Affiliations: [a] Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China
| [b] School of Sciences, Hebei University of Science and Technology, Shijiazhuang, China
Correspondence:
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Corresponding author. Shao-Pu Zhang, Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang, China. E-mail: [email protected].
Abstract: Rough set theory is a powerful tool for handling uncertainty and vagueness in various fields. The hesitant fuzzy rough set, as a generalization of rough sets, can solve more complex problems. However, existing hesitant fuzzy rough sets do not satisfy the inclusive property. To address this issue, a novel hesitant fuzzy rough set model based on dual score functions is proposed. Four generalized hesitant fuzzy rough sets and their discernibility matrices are also presented. Additionally, the lower approximation distribution reductions can be obtained by the discernibility matrix. Meanwhile, hypergraphs provide an accurate description of relationships between multiple objects and offer a concise operational approach. Then it is discovered that finding the lower approximation distribution reductions of a hesitant fuzzy decision system is equivalent to finding the minimal transversals of its hypergraph. Moreover, an improved algorithm for hesitant fuzzy decision systems based on hypergraphs is presented to accelerate the reduction process. Finally, the proposed algorithm is applied to the hybrid data of Hepatitis C Virus from UCI to demonstrate its feasibility.
