Attribute reduction approaches based on Boolean reasoning and hypergraph for inconsistent fuzzy formal decision contexts

Jing Zhang; Zengtai Gong; Huai Yu; Jing Zhang; Zengtai Gong; Huai Yu

doi:10.3934/math.20261308

AIMS Mathematics

2026, Volume 11, Issue 10: 33422-33451. doi: 10.3934/math.20261308

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Research article

Attribute reduction approaches based on Boolean reasoning and hypergraph for inconsistent fuzzy formal decision contexts

Jing Zhang ^{1
,
,},
Zengtai Gong ^{2
,
,},
Huai Yu ³

1.
School of Mathematical Sciences, Northwest Minzu University, Lanzhou 730030, China
2.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
3.
Human Resources Department, Northwest Minzu University, Lanzhou 730030, China

Received: 18 July 2026 Revised: 14 September 2026 Accepted: 29 September 2026 Published: 14 October 2026
MSC : 03E72, 68T30

Attribute reduction in fuzzy formal concept analysis (FFCA) constitutes a core research issue of FFCA, which denotes the process of eliminating redundant attributes while preserving the specific structural properties of the concept lattice. Nevertheless, most existing attribute reduction methods work well merely for consistent fuzzy formal decision contexts (CFFDCs), yet fail to produce valid outcomes for inconsistent fuzzy formal decision contexts (IFFDCs). Motivated by this limitation, this paper concentrates on the research of IFFDCs. First, drawing on the upper and lower approximation operators of rough sets, this paper defines the assignment function, distribution function, maximum distribution function, upper approximation sum function, as well as their corresponding reductions, and further explores the internal relationships among these diverse reductions. Second, reduction approaches based on Boolean reasoning and hypergraph minimal transversals are investigated, and the consistency of results yielded by these two approaches is theoretically proven. On the basis of the above theoretical derivations, the algorithms corresponding to each reduction theory are developed. Numerical examples are further utilized to verify the validity and correctness of the proposed reduction theories and algorithms.
- inconsistent fuzzy formal decision contexts,
- attribute reduction,
- rough set,
- Boolean reasoning,
- hypergraph minimal transversal
Citation: Jing Zhang, Zengtai Gong, Huai Yu. Attribute reduction approaches based on Boolean reasoning and hypergraph for inconsistent fuzzy formal decision contexts[J]. AIMS Mathematics, 2026, 11(10): 33422-33451. doi: 10.3934/math.20261308

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Abstract

Attribute reduction in fuzzy formal concept analysis (FFCA) constitutes a core research issue of FFCA, which denotes the process of eliminating redundant attributes while preserving the specific structural properties of the concept lattice. Nevertheless, most existing attribute reduction methods work well merely for consistent fuzzy formal decision contexts (CFFDCs), yet fail to produce valid outcomes for inconsistent fuzzy formal decision contexts (IFFDCs). Motivated by this limitation, this paper concentrates on the research of IFFDCs. First, drawing on the upper and lower approximation operators of rough sets, this paper defines the assignment function, distribution function, maximum distribution function, upper approximation sum function, as well as their corresponding reductions, and further explores the internal relationships among these diverse reductions. Second, reduction approaches based on Boolean reasoning and hypergraph minimal transversals are investigated, and the consistency of results yielded by these two approaches is theoretically proven. On the basis of the above theoretical derivations, the algorithms corresponding to each reduction theory are developed. Numerical examples are further utilized to verify the validity and correctness of the proposed reduction theories and algorithms.

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