements,
- granulation-monotonicity
Citation: Hongyuan Gou, Meng Chen, Benwei Chen. Composite uncertainty measurements in relative weighted fuzzy rough sets for feature selection[J]. AIMS Mathematics, 2026, 11(8): 26186-26223. doi: 10.3934/math.20261049

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Abstract

Feature selection is strongly influenced by the appropriateness of distance modeling and the reliability of uncertainty evaluation. Existing fuzzy rough set-based approaches often suffer from insufficient sensitivity to data dispersion and limited ability to reflect class discrimination. To overcome these issues, this paper proposes a two-dimensional enhanced fuzzy rough set framework that refines distance measurement and uncertainty quantification. Feature variability is quantified via statistical dispersion. A relative distance scheme and a knowledge-granulation weighted fuzzy rough model are developed accordingly. Furthermore, the correlation information between samples and class centers is incorporated to enhance the discrimination capability of similarity evaluation. On this basis, three novel uncertainty measurements, namely relative fuzzy dependency degree (RFD), relative fuzzy composite entropy (RFCE), and relative fuzzy dependency-based composite entropy (RFDCE), are developed, together with their corresponding quantification principles and granulation-monotonicity properties. Corresponding feature selection algorithms are then designed. Experimental results demonstrate that the proposed methods achieve superior feature selection capability and classification accuracy compared with fuzzy rough set models and competing techniques.

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